Free Essay

Statistical Tables

In: Business and Management

Submitted By jmgaivao
Words 51801
Pages 208
STATISTICAL TABLES

UNDERGRADUATE DEGREES in
MANAGEMENT
and
ECONOMICS

Binomial Distribution – probability function

1

Binomial Distribution – f(x) f (x; n, p) = f (x) n x
1 0
1 1
2 0
2 1
2 2
3 0
3 1
3 2
3 3
4 0
4 1
4 2
4 3
4 4
5 0
5 1
5 2
5 3
5 4

n x px qn−x p 0.05
0.9500
0.0500
0.9025
0.0950
0.0025
0.8574
0.1354
0.0071
0.0001
0.8145
0.1715
0.0135
0.0005
0.0000
0.7738
0.2036
0.0214
0.0011
0.0000

0.1
0.9000
0.1000
0.8100
0.1800
0.0100
0.7290
0.2430
0.0270
0.0010
0.6561
0.2916
0.0486
0.0036
0.0001
0.5905
0.3281
0.0729
0.0081
0.0005

0.15
0.8500
0.1500
0.7225
0.2550
0.0225
0.6141
0.3251
0.0574
0.0034
0.5220
0.3685
0.0975
0.0115
0.0005
0.4437
0.3915
0.1382
0.0244
0.0022

0.2
0.8000
0.2000
0.6400
0.3200
0.0400
0.5120
0.3840
0.0960
0.0080
0.4096
0.4096
0.1536
0.0256
0.0016
0.3277
0.4096
0.2048
0.0512
0.0064

0.25
0.7500
0.2500
0.5625
0.3750
0.0625
0.4219
0.4219
0.1406
0.0156
0.3164
0.4219
0.2109
0.0469
0.0039
0.2373
0.3955
0.2637
0.0879
0.0146

0.3
0.7000
0.3000
0.4900
0.4200
0.0900
0.3430
0.4410
0.1890
0.0270
0.2401
0.4116
0.2646
0.0756
0.0081
0.1681
0.3601
0.3087
0.1323
0.0283

0.35
0.6500
0.3500
0.4225
0.4550
0.1225
0.2746
0.4436
0.2389
0.0429
0.1785
0.3845
0.3105
0.1115
0.0150
0.1160
0.3124
0.3364
0.1811
0.0488

0.4
0.6000
0.4000
0.3600
0.4800
0.1600
0.2160
0.4320
0.2880
0.0640
0.1296
0.3456
0.3456
0.1536
0.0256
0.0778
0.2592
0.3456
0.2304
0.0768

0.45
0.5500
0.4500
0.3025
0.4950
0.2025
0.1664
0.4084
0.3341
0.0911
0.0915
0.2995
0.3675
0.2005
0.0410
0.0503
0.2059
0.3369
0.2757
0.1128

0.5
0.5000
0.5000
0.2500
0.5000
0.2500
0.1250
0.3750
0.3750
0.1250
0.0625
0.2500
0.3750
0.2500
0.0625
0.0312
0.1562
0.3125
0.3125
0.1562

5
6
6
6
6
6

5
0
1
2
3
4

0.0000
0.7351
0.2321
0.0305
0.0021
0.0001

0.0000
0.5314
0.3543
0.0984
0.0146
0.0012

0.0001
0.3771
0.3993
0.1762
0.0415
0.0055

0.0003
0.2621
0.3932
0.2458
0.0819
0.0154

0.0010
0.1780
0.3560
0.2966
0.1318
0.0330

0.0024
0.1176
0.3025
0.3241
0.1852
0.0595

0.0053
0.0754
0.2437
0.3280
0.2355
0.0951

0.0102
0.0467
0.1866
0.3110
0.2765
0.1382

0.0185
0.0277
0.1359
0.2780
0.3032
0.1861

0.0312
0.0156
0.0938
0.2344
0.3125
0.2344

6
6
7
7
7
7
7

5
6
0
1
2
3
4

0.0000
0.0000
0.6983
0.2573
0.0406
0.0036
0.0002

0.0001
0.0000
0.4783
0.3720
0.1240
0.0230
0.0026

0.0004
0.0000
0.3206
0.3960
0.2097
0.0617
0.0109

0.0015
0.0001
0.2097
0.3670
0.2753
0.1147
0.0287

0.0044
0.0002
0.1335
0.3115
0.3115
0.1730
0.0577

0.0102
0.0007
0.0824
0.2471
0.3177
0.2269
0.0972

0.0205
0.0018
0.0490
0.1848
0.2985
0.2679
0.1442

0.0369
0.0041
0.0280
0.1306
0.2613
0.2903
0.1935

0.0609
0.0083
0.0152
0.0872
0.2140
0.2918
0.2388

0.0938
0.0156
0.0078
0.0547
0.1641
0.2734
0.2734

7
7
7
8
8
8
8
8

5
6
7
0
1
2
3
4

0.0000
0.0000
0.0000
0.6634
0.2793
0.0515
0.0054
0.0004

0.0002
0.0000
0.0000
0.4305
0.3826
0.1488
0.0331
0.0046

0.0012
0.0001
0.0000
0.2725
0.3847
0.2376
0.0839
0.0185

0.0043
0.0004
0.0000
0.1678
0.3355
0.2936
0.1468
0.0459

0.0115
0.0013
0.0001
0.1001
0.2670
0.3115
0.2076
0.0865

0.0250
0.0036
0.0002
0.0576
0.1977
0.2965
0.2541
0.1361

0.0466
0.0084
0.0006
0.0319
0.1373
0.2587
0.2786
0.1875

0.0774
0.0172
0.0016
0.0168
0.0896
0.2090
0.2787
0.2322

0.1172
0.0320
0.0037
0.0084
0.0548
0.1569
0.2568
0.2627

0.1641
0.0547
0.0078
0.0039
0.0312
0.1094
0.2188
0.2734

8
8
8
8
9
9
9
9
9

5
6
7
8
0
1
2
3
4

0.0000
0.0000
0.0000
0.0000
0.6302
0.2985
0.0629
0.0077
0.0006

0.0004
0.0000
0.0000
0.0000
0.3874
0.3874
0.1722
0.0446
0.0074

0.0026
0.0002
0.0000
0.0000
0.2316
0.3679
0.2597
0.1069
0.0283

0.0092
0.0011
0.0001
0.0000
0.1342
0.3020
0.3020
0.1762
0.0661

0.0231
0.0038
0.0004
0.0000
0.0751
0.2253
0.3003
0.2336
0.1168

0.0467
0.0100
0.0012
0.0001
0.0404
0.1556
0.2668
0.2668
0.1715

0.0808
0.0217
0.0033
0.0002
0.0207
0.1004
0.2162
0.2716
0.2194

0.1239
0.0413
0.0079
0.0007
0.0101
0.0605
0.1612
0.2508
0.2508

0.1719
0.0703
0.0164
0.0017
0.0046
0.0339
0.1110
0.2119
0.2600

0.2188
0.1094
0.0312
0.0039
0.0020
0.0176
0.0703
0.1641
0.2461

9
9
9
9
9
10
10
10
10
10

5
6
7
8
9
0
1
2
3
4

0.0000
0.0000
0.0000
0.0000
0.0000
0.5987
0.3151
0.0746
0.0105
0.0010

0.0008
0.0001
0.0000
0.0000
0.0000
0.3487
0.3874
0.1937
0.0574
0.0112

0.0050
0.0006
0.0000
0.0000
0.0000
0.1969
0.3474
0.2759
0.1298
0.0401

0.0165
0.0028
0.0003
0.0000
0.0000
0.1074
0.2684
0.3020
0.2013
0.0881

0.0389
0.0087
0.0012
0.0001
0.0000
0.0563
0.1877
0.2816
0.2503
0.1460

0.0735
0.0210
0.0039
0.0004
0.0000
0.0282
0.1211
0.2335
0.2668
0.2001

0.1181
0.0424
0.0098
0.0013
0.0001
0.0135
0.0725
0.1757
0.2522
0.2377

0.1672
0.0743
0.0212
0.0035
0.0003
0.0060
0.0403
0.1209
0.2150
0.2508

0.2128
0.1160
0.0407
0.0083
0.0008
0.0025
0.0207
0.0763
0.1665
0.2384

0.2461
0.1641
0.0703
0.0176
0.0020
0.0010
0.0098
0.0439
0.1172
0.2051

10
10

5
6

0.0001
0.0000

0.0015
0.0001

0.0085
0.0012

0.0264
0.0055

0.0584
0.0162

0.1029
0.0368

0.1536
0.0689

0.2007
0.1115

0.2340
0.1596

0.2461
0.2051

´
CATOLICA-LISBON

Statistical Tables

Binomial Distribution – probability function

2

f (x) n x
10
7
10
8
10
9

0.05
0.0000
0.0000
0.0000

0.1
0.0000
0.0000
0.0000

0.15
0.0001
0.0000
0.0000

0.2
0.0008
0.0001
0.0000

0.25
0.0031
0.0004
0.0000

0.3
0.0090
0.0014
0.0001

0.35
0.0212
0.0043
0.0005

0.4
0.0425
0.0106
0.0016

0.45
0.0746
0.0229
0.0042

0.5
0.1172
0.0439
0.0098

10
11
11
11
11
11

10
0
1
2
3
4

0.0000
0.5688
0.3293
0.0867
0.0137
0.0014

0.0000
0.3138
0.3835
0.2131
0.0710
0.0158

0.0000
0.1673
0.3248
0.2866
0.1517
0.0536

0.0000
0.0859
0.2362
0.2953
0.2215
0.1107

0.0000
0.0422
0.1549
0.2581
0.2581
0.1721

0.0000
0.0198
0.0932
0.1998
0.2568
0.2201

0.0000
0.0088
0.0518
0.1395
0.2254
0.2428

0.0001
0.0036
0.0266
0.0887
0.1774
0.2365

0.0003
0.0014
0.0125
0.0513
0.1259
0.2060

0.0010
0.0005
0.0054
0.0269
0.0806
0.1611

11
11
11
11
11

5
6
7
8
9

0.0001
0.0000
0.0000
0.0000
0.0000

0.0025
0.0003
0.0000
0.0000
0.0000

0.0132
0.0023
0.0003
0.0000
0.0000

0.0388
0.0097
0.0017
0.0002
0.0000

0.0803
0.0268
0.0064
0.0011
0.0001

0.1321
0.0566
0.0173
0.0037
0.0005

0.1830
0.0985
0.0379
0.0102
0.0018

0.2207
0.1471
0.0701
0.0234
0.0052

0.2360
0.1931
0.1128
0.0462
0.0126

0.2256
0.2256
0.1611
0.0806
0.0269

11
11
12
12
12
12
12

10
11
0
1
2
3
4

0.0000
0.0000
0.5404
0.3413
0.0988
0.0173
0.0021

0.0000
0.0000
0.2824
0.3766
0.2301
0.0852
0.0213

0.0000
0.0000
0.1422
0.3012
0.2924
0.1720
0.0683

0.0000
0.0000
0.0687
0.2062
0.2835
0.2362
0.1329

0.0000
0.0000
0.0317
0.1267
0.2323
0.2581
0.1936

0.0000
0.0000
0.0138
0.0712
0.1678
0.2397
0.2311

0.0002
0.0000
0.0057
0.0368
0.1088
0.1954
0.2367

0.0007
0.0000
0.0022
0.0174
0.0639
0.1419
0.2128

0.0021
0.0002
0.0008
0.0075
0.0339
0.0923
0.1700

0.0054
0.0005
0.0002
0.0029
0.0161
0.0537
0.1208

12
12
12
12
12

5
6
7
8
9

0.0002
0.0000
0.0000
0.0000
0.0000

0.0038
0.0005
0.0000
0.0000
0.0000

0.0193
0.0040
0.0006
0.0001
0.0000

0.0532
0.0155
0.0033
0.0005
0.0001

0.1032
0.0401
0.0115
0.0024
0.0004

0.1585
0.0792
0.0291
0.0078
0.0015

0.2039
0.1281
0.0591
0.0199
0.0048

0.2270
0.1766
0.1009
0.0420
0.0125

0.2225
0.2124
0.1489
0.0762
0.0277

0.1934
0.2256
0.1934
0.1208
0.0537

12
12
12
13
13
13
13
13

10
11
12
0
1
2
3
4

0.0000
0.0000
0.0000
0.5133
0.3512
0.1109
0.0214
0.0028

0.0000
0.0000
0.0000
0.2542
0.3672
0.2448
0.0997
0.0277

0.0000
0.0000
0.0000
0.1209
0.2774
0.2937
0.1900
0.0838

0.0000
0.0000
0.0000
0.0550
0.1787
0.2680
0.2457
0.1535

0.0000
0.0000
0.0000
0.0238
0.1029
0.2059
0.2517
0.2097

0.0002
0.0000
0.0000
0.0097
0.0540
0.1388
0.2181
0.2337

0.0008
0.0001
0.0000
0.0037
0.0259
0.0836
0.1651
0.2222

0.0025
0.0003
0.0000
0.0013
0.0113
0.0453
0.1107
0.1845

0.0068
0.0010
0.0001
0.0004
0.0045
0.0220
0.0660
0.1350

0.0161
0.0029
0.0002
0.0001
0.0016
0.0095
0.0349
0.0873

13
13
13
13
13

5
6
7
8
9

0.0003
0.0000
0.0000
0.0000
0.0000

0.0055
0.0008
0.0001
0.0000
0.0000

0.0266
0.0063
0.0011
0.0001
0.0000

0.0691
0.0230
0.0058
0.0011
0.0001

0.1258
0.0559
0.0186
0.0047
0.0009

0.1803
0.1030
0.0442
0.0142
0.0034

0.2154
0.1546
0.0833
0.0336
0.0101

0.2214
0.1968
0.1312
0.0656
0.0243

0.1989
0.2169
0.1775
0.1089
0.0495

0.1571
0.2095
0.2095
0.1571
0.0873

13
13
13
13
14
14
14
14
14

10
11
12
13
0
1
2
3
4

0.0000
0.0000
0.0000
0.0000
0.4877
0.3593
0.1229
0.0259
0.0037

0.0000
0.0000
0.0000
0.0000
0.2288
0.3559
0.2570
0.1142
0.0349

0.0000
0.0000
0.0000
0.0000
0.1028
0.2539
0.2912
0.2056
0.0998

0.0000
0.0000
0.0000
0.0000
0.0440
0.1539
0.2501
0.2501
0.1720

0.0001
0.0000
0.0000
0.0000
0.0178
0.0832
0.1802
0.2402
0.2202

0.0006
0.0001
0.0000
0.0000
0.0068
0.0407
0.1134
0.1943
0.2290

0.0022
0.0003
0.0000
0.0000
0.0024
0.0181
0.0634
0.1366
0.2022

0.0065
0.0012
0.0001
0.0000
0.0008
0.0073
0.0317
0.0845
0.1549

0.0162
0.0036
0.0005
0.0000
0.0002
0.0027
0.0141
0.0462
0.1040

0.0349
0.0095
0.0016
0.0001
0.0001
0.0009
0.0056
0.0222
0.0611

14
14
14
14
14

5
6
7
8
9

0.0004
0.0000
0.0000
0.0000
0.0000

0.0078
0.0013
0.0002
0.0000
0.0000

0.0352
0.0093
0.0019
0.0003
0.0000

0.0860
0.0322
0.0092
0.0020
0.0003

0.1468
0.0734
0.0280
0.0082
0.0018

0.1963
0.1262
0.0618
0.0232
0.0066

0.2178
0.1759
0.1082
0.0510
0.0183

0.2066
0.2066
0.1574
0.0918
0.0408

0.1701
0.2088
0.1952
0.1398
0.0762

0.1222
0.1833
0.2095
0.1833
0.1222

14
14
14
14
14
15
15
15
15
15

10
11
12
13
14
0
1
2
3
4

0.0000
0.0000
0.0000
0.0000
0.0000
0.4633
0.3658
0.1348
0.0307
0.0049

0.0000
0.0000
0.0000
0.0000
0.0000
0.2059
0.3432
0.2669
0.1285
0.0428

0.0000
0.0000
0.0000
0.0000
0.0000
0.0874
0.2312
0.2856
0.2184
0.1156

0.0000
0.0000
0.0000
0.0000
0.0000
0.0352
0.1319
0.2309
0.2501
0.1876

0.0003
0.0000
0.0000
0.0000
0.0000
0.0134
0.0668
0.1559
0.2252
0.2252

0.0014
0.0002
0.0000
0.0000
0.0000
0.0047
0.0305
0.0916
0.1700
0.2186

0.0049
0.0010
0.0001
0.0000
0.0000
0.0016
0.0126
0.0476
0.1110
0.1792

0.0136
0.0033
0.0005
0.0001
0.0000
0.0005
0.0047
0.0219
0.0634
0.1268

0.0312
0.0093
0.0019
0.0002
0.0000
0.0001
0.0016
0.0090
0.0318
0.0780

0.0611
0.0222
0.0056
0.0009
0.0001
0.0000
0.0005
0.0032
0.0139
0.0417

15
15

5
6

0.0006
0.0000

0.0105
0.0019

0.0449
0.0132

0.1032
0.0430

0.1651
0.0917

0.2061
0.1472

0.2123
0.1906

0.1859
0.2066

0.1404
0.1914

0.0916
0.1527

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – probability function

3

f (x) n x
15
7
15
8
15
9

0.05
0.0000
0.0000
0.0000

0.1
0.0003
0.0000
0.0000

0.15
0.0030
0.0005
0.0001

0.2
0.0138
0.0035
0.0007

0.25
0.0393
0.0131
0.0034

0.3
0.0811
0.0348
0.0116

0.35
0.1319
0.0710
0.0298

0.4
0.1771
0.1181
0.0612

0.45
0.2013
0.1647
0.1048

0.5
0.1964
0.1964
0.1527

15
15
15
15
15

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0007
0.0001
0.0000
0.0000
0.0000

0.0030
0.0006
0.0001
0.0000
0.0000

0.0096
0.0024
0.0004
0.0001
0.0000

0.0245
0.0074
0.0016
0.0003
0.0000

0.0515
0.0191
0.0052
0.0010
0.0001

0.0916
0.0417
0.0139
0.0032
0.0005

15
16
16
16
16
16

15
0
1
2
3
4

0.0000
0.4401
0.3706
0.1463
0.0359
0.0061

0.0000
0.1853
0.3294
0.2745
0.1423
0.0514

0.0000
0.0743
0.2097
0.2775
0.2285
0.1311

0.0000
0.0281
0.1126
0.2111
0.2463
0.2001

0.0000
0.0100
0.0535
0.1336
0.2079
0.2252

0.0000
0.0033
0.0228
0.0732
0.1465
0.2040

0.0000
0.0010
0.0087
0.0353
0.0888
0.1553

0.0000
0.0003
0.0030
0.0150
0.0468
0.1014

0.0000
0.0001
0.0009
0.0056
0.0215
0.0572

0.0000
0.0000
0.0002
0.0018
0.0085
0.0278

16
16
16
16
16

5
6
7
8
9

0.0008
0.0001
0.0000
0.0000
0.0000

0.0137
0.0028
0.0004
0.0001
0.0000

0.0555
0.0180
0.0045
0.0009
0.0001

0.1201
0.0550
0.0197
0.0055
0.0012

0.1802
0.1101
0.0524
0.0197
0.0058

0.2099
0.1649
0.1010
0.0487
0.0185

0.2008
0.1982
0.1524
0.0923
0.0442

0.1623
0.1983
0.1889
0.1417
0.0840

0.1123
0.1684
0.1969
0.1812
0.1318

0.0667
0.1222
0.1746
0.1964
0.1746

16
16
16
16
16

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0000
0.0000
0.0000
0.0000

0.0014
0.0002
0.0000
0.0000
0.0000

0.0056
0.0013
0.0002
0.0000
0.0000

0.0167
0.0049
0.0011
0.0002
0.0000

0.0392
0.0142
0.0040
0.0008
0.0001

0.0755
0.0337
0.0115
0.0029
0.0005

0.1222
0.0667
0.0278
0.0085
0.0018

16
16
17
17
17
17
17

15
16
0
1
2
3
4

0.0000
0.0000
0.4181
0.3741
0.1575
0.0415
0.0076

0.0000
0.0000
0.1668
0.3150
0.2800
0.1556
0.0605

0.0000
0.0000
0.0631
0.1893
0.2673
0.2359
0.1457

0.0000
0.0000
0.0225
0.0957
0.1914
0.2393
0.2093

0.0000
0.0000
0.0075
0.0426
0.1136
0.1893
0.2209

0.0000
0.0000
0.0023
0.0169
0.0581
0.1245
0.1868

0.0000
0.0000
0.0007
0.0060
0.0260
0.0701
0.1320

0.0000
0.0000
0.0002
0.0019
0.0102
0.0341
0.0796

0.0001
0.0000
0.0000
0.0005
0.0035
0.0144
0.0411

0.0002
0.0000
0.0000
0.0001
0.0010
0.0052
0.0182

17
17
17
17
17

5
6
7
8
9

0.0010
0.0001
0.0000
0.0000
0.0000

0.0175
0.0039
0.0007
0.0001
0.0000

0.0668
0.0236
0.0065
0.0014
0.0003

0.1361
0.0680
0.0267
0.0084
0.0021

0.1914
0.1276
0.0668
0.0279
0.0093

0.2081
0.1784
0.1201
0.0644
0.0276

0.1849
0.1991
0.1685
0.1134
0.0611

0.1379
0.1839
0.1927
0.1606
0.1070

0.0875
0.1432
0.1841
0.1883
0.1540

0.0472
0.0944
0.1484
0.1855
0.1855

17
17
17
17
17

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0004
0.0001
0.0000
0.0000
0.0000

0.0025
0.0005
0.0001
0.0000
0.0000

0.0095
0.0026
0.0006
0.0001
0.0000

0.0263
0.0090
0.0024
0.0005
0.0001

0.0571
0.0242
0.0081
0.0021
0.0004

0.1008
0.0525
0.0215
0.0068
0.0016

0.1484
0.0944
0.0472
0.0182
0.0052

17
17
17
18
18
18
18
18

15
16
17
0
1
2
3
4

0.0000
0.0000
0.0000
0.3972
0.3763
0.1683
0.0473
0.0093

0.0000
0.0000
0.0000
0.1501
0.3002
0.2835
0.1680
0.0700

0.0000
0.0000
0.0000
0.0536
0.1704
0.2556
0.2406
0.1592

0.0000
0.0000
0.0000
0.0180
0.0811
0.1723
0.2297
0.2153

0.0000
0.0000
0.0000
0.0056
0.0338
0.0958
0.1704
0.2130

0.0000
0.0000
0.0000
0.0016
0.0126
0.0458
0.1046
0.1681

0.0000
0.0000
0.0000
0.0004
0.0042
0.0190
0.0547
0.1104

0.0001
0.0000
0.0000
0.0001
0.0012
0.0069
0.0246
0.0614

0.0003
0.0000
0.0000
0.0000
0.0003
0.0022
0.0095
0.0291

0.0010
0.0001
0.0000
0.0000
0.0001
0.0006
0.0031
0.0117

18
18
18
18
18

5
6
7
8
9

0.0014
0.0002
0.0000
0.0000
0.0000

0.0218
0.0052
0.0010
0.0002
0.0000

0.0787
0.0301
0.0091
0.0022
0.0004

0.1507
0.0816
0.0350
0.0120
0.0033

0.1988
0.1436
0.0820
0.0376
0.0139

0.2017
0.1873
0.1376
0.0811
0.0386

0.1664
0.1941
0.1792
0.1327
0.0794

0.1146
0.1655
0.1892
0.1734
0.1284

0.0666
0.1181
0.1657
0.1864
0.1694

0.0327
0.0708
0.1214
0.1669
0.1855

18
18
18
18
18

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0008
0.0001
0.0000
0.0000
0.0000

0.0042
0.0010
0.0002
0.0000
0.0000

0.0149
0.0046
0.0012
0.0002
0.0000

0.0385
0.0151
0.0047
0.0012
0.0002

0.0771
0.0374
0.0145
0.0045
0.0011

0.1248
0.0742
0.0354
0.0134
0.0039

0.1669
0.1214
0.0708
0.0327
0.0117

18
18
18
18
19
19

15
16
17
18
0
1

0.0000
0.0000
0.0000
0.0000
0.3774
0.3774

0.0000
0.0000
0.0000
0.0000
0.1351
0.2852

0.0000
0.0000
0.0000
0.0000
0.0456
0.1529

0.0000
0.0000
0.0000
0.0000
0.0144
0.0685

0.0000
0.0000
0.0000
0.0000
0.0042
0.0268

0.0000
0.0000
0.0000
0.0000
0.0011
0.0093

0.0000
0.0000
0.0000
0.0000
0.0003
0.0029

0.0002
0.0000
0.0000
0.0000
0.0001
0.0008

0.0009
0.0001
0.0000
0.0000
0.0000
0.0002

0.0031
0.0006
0.0001
0.0000
0.0000
0.0000

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – probability function

4

f (x) n x
19
2
19
3
19
4

0.05
0.1787
0.0533
0.0112

0.1
0.2852
0.1796
0.0798

0.15
0.2428
0.2428
0.1714

0.2
0.1540
0.2182
0.2182

0.25
0.0803
0.1517
0.2023

0.3
0.0358
0.0869
0.1491

0.35
0.0138
0.0422
0.0909

0.4
0.0046
0.0175
0.0467

0.45
0.0013
0.0062
0.0203

0.5
0.0003
0.0018
0.0074

19
19
19
19
19

5
6
7
8
9

0.0018
0.0002
0.0000
0.0000
0.0000

0.0266
0.0069
0.0014
0.0002
0.0000

0.0907
0.0374
0.0122
0.0032
0.0007

0.1636
0.0955
0.0443
0.0166
0.0051

0.2023
0.1574
0.0974
0.0487
0.0198

0.1916
0.1916
0.1525
0.0981
0.0514

0.1468
0.1844
0.1844
0.1489
0.0980

0.0933
0.1451
0.1797
0.1797
0.1464

0.0497
0.0949
0.1443
0.1771
0.1771

0.0222
0.0518
0.0961
0.1442
0.1762

19
19
19
19
19

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0013
0.0003
0.0000
0.0000
0.0000

0.0066
0.0018
0.0004
0.0001
0.0000

0.0220
0.0077
0.0022
0.0005
0.0001

0.0528
0.0233
0.0083
0.0024
0.0006

0.0976
0.0532
0.0237
0.0085
0.0024

0.1449
0.0970
0.0529
0.0233
0.0082

0.1762
0.1442
0.0961
0.0518
0.0222

19
19
19
19
19
20
20
20
20
20

15
16
17
18
19
0
1
2
3
4

0.0000
0.0000
0.0000
0.0000
0.0000
0.3585
0.3774
0.1887
0.0596
0.0133

0.0000
0.0000
0.0000
0.0000
0.0000
0.1216
0.2702
0.2852
0.1901
0.0898

0.0000
0.0000
0.0000
0.0000
0.0000
0.0388
0.1368
0.2293
0.2428
0.1821

0.0000
0.0000
0.0000
0.0000
0.0000
0.0115
0.0576
0.1369
0.2054
0.2182

0.0000
0.0000
0.0000
0.0000
0.0000
0.0032
0.0211
0.0669
0.1339
0.1897

0.0000
0.0000
0.0000
0.0000
0.0000
0.0008
0.0068
0.0278
0.0716
0.1304

0.0001
0.0000
0.0000
0.0000
0.0000
0.0002
0.0020
0.0100
0.0323
0.0738

0.0005
0.0001
0.0000
0.0000
0.0000
0.0000
0.0005
0.0031
0.0123
0.0350

0.0022
0.0005
0.0001
0.0000
0.0000
0.0000
0.0001
0.0008
0.0040
0.0139

0.0074
0.0018
0.0003
0.0000
0.0000
0.0000
0.0000
0.0002
0.0011
0.0046

20
20
20
20
20

5
6
7
8
9

0.0022
0.0003
0.0000
0.0000
0.0000

0.0319
0.0089
0.0020
0.0004
0.0001

0.1028
0.0454
0.0160
0.0046
0.0011

0.1746
0.1091
0.0545
0.0222
0.0074

0.2023
0.1686
0.1124
0.0609
0.0271

0.1789
0.1916
0.1643
0.1144
0.0654

0.1272
0.1712
0.1844
0.1614
0.1158

0.0746
0.1244
0.1659
0.1797
0.1597

0.0365
0.0746
0.1221
0.1623
0.1771

0.0148
0.0370
0.0739
0.1201
0.1602

20
20
20
20
20

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0000
0.0000
0.0000
0.0000

0.0020
0.0005
0.0001
0.0000
0.0000

0.0099
0.0030
0.0008
0.0002
0.0000

0.0308
0.0120
0.0039
0.0010
0.0002

0.0686
0.0336
0.0136
0.0045
0.0012

0.1171
0.0710
0.0355
0.0146
0.0049

0.1593
0.1185
0.0727
0.0366
0.0150

0.1762
0.1602
0.1201
0.0739
0.0370

20
20
20
20
20

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0003
0.0000
0.0000
0.0000
0.0000

0.0013
0.0003
0.0000
0.0000
0.0000

0.0049
0.0013
0.0002
0.0000
0.0000

0.0148
0.0046
0.0011
0.0002
0.0000

20
21
21
21
21
21

20
0
1
2
3
4

0.0000
0.3406
0.3764
0.1981
0.0660
0.0156

0.0000
0.1094
0.2553
0.2837
0.1996
0.0998

0.0000
0.0329
0.1221
0.2155
0.2408
0.1912

0.0000
0.0092
0.0484
0.1211
0.1917
0.2156

0.0000
0.0024
0.0166
0.0555
0.1172
0.1757

0.0000
0.0006
0.0050
0.0215
0.0585
0.1128

0.0000
0.0001
0.0013
0.0072
0.0245
0.0593

0.0000
0.0000
0.0003
0.0020
0.0086
0.0259

0.0000
0.0000
0.0001
0.0005
0.0026
0.0095

0.0000
0.0000
0.0000
0.0001
0.0006
0.0029

21
21
21
21
21

5
6
7
8
9

0.0028
0.0004
0.0000
0.0000
0.0000

0.0377
0.0112
0.0027
0.0005
0.0001

0.1147
0.0540
0.0204
0.0063
0.0016

0.1833
0.1222
0.0655
0.0286
0.0103

0.1992
0.1770
0.1265
0.0738
0.0355

0.1643
0.1878
0.1725
0.1294
0.0801

0.1085
0.1558
0.1798
0.1694
0.1318

0.0588
0.1045
0.1493
0.1742
0.1677

0.0263
0.0574
0.1007
0.1442
0.1704

0.0097
0.0259
0.0554
0.0970
0.1402

21
21
21
21
21

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0003
0.0001
0.0000
0.0000
0.0000

0.0031
0.0008
0.0002
0.0000
0.0000

0.0142
0.0047
0.0013
0.0003
0.0001

0.0412
0.0176
0.0063
0.0019
0.0005

0.0851
0.0458
0.0206
0.0077
0.0024

0.1342
0.0895
0.0497
0.0229
0.0087

0.1673
0.1369
0.0933
0.0529
0.0247

0.1682
0.1682
0.1402
0.0970
0.0554

21
21
21
21
21

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0006
0.0001
0.0000
0.0000
0.0000

0.0027
0.0007
0.0001
0.0000
0.0000

0.0094
0.0029
0.0007
0.0001
0.0000

0.0259
0.0097
0.0029
0.0006
0.0001

21
21
22
22
22
22

20
21
0
1
2
3

0.0000
0.0000
0.3235
0.3746
0.2070
0.0726

0.0000
0.0000
0.0985
0.2407
0.2808
0.2080

0.0000
0.0000
0.0280
0.1087
0.2015
0.2370

0.0000
0.0000
0.0074
0.0406
0.1065
0.1775

0.0000
0.0000
0.0018
0.0131
0.0458
0.1017

0.0000
0.0000
0.0004
0.0037
0.0166
0.0474

0.0000
0.0000
0.0001
0.0009
0.0051
0.0184

0.0000
0.0000
0.0000
0.0002
0.0014
0.0060

0.0000
0.0000
0.0000
0.0000
0.0003
0.0016

0.0000
0.0000
0.0000
0.0000
0.0001
0.0004

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – probability function

5

f (x) n x
22
4

0.05
0.0182

0.1
0.1098

0.15
0.1987

0.2
0.2108

0.25
0.1611

0.3
0.0965

0.35
0.0471

0.4
0.0190

0.45
0.0064

0.5
0.0017

22
22
22
22
22

5
6
7
8
9

0.0034
0.0005
0.0001
0.0000
0.0000

0.0439
0.0138
0.0035
0.0007
0.0001

0.1262
0.0631
0.0255
0.0084
0.0023

0.1898
0.1344
0.0768
0.0360
0.0140

0.1933
0.1826
0.1391
0.0869
0.0451

0.1489
0.1808
0.1771
0.1423
0.0949

0.0913
0.1393
0.1714
0.1730
0.1449

0.0456
0.0862
0.1314
0.1642
0.1703

0.0187
0.0434
0.0812
0.1246
0.1586

0.0063
0.0178
0.0407
0.0762
0.1186

22
22
22
22
22

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0005
0.0001
0.0000
0.0000
0.0000

0.0046
0.0012
0.0003
0.0001
0.0000

0.0195
0.0071
0.0022
0.0006
0.0001

0.0529
0.0247
0.0097
0.0032
0.0009

0.1015
0.0596
0.0294
0.0122
0.0042

0.1476
0.1073
0.0656
0.0336
0.0144

0.1687
0.1506
0.1129
0.0711
0.0374

0.1542
0.1682
0.1542
0.1186
0.0762

22
22
22
22
22

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0000
0.0000
0.0000
0.0000

0.0012
0.0003
0.0001
0.0000
0.0000

0.0051
0.0015
0.0004
0.0001
0.0000

0.0163
0.0058
0.0017
0.0004
0.0001

0.0407
0.0178
0.0063
0.0017
0.0004

22
22
22
23
23
23
23
23

20
21
22
0
1
2
3
4

0.0000
0.0000
0.0000
0.3074
0.3721
0.2154
0.0794
0.0209

0.0000
0.0000
0.0000
0.0886
0.2265
0.2768
0.2153
0.1196

0.0000
0.0000
0.0000
0.0238
0.0966
0.1875
0.2317
0.2044

0.0000
0.0000
0.0000
0.0059
0.0339
0.0933
0.1633
0.2042

0.0000
0.0000
0.0000
0.0013
0.0103
0.0376
0.0878
0.1463

0.0000
0.0000
0.0000
0.0003
0.0027
0.0127
0.0382
0.0818

0.0000
0.0000
0.0000
0.0000
0.0006
0.0037
0.0138
0.0371

0.0000
0.0000
0.0000
0.0000
0.0001
0.0009
0.0041
0.0138

0.0000
0.0000
0.0000
0.0000
0.0000
0.0002
0.0010
0.0042

0.0001
0.0000
0.0000
0.0000
0.0000
0.0000
0.0002
0.0011

23
23
23
23
23

5
6
7
8
9

0.0042
0.0007
0.0001
0.0000
0.0000

0.0505
0.0168
0.0045
0.0010
0.0002

0.1371
0.0726
0.0311
0.0110
0.0032

0.1940
0.1455
0.0883
0.0442
0.0184

0.1853
0.1853
0.1500
0.1000
0.0555

0.1332
0.1712
0.1782
0.1527
0.1091

0.0758
0.1225
0.1602
0.1725
0.1548

0.0350
0.0700
0.1133
0.1511
0.1679

0.0132
0.0323
0.0642
0.1051
0.1433

0.0040
0.0120
0.0292
0.0584
0.0974

23
23
23
23
23

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0008
0.0002
0.0000
0.0000
0.0000

0.0064
0.0019
0.0005
0.0001
0.0000

0.0259
0.0102
0.0034
0.0010
0.0002

0.0655
0.0332
0.0142
0.0052
0.0016

0.1167
0.0743
0.0400
0.0182
0.0070

0.1567
0.1234
0.0823
0.0464
0.0221

0.1642
0.1587
0.1299
0.0899
0.0525

0.1364
0.1612
0.1612
0.1364
0.0974

23
23
23
23
23

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0004
0.0001
0.0000
0.0000
0.0000

0.0023
0.0006
0.0001
0.0000
0.0000

0.0088
0.0029
0.0008
0.0002
0.0000

0.0258
0.0106
0.0036
0.0010
0.0002

0.0584
0.0292
0.0120
0.0040
0.0011

23
23
23
23
24
24
24
24
24

20
21
22
23
0
1
2
3
4

0.0000
0.0000
0.0000
0.0000
0.2920
0.3688
0.2232
0.0862
0.0238

0.0000
0.0000
0.0000
0.0000
0.0798
0.2127
0.2718
0.2215
0.1292

0.0000
0.0000
0.0000
0.0000
0.0202
0.0857
0.1739
0.2251
0.2085

0.0000
0.0000
0.0000
0.0000
0.0047
0.0283
0.0815
0.1493
0.1960

0.0000
0.0000
0.0000
0.0000
0.0010
0.0080
0.0308
0.0752
0.1316

0.0000
0.0000
0.0000
0.0000
0.0002
0.0020
0.0097
0.0305
0.0687

0.0000
0.0000
0.0000
0.0000
0.0000
0.0004
0.0026
0.0102
0.0289

0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0006
0.0028
0.0099

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0007
0.0028

0.0002
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0006

24
24
24
24
24

5
6
7
8
9

0.0050
0.0008
0.0001
0.0000
0.0000

0.0574
0.0202
0.0058
0.0014
0.0003

0.1472
0.0822
0.0373
0.0140
0.0044

0.1960
0.1552
0.0998
0.0530
0.0236

0.1755
0.1853
0.1588
0.1125
0.0667

0.1177
0.1598
0.1761
0.1604
0.1222

0.0622
0.1061
0.1470
0.1682
0.1610

0.0265
0.0560
0.0960
0.1360
0.1612

0.0091
0.0237
0.0499
0.0867
0.1261

0.0025
0.0080
0.0206
0.0438
0.0779

24
24
24
24
24

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0012
0.0003
0.0000
0.0000
0.0000

0.0088
0.0028
0.0008
0.0002
0.0000

0.0333
0.0141
0.0051
0.0016
0.0004

0.0785
0.0428
0.0199
0.0079
0.0026

0.1300
0.0891
0.0520
0.0258
0.0109

0.1612
0.1367
0.0988
0.0608
0.0318

0.1548
0.1612
0.1429
0.1079
0.0694

0.1169
0.1488
0.1612
0.1488
0.1169

24
24
24
24
24

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0008
0.0002
0.0000
0.0000
0.0000

0.0039
0.0012
0.0003
0.0001
0.0000

0.0141
0.0053
0.0017
0.0004
0.0001

0.0378
0.0174
0.0067
0.0021
0.0006

0.0779
0.0438
0.0206
0.0080
0.0025

24
24

20
21

0.0000
0.0000

0.0000
0.0000

0.0000
0.0000

0.0000
0.0000

0.0000
0.0000

0.0000
0.0000

0.0000
0.0000

0.0000
0.0000

0.0001
0.0000

0.0006
0.0001

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – probability function

6

f (x) n x
24 22
24 23
24 24
25
0
25
1
25
2
25
3
25
4

0.05
0.0000
0.0000
0.0000
0.2774
0.3650
0.2305
0.0930
0.0269

0.1
0.0000
0.0000
0.0000
0.0718
0.1994
0.2659
0.2265
0.1384

0.15
0.0000
0.0000
0.0000
0.0172
0.0759
0.1607
0.2174
0.2110

0.2
0.0000
0.0000
0.0000
0.0038
0.0236
0.0708
0.1358
0.1867

0.25
0.0000
0.0000
0.0000
0.0008
0.0063
0.0251
0.0641
0.1175

0.3
0.0000
0.0000
0.0000
0.0001
0.0014
0.0074
0.0243
0.0572

0.35
0.0000
0.0000
0.0000
0.0000
0.0003
0.0018
0.0076
0.0224

0.4
0.0000
0.0000
0.0000
0.0000
0.0000
0.0004
0.0019
0.0071

0.45
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0004
0.0018

0.5
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0004

25
25
25
25
25

5
6
7
8
9

0.0060
0.0010
0.0001
0.0000
0.0000

0.0646
0.0239
0.0072
0.0018
0.0004

0.1564
0.0920
0.0441
0.0175
0.0058

0.1960
0.1633
0.1108
0.0623
0.0294

0.1645
0.1828
0.1654
0.1241
0.0781

0.1030
0.1472
0.1712
0.1651
0.1336

0.0506
0.0908
0.1327
0.1607
0.1635

0.0199
0.0442
0.0800
0.1200
0.1511

0.0063
0.0172
0.0381
0.0701
0.1084

0.0016
0.0053
0.0143
0.0322
0.0609

25
25
25
25
25

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0016
0.0004
0.0001
0.0000
0.0000

0.0118
0.0040
0.0012
0.0003
0.0001

0.0417
0.0189
0.0074
0.0025
0.0007

0.0916
0.0536
0.0268
0.0115
0.0042

0.1409
0.1034
0.0650
0.0350
0.0161

0.1612
0.1465
0.1140
0.0760
0.0434

0.1419
0.1583
0.1511
0.1236
0.0867

0.0974
0.1328
0.1550
0.1550
0.1328

25
25
25
25
25

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0000
0.0000
0.0000
0.0000

0.0013
0.0004
0.0001
0.0000
0.0000

0.0064
0.0021
0.0006
0.0001
0.0000

0.0212
0.0088
0.0031
0.0009
0.0002

0.0520
0.0266
0.0115
0.0042
0.0013

0.0974
0.0609
0.0322
0.0143
0.0053

25
25
25
25
25

20
21
22
23
24

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0003
0.0001
0.0000
0.0000
0.0000

0.0016
0.0004
0.0001
0.0000
0.0000

25
30
30
30
30
30

25
0
1
2
3
4

0.0000
0.2146
0.3389
0.2586
0.1270
0.0451

0.0000
0.0424
0.1413
0.2277
0.2361
0.1771

0.0000
0.0076
0.0404
0.1034
0.1703
0.2028

0.0000
0.0012
0.0093
0.0337
0.0785
0.1325

0.0000
0.0002
0.0018
0.0086
0.0269
0.0604

0.0000
0.0000
0.0003
0.0018
0.0072
0.0208

0.0000
0.0000
0.0000
0.0003
0.0015
0.0056

0.0000
0.0000
0.0000
0.0000
0.0003
0.0012

0.0000
0.0000
0.0000
0.0000
0.0000
0.0002

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

30
30
30
30
30

5
6
7
8
9

0.0124
0.0027
0.0005
0.0001
0.0000

0.1023
0.0474
0.0180
0.0058
0.0016

0.1861
0.1368
0.0828
0.0420
0.0181

0.1723
0.1795
0.1538
0.1106
0.0676

0.1047
0.1455
0.1662
0.1593
0.1298

0.0464
0.0829
0.1219
0.1501
0.1573

0.0157
0.0353
0.0652
0.1009
0.1328

0.0041
0.0115
0.0263
0.0505
0.0823

0.0008
0.0029
0.0081
0.0191
0.0382

0.0001
0.0006
0.0019
0.0055
0.0133

30
30
30
30
30

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0004
0.0001
0.0000
0.0000
0.0000

0.0067
0.0022
0.0006
0.0001
0.0000

0.0355
0.0161
0.0064
0.0022
0.0007

0.0909
0.0551
0.0291
0.0134
0.0054

0.1416
0.1103
0.0749
0.0444
0.0231

0.1502
0.1471
0.1254
0.0935
0.0611

0.1152
0.1396
0.1474
0.1360
0.1101

0.0656
0.0976
0.1265
0.1433
0.1424

0.0280
0.0509
0.0806
0.1115
0.1354

30
30
30
30
30

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0000
0.0000
0.0000
0.0000

0.0019
0.0006
0.0002
0.0000
0.0000

0.0106
0.0042
0.0015
0.0005
0.0001

0.0351
0.0177
0.0079
0.0031
0.0010

0.0783
0.0489
0.0269
0.0129
0.0054

0.1242
0.0953
0.0642
0.0379
0.0196

0.1445
0.1354
0.1115
0.0806
0.0509

30
30
30
30
30

20
21
22
23
24

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0003
0.0001
0.0000
0.0000
0.0000

0.0020
0.0006
0.0002
0.0000
0.0000

0.0088
0.0034
0.0012
0.0003
0.0001

0.0280
0.0133
0.0055
0.0019
0.0006

30
30
30
30
30

25
26
27
28
29

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

30
35
35
35
35
35

30
0
1
2
3
4

0.0000
0.1661
0.3059
0.2737
0.1585
0.0667

0.0000
0.0250
0.0973
0.1839
0.2247
0.1998

0.0000
0.0034
0.0209
0.0627
0.1218
0.1719

0.0000
0.0004
0.0035
0.0151
0.0415
0.0830

0.0000
0.0000
0.0005
0.0028
0.0103
0.0274

0.0000
0.0000
0.0001
0.0004
0.0020
0.0067

0.0000
0.0000
0.0000
0.0000
0.0003
0.0012

0.0000
0.0000
0.0000
0.0000
0.0000
0.0002

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – probability function

7

f (x) n x
35
5
35
6
35
7
35
8
35
9

0.05
0.0218
0.0057
0.0012
0.0002
0.0000

0.1
0.1376
0.0765
0.0352
0.0137
0.0046

0.15
0.1881
0.1660
0.1213
0.0749
0.0397

0.2
0.1286
0.1607
0.1665
0.1457
0.1093

0.25
0.0566
0.0944
0.1303
0.1520
0.1520

0.3
0.0178
0.0381
0.0676
0.1015
0.1305

0.35
0.0042
0.0112
0.0250
0.0471
0.0761

0.4
0.0007
0.0024
0.0068
0.0158
0.0316

0.45
0.0001
0.0004
0.0013
0.0039
0.0095

0.5
0.0000
0.0000
0.0002
0.0007
0.0021

35
35
35
35
35

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0013
0.0003
0.0001
0.0000
0.0000

0.0182
0.0073
0.0026
0.0008
0.0002

0.0710
0.0404
0.0202
0.0089
0.0035

0.1318
0.0998
0.0665
0.0392
0.0206

0.1454
0.1416
0.1214
0.0920
0.0620

0.1065
0.1303
0.1404
0.1337
0.1131

0.0547
0.0829
0.1106
0.1304
0.1366

0.0202
0.0375
0.0614
0.0889
0.1143

0.0053
0.0121
0.0243
0.0430
0.0675

35
35
35
35
35

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0012
0.0004
0.0001
0.0000
0.0000

0.0096
0.0040
0.0015
0.0005
0.0001

0.0372
0.0199
0.0095
0.0041
0.0016

0.0853
0.0574
0.0345
0.0186
0.0090

0.1275
0.1063
0.0792
0.0528
0.0315

0.1309
0.1339
0.1225
0.1002
0.0733

0.0945
0.1182
0.1321
0.1321
0.1182

35
35
35
35
35

20
21
22
23
24

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0005
0.0002
0.0000
0.0000
0.0000

0.0039
0.0015
0.0005
0.0002
0.0000

0.0168
0.0080
0.0034
0.0013
0.0004

0.0480
0.0281
0.0146
0.0068
0.0028

0.0945
0.0675
0.0430
0.0243
0.0121

35
35
35
35
35

25
26
27
28
29

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0010
0.0003
0.0001
0.0000
0.0000

0.0053
0.0021
0.0007
0.0002
0.0000

35
35
35
35
35

30
31
32
33
34

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

35
40
40
40
40
40

35
0
1
2
3
4

0.0000
0.1285
0.2706
0.2777
0.1851
0.0901

0.0000
0.0148
0.0657
0.1423
0.2003
0.2059

0.0000
0.0015
0.0106
0.0365
0.0816
0.1332

0.0000
0.0001
0.0013
0.0065
0.0205
0.0475

0.0000
0.0000
0.0001
0.0009
0.0037
0.0113

0.0000
0.0000
0.0000
0.0001
0.0005
0.0020

0.0000
0.0000
0.0000
0.0000
0.0001
0.0003

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

40
40
40
40
40

5
6
7
8
9

0.0342
0.0105
0.0027
0.0006
0.0001

0.1647
0.1068
0.0576
0.0264
0.0104

0.1692
0.1742
0.1493
0.1087
0.0682

0.0854
0.1246
0.1513
0.1560
0.1386

0.0272
0.0530
0.0857
0.1179
0.1397

0.0061
0.0151
0.0315
0.0557
0.0849

0.0010
0.0031
0.0080
0.0179
0.0342

0.0001
0.0005
0.0015
0.0040
0.0095

0.0000
0.0000
0.0002
0.0006
0.0018

0.0000
0.0000
0.0000
0.0001
0.0002

40
40
40
40
40

10
11
12
13
14

0.0000
0.0000
0.0000
0.0000
0.0000

0.0036
0.0011
0.0003
0.0001
0.0000

0.0373
0.0180
0.0077
0.0029
0.0010

0.1075
0.0733
0.0443
0.0238
0.0115

0.1444
0.1312
0.1057
0.0759
0.0488

0.1128
0.1319
0.1366
0.1261
0.1042

0.0571
0.0838
0.1090
0.1265
0.1313

0.0196
0.0357
0.0576
0.0827
0.1063

0.0047
0.0105
0.0207
0.0365
0.0575

0.0008
0.0021
0.0051
0.0109
0.0211

40
40
40
40
40

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0003
0.0001
0.0000
0.0000
0.0000

0.0050
0.0019
0.0007
0.0002
0.0001

0.0282
0.0147
0.0069
0.0029
0.0011

0.0774
0.0518
0.0314
0.0172
0.0085

0.1226
0.1031
0.0784
0.0539
0.0336

0.1228
0.1279
0.1204
0.1026
0.0792

0.0816
0.1043
0.1205
0.1260
0.1194

0.0366
0.0572
0.0807
0.1031
0.1194

40
40
40
40
40

20
21
22
23
24

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0004
0.0001
0.0000
0.0000
0.0000

0.0038
0.0016
0.0006
0.0002
0.0001

0.0190
0.0097
0.0045
0.0019
0.0007

0.0554
0.0352
0.0203
0.0106
0.0050

0.1025
0.0799
0.0565
0.0362
0.0210

0.1254
0.1194
0.1031
0.0807
0.0572

40
40
40
40
40

25
26
27
28
29

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0003
0.0001
0.0000
0.0000
0.0000

0.0021
0.0008
0.0003
0.0001
0.0000

0.0110
0.0052
0.0022
0.0008
0.0003

0.0366
0.0211
0.0109
0.0051
0.0021

40
40
40
40

30
31
32
33

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000

0.0008
0.0002
0.0001
0.0000

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – probability function

8

f (x) n x
40 34

0.05
0.0000

0.1
0.0000

0.15
0.0000

0.2
0.0000

0.25
0.0000

0.3
0.0000

0.35
0.0000

0.4
0.0000

0.45
0.0000

0.5
0.0000

40
40
40
40
40

35
36
37
38
39

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

40
45
45
45
45
45

40
0
1
2
3
4

0.0000
0.0994
0.2355
0.2727
0.2057
0.1137

0.0000
0.0087
0.0436
0.1067
0.1699
0.1982

0.0000
0.0007
0.0053
0.0206
0.0520
0.0963

0.0000
0.0000
0.0005
0.0027
0.0097
0.0254

0.0000
0.0000
0.0000
0.0003
0.0013
0.0044

0.0000
0.0000
0.0000
0.0000
0.0001
0.0005

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

45
45
45
45
45

5
6
7
8
9

0.0491
0.0172
0.0050
0.0013
0.0003

0.1806
0.1338
0.0828
0.0437
0.0200

0.1394
0.1640
0.1612
0.1351
0.0980

0.0520
0.0866
0.1206
0.1433
0.1472

0.0120
0.0267
0.0495
0.0784
0.1074

0.0019
0.0054
0.0129
0.0263
0.0463

0.0002
0.0008
0.0023
0.0058
0.0129

0.0000
0.0001
0.0003
0.0009
0.0024

0.0000
0.0000
0.0000
0.0001
0.0003

0.0000
0.0000
0.0000
0.0000
0.0000

45
45
45
45
45

10
11
12
13
14

0.0001
0.0000
0.0000
0.0000
0.0000

0.0080
0.0028
0.0009
0.0003
0.0001

0.0623
0.0350
0.0175
0.0078
0.0032

0.1325
0.1054
0.0747
0.0474
0.0271

0.1289
0.1367
0.1291
0.1093
0.0833

0.0714
0.0973
0.1182
0.1286
0.1259

0.0249
0.0427
0.0651
0.0890
0.1096

0.0058
0.0122
0.0230
0.0390
0.0594

0.0009
0.0023
0.0054
0.0111
0.0208

0.0001
0.0003
0.0008
0.0021
0.0047

45
45
45
45
45

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0012
0.0004
0.0001
0.0000
0.0000

0.0140
0.0066
0.0028
0.0011
0.0004

0.0574
0.0358
0.0204
0.0106
0.0050

0.1115
0.0896
0.0655
0.0437
0.0266

0.1219
0.1231
0.1131
0.0947
0.0725

0.0819
0.1023
0.1164
0.1207
0.1143

0.0352
0.0540
0.0754
0.0960
0.1116

0.0098
0.0184
0.0314
0.0488
0.0693

45
45
45
45
45

20
21
22
23
24

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0022
0.0009
0.0003
0.0001
0.0000

0.0148
0.0076
0.0035
0.0015
0.0006

0.0507
0.0325
0.0191
0.0103
0.0051

0.0991
0.0786
0.0572
0.0381
0.0233

0.1187
0.1156
0.1032
0.0844
0.0633

0.0901
0.1073
0.1170
0.1170
0.1073

45
45
45
45
45

25
26
27
28
29

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0001
0.0000
0.0000
0.0000

0.0023
0.0010
0.0004
0.0001
0.0000

0.0130
0.0067
0.0031
0.0013
0.0005

0.0435
0.0274
0.0158
0.0083
0.0040

0.0901
0.0693
0.0488
0.0314
0.0184

45
45
45
45
45

30
31
32
33
34

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0001
0.0000
0.0000
0.0000

0.0017
0.0007
0.0002
0.0001
0.0000

0.0098
0.0047
0.0021
0.0008
0.0003

45
45
45
45
45

35
36
37
38
39

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

45
45
45
45
45

40
41
42
43
44

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

45
50
50
50
50
50

45
0
1
2
3
4

0.0000
0.0769
0.2025
0.2611
0.2199
0.1360

0.0000
0.0052
0.0286
0.0779
0.1386
0.1809

0.0000
0.0003
0.0026
0.0113
0.0319
0.0661

0.0000
0.0000
0.0002
0.0011
0.0044
0.0128

0.0000
0.0000
0.0000
0.0001
0.0004
0.0016

0.0000
0.0000
0.0000
0.0000
0.0000
0.0001

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

50
50
50
50
50

5
6
7
8
9

0.0658
0.0260
0.0086
0.0024
0.0006

0.1849
0.1541
0.1076
0.0643
0.0333

0.1072
0.1419
0.1575
0.1493
0.1230

0.0295
0.0554
0.0870
0.1169
0.1364

0.0049
0.0123
0.0259
0.0463
0.0721

0.0006
0.0018
0.0048
0.0110
0.0220

0.0000
0.0002
0.0006
0.0017
0.0042

0.0000
0.0000
0.0000
0.0002
0.0005

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

50
50

10
11

0.0001
0.0000

0.0152
0.0061

0.0890
0.0571

0.1398
0.1271

0.0985
0.1194

0.0386
0.0602

0.0093
0.0182

0.0014
0.0035

0.0001
0.0004

0.0000
0.0000

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – probability function

9

f (x) n x
50 12
50 13
50 14

0.05
0.0000
0.0000
0.0000

0.1
0.0022
0.0007
0.0002

0.15
0.0328
0.0169
0.0079

0.2
0.1033
0.0755
0.0499

0.25
0.1294
0.1261
0.1110

0.3
0.0838
0.1050
0.1189

0.35
0.0319
0.0502
0.0714

0.4
0.0076
0.0147
0.0260

0.45
0.0011
0.0027
0.0059

0.5
0.0001
0.0003
0.0008

50
50
50
50
50

15
16
17
18
19

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0033
0.0013
0.0005
0.0001
0.0000

0.0299
0.0164
0.0082
0.0037
0.0016

0.0888
0.0648
0.0432
0.0264
0.0148

0.1223
0.1147
0.0983
0.0772
0.0558

0.0923
0.1088
0.1171
0.1156
0.1048

0.0415
0.0606
0.0808
0.0987
0.1109

0.0116
0.0207
0.0339
0.0508
0.0700

0.0020
0.0044
0.0087
0.0160
0.0270

50
50
50
50
50

20
21
22
23
24

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0006
0.0002
0.0001
0.0000
0.0000

0.0077
0.0036
0.0016
0.0006
0.0002

0.0370
0.0227
0.0128
0.0067
0.0032

0.0875
0.0673
0.0478
0.0313
0.0190

0.1146
0.1091
0.0959
0.0778
0.0584

0.0888
0.1038
0.1119
0.1115
0.1026

0.0419
0.0598
0.0788
0.0960
0.1080

50
50
50
50
50

25
26
27
28
29

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0014
0.0006
0.0002
0.0001
0.0000

0.0106
0.0055
0.0026
0.0012
0.0005

0.0405
0.0259
0.0154
0.0084
0.0043

0.0873
0.0687
0.0500
0.0336
0.0208

0.1123
0.1080
0.0960
0.0788
0.0598

50
50
50
50
50

30
31
32
33
34

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0001
0.0000
0.0000
0.0000

0.0020
0.0009
0.0003
0.0001
0.0000

0.0119
0.0063
0.0031
0.0014
0.0006

0.0419
0.0270
0.0160
0.0087
0.0044

50
50
50
50
50

35
36
37
38
39

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0002
0.0001
0.0000
0.0000
0.0000

0.0020
0.0008
0.0003
0.0001
0.0000

50
50
50
50
50

40
41
42
43
44

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

50
50
50
50
50

45
46
47
48
49

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

50

50

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – distribution function

10

Binomial Distribution – F(x)
F (x) n x
1 0
1 1
2 0
2 1
2 2
3 0
3 1
3 2
3 3
4 0
4 1
4 2
4 3
4 4
5 0
5 1
5 2
5 3
5 4

p
0.05
0.9500
1.0000
0.9025
0.9975
1.0000
0.8574
0.9928
0.9999
1.0000
0.8145
0.9860
0.9995
1.0000
1.0000
0.7738
0.9774
0.9988
1.0000
1.0000

0.1
0.9000
1.0000
0.8100
0.9900
1.0000
0.7290
0.9720
0.9990
1.0000
0.6561
0.9477
0.9963
0.9999
1.0000
0.5905
0.9185
0.9914
0.9995
1.0000

0.15
0.8500
1.0000
0.7225
0.9775
1.0000
0.6141
0.9393
0.9966
1.0000
0.5220
0.8905
0.9880
0.9995
1.0000
0.4437
0.8352
0.9734
0.9978
0.9999

0.2
0.8000
1.0000
0.6400
0.9600
1.0000
0.5120
0.8960
0.9920
1.0000
0.4096
0.8192
0.9728
0.9984
1.0000
0.3277
0.7373
0.9421
0.9933
0.9997

0.25
0.7500
1.0000
0.5625
0.9375
1.0000
0.4219
0.8438
0.9844
1.0000
0.3164
0.7383
0.9492
0.9961
1.0000
0.2373
0.6328
0.8965
0.9844
0.9990

0.3
0.7000
1.0000
0.4900
0.9100
1.0000
0.3430
0.7840
0.9730
1.0000
0.2401
0.6517
0.9163
0.9919
1.0000
0.1681
0.5282
0.8369
0.9692
0.9976

0.35
0.6500
1.0000
0.4225
0.8775
1.0000
0.2746
0.7183
0.9571
1.0000
0.1785
0.5630
0.8735
0.9850
1.0000
0.1160
0.4284
0.7648
0.9460
0.9947

0.4
0.6000
1.0000
0.3600
0.8400
1.0000
0.2160
0.6480
0.9360
1.0000
0.1296
0.4752
0.8208
0.9744
1.0000
0.0778
0.3370
0.6826
0.9130
0.9898

0.45
0.5500
1.0000
0.3025
0.7975
1.0000
0.1664
0.5747
0.9089
1.0000
0.0915
0.3910
0.7585
0.9590
1.0000
0.0503
0.2562
0.5931
0.8688
0.9815

0.5
0.5000
1.0000
0.2500
0.7500
1.0000
0.1250
0.5000
0.8750
1.0000
0.0625
0.3125
0.6875
0.9375
1.0000
0.0312
0.1875
0.5000
0.8125
0.9688

5
6
6
6
6
6

5
0
1
2
3
4

1.0000
0.7351
0.9672
0.9978
0.9999
1.0000

1.0000
0.5314
0.8857
0.9842
0.9987
0.9999

1.0000
0.3771
0.7765
0.9527
0.9941
0.9996

1.0000
0.2621
0.6554
0.9011
0.9830
0.9984

1.0000
0.1780
0.5339
0.8306
0.9624
0.9954

1.0000
0.1176
0.4202
0.7443
0.9295
0.9891

1.0000
0.0754
0.3191
0.6471
0.8826
0.9777

1.0000
0.0467
0.2333
0.5443
0.8208
0.9590

1.0000
0.0277
0.1636
0.4415
0.7447
0.9308

1.0000
0.0156
0.1094
0.3438
0.6562
0.8906

6
6
7
7
7
7
7

5
6
0
1
2
3
4

1.0000
1.0000
0.6983
0.9556
0.9962
0.9998
1.0000

1.0000
1.0000
0.4783
0.8503
0.9743
0.9973
0.9998

1.0000
1.0000
0.3206
0.7166
0.9262
0.9879
0.9988

0.9999
1.0000
0.2097
0.5767
0.8520
0.9667
0.9953

0.9998
1.0000
0.1335
0.4449
0.7564
0.9294
0.9871

0.9993
1.0000
0.0824
0.3294
0.6471
0.8740
0.9712

0.9982
1.0000
0.0490
0.2338
0.5323
0.8002
0.9444

0.9959
1.0000
0.0280
0.1586
0.4199
0.7102
0.9037

0.9917
1.0000
0.0152
0.1024
0.3164
0.6083
0.8471

0.9844
1.0000
0.0078
0.0625
0.2266
0.5000
0.7734

7
7
7
8
8
8
8
8

5
6
7
0
1
2
3
4

1.0000
1.0000
1.0000
0.6634
0.9428
0.9942
0.9996
1.0000

1.0000
1.0000
1.0000
0.4305
0.8131
0.9619
0.9950
0.9996

0.9999
1.0000
1.0000
0.2725
0.6572
0.8948
0.9786
0.9971

0.9996
1.0000
1.0000
0.1678
0.5033
0.7969
0.9437
0.9896

0.9987
0.9999
1.0000
0.1001
0.3671
0.6785
0.8862
0.9727

0.9962
0.9998
1.0000
0.0576
0.2553
0.5518
0.8059
0.9420

0.9910
0.9994
1.0000
0.0319
0.1691
0.4278
0.7064
0.8939

0.9812
0.9984
1.0000
0.0168
0.1064
0.3154
0.5941
0.8263

0.9643
0.9963
1.0000
0.0084
0.0632
0.2201
0.4770
0.7396

0.9375
0.9922
1.0000
0.0039
0.0352
0.1445
0.3633
0.6367

8
8
8
8
9
9
9
9
9

5
6
7
8
0
1
2
3
4

1.0000
1.0000
1.0000
1.0000
0.6302
0.9288
0.9916
0.9994
1.0000

1.0000
1.0000
1.0000
1.0000
0.3874
0.7748
0.9470
0.9917
0.9991

0.9998
1.0000
1.0000
1.0000
0.2316
0.5995
0.8591
0.9661
0.9944

0.9988
0.9999
1.0000
1.0000
0.1342
0.4362
0.7382
0.9144
0.9804

0.9958
0.9996
1.0000
1.0000
0.0751
0.3003
0.6007
0.8343
0.9511

0.9887
0.9987
0.9999
1.0000
0.0404
0.1960
0.4628
0.7297
0.9012

0.9747
0.9964
0.9998
1.0000
0.0207
0.1211
0.3373
0.6089
0.8283

0.9502
0.9915
0.9993
1.0000
0.0101
0.0705
0.2318
0.4826
0.7334

0.9115
0.9819
0.9983
1.0000
0.0046
0.0385
0.1495
0.3614
0.6214

0.8555
0.9648
0.9961
1.0000
0.0020
0.0195
0.0898
0.2539
0.5000

9
9
9
9
9
10
10
10
10
10

5
6
7
8
9
0
1
2
3
4

1.0000
1.0000
1.0000
1.0000
1.0000
0.5987
0.9139
0.9885
0.9990
0.9999

0.9999
1.0000
1.0000
1.0000
1.0000
0.3487
0.7361
0.9298
0.9872
0.9984

0.9994
1.0000
1.0000
1.0000
1.0000
0.1969
0.5443
0.8202
0.9500
0.9901

0.9969
0.9997
1.0000
1.0000
1.0000
0.1074
0.3758
0.6778
0.8791
0.9672

0.9900
0.9987
0.9999
1.0000
1.0000
0.0563
0.2440
0.5256
0.7759
0.9219

0.9747
0.9957
0.9996
1.0000
1.0000
0.0282
0.1493
0.3828
0.6496
0.8497

0.9464
0.9888
0.9986
0.9999
1.0000
0.0135
0.0860
0.2616
0.5138
0.7515

0.9006
0.9750
0.9962
0.9997
1.0000
0.0060
0.0464
0.1673
0.3823
0.6331

0.8342
0.9502
0.9909
0.9992
1.0000
0.0025
0.0233
0.0996
0.2660
0.5044

0.7461
0.9102
0.9805
0.9980
1.0000
0.0010
0.0107
0.0547
0.1719
0.3770

10
10
10
10
10

5
6
7
8
9

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9986
0.9999
1.0000
1.0000
1.0000

0.9936
0.9991
0.9999
1.0000
1.0000

0.9803
0.9965
0.9996
1.0000
1.0000

0.9527
0.9894
0.9984
0.9999
1.0000

0.9051
0.9740
0.9952
0.9995
1.0000

0.8338
0.9452
0.9877
0.9983
0.9999

0.7384
0.8980
0.9726
0.9955
0.9997

0.6230
0.8281
0.9453
0.9893
0.9990

´
CATOLICA-LISBON

Statistical Tables

Binomial Distribution – distribution function

11

F (x) n x
10 10
11
0
11
1
11
2
11
3
11
4

0.05
1.0000
0.5688
0.8981
0.9848
0.9984
0.9999

0.1
1.0000
0.3138
0.6974
0.9104
0.9815
0.9972

0.15
1.0000
0.1673
0.4922
0.7788
0.9306
0.9841

0.2
1.0000
0.0859
0.3221
0.6174
0.8389
0.9496

0.25
1.0000
0.0422
0.1971
0.4552
0.7133
0.8854

0.3
1.0000
0.0198
0.1130
0.3127
0.5696
0.7897

0.35
1.0000
0.0088
0.0606
0.2001
0.4256
0.6683

0.4
1.0000
0.0036
0.0302
0.1189
0.2963
0.5328

0.45
1.0000
0.0014
0.0139
0.0652
0.1911
0.3971

0.5
1.0000
0.0005
0.0059
0.0327
0.1133
0.2744

11
11
11
11
11

5
6
7
8
9

1.0000
1.0000
1.0000
1.0000
1.0000

0.9997
1.0000
1.0000
1.0000
1.0000

0.9973
0.9997
1.0000
1.0000
1.0000

0.9883
0.9980
0.9998
1.0000
1.0000

0.9657
0.9924
0.9988
0.9999
1.0000

0.9218
0.9784
0.9957
0.9994
1.0000

0.8513
0.9499
0.9878
0.9980
0.9998

0.7535
0.9006
0.9707
0.9941
0.9993

0.6331
0.8262
0.9390
0.9852
0.9978

0.5000
0.7256
0.8867
0.9673
0.9941

11
11
12
12
12
12
12

10
11
0
1
2
3
4

1.0000
1.0000
0.5404
0.8816
0.9804
0.9978
0.9998

1.0000
1.0000
0.2824
0.6590
0.8891
0.9744
0.9957

1.0000
1.0000
0.1422
0.4435
0.7358
0.9078
0.9761

1.0000
1.0000
0.0687
0.2749
0.5583
0.7946
0.9274

1.0000
1.0000
0.0317
0.1584
0.3907
0.6488
0.8424

1.0000
1.0000
0.0138
0.0850
0.2528
0.4925
0.7237

1.0000
1.0000
0.0057
0.0424
0.1513
0.3467
0.5833

1.0000
1.0000
0.0022
0.0196
0.0834
0.2253
0.4382

0.9998
1.0000
0.0008
0.0083
0.0421
0.1345
0.3044

0.9995
1.0000
0.0002
0.0032
0.0193
0.0730
0.1938

12
12
12
12
12

5
6
7
8
9

1.0000
1.0000
1.0000
1.0000
1.0000

0.9995
0.9999
1.0000
1.0000
1.0000

0.9954
0.9993
0.9999
1.0000
1.0000

0.9806
0.9961
0.9994
0.9999
1.0000

0.9456
0.9857
0.9972
0.9996
1.0000

0.8822
0.9614
0.9905
0.9983
0.9998

0.7873
0.9154
0.9745
0.9944
0.9992

0.6652
0.8418
0.9427
0.9847
0.9972

0.5269
0.7393
0.8883
0.9644
0.9921

0.3872
0.6128
0.8062
0.9270
0.9807

12
12
12
13
13
13
13
13

10
11
12
0
1
2
3
4

1.0000
1.0000
1.0000
0.5133
0.8646
0.9755
0.9969
0.9997

1.0000
1.0000
1.0000
0.2542
0.6213
0.8661
0.9658
0.9935

1.0000
1.0000
1.0000
0.1209
0.3983
0.6920
0.8820
0.9658

1.0000
1.0000
1.0000
0.0550
0.2336
0.5017
0.7473
0.9009

1.0000
1.0000
1.0000
0.0238
0.1267
0.3326
0.5843
0.7940

1.0000
1.0000
1.0000
0.0097
0.0637
0.2025
0.4206
0.6543

0.9999
1.0000
1.0000
0.0037
0.0296
0.1132
0.2783
0.5005

0.9997
1.0000
1.0000
0.0013
0.0126
0.0579
0.1686
0.3530

0.9989
0.9999
1.0000
0.0004
0.0049
0.0269
0.0929
0.2279

0.9968
0.9998
1.0000
0.0001
0.0017
0.0112
0.0461
0.1334

13
13
13
13
13

5
6
7
8
9

1.0000
1.0000
1.0000
1.0000
1.0000

0.9991
0.9999
1.0000
1.0000
1.0000

0.9925
0.9987
0.9998
1.0000
1.0000

0.9700
0.9930
0.9988
0.9998
1.0000

0.9198
0.9757
0.9944
0.9990
0.9999

0.8346
0.9376
0.9818
0.9960
0.9993

0.7159
0.8705
0.9538
0.9874
0.9975

0.5744
0.7712
0.9023
0.9679
0.9922

0.4268
0.6437
0.8212
0.9302
0.9797

0.2905
0.5000
0.7095
0.8666
0.9539

13
13
13
13
14
14
14
14
14

10
11
12
13
0
1
2
3
4

1.0000
1.0000
1.0000
1.0000
0.4877
0.8470
0.9699
0.9958
0.9996

1.0000
1.0000
1.0000
1.0000
0.2288
0.5846
0.8416
0.9559
0.9908

1.0000
1.0000
1.0000
1.0000
0.1028
0.3567
0.6479
0.8535
0.9533

1.0000
1.0000
1.0000
1.0000
0.0440
0.1979
0.4481
0.6982
0.8702

1.0000
1.0000
1.0000
1.0000
0.0178
0.1010
0.2811
0.5213
0.7415

0.9999
1.0000
1.0000
1.0000
0.0068
0.0475
0.1608
0.3552
0.5842

0.9997
1.0000
1.0000
1.0000
0.0024
0.0205
0.0839
0.2205
0.4227

0.9987
0.9999
1.0000
1.0000
0.0008
0.0081
0.0398
0.1243
0.2793

0.9959
0.9995
1.0000
1.0000
0.0002
0.0029
0.0170
0.0632
0.1672

0.9888
0.9983
0.9999
1.0000
0.0001
0.0009
0.0065
0.0287
0.0898

14
14
14
14
14

5
6
7
8
9

1.0000
1.0000
1.0000
1.0000
1.0000

0.9985
0.9998
1.0000
1.0000
1.0000

0.9885
0.9978
0.9997
1.0000
1.0000

0.9561
0.9884
0.9976
0.9996
1.0000

0.8883
0.9617
0.9897
0.9978
0.9997

0.7805
0.9067
0.9685
0.9917
0.9983

0.6405
0.8164
0.9247
0.9757
0.9940

0.4859
0.6925
0.8499
0.9417
0.9825

0.3373
0.5461
0.7414
0.8811
0.9574

0.2120
0.3953
0.6047
0.7880
0.9102

14
14
14
14
14
15
15
15
15
15

10
11
12
13
14
0
1
2
3
4

1.0000
1.0000
1.0000
1.0000
1.0000
0.4633
0.8290
0.9638
0.9945
0.9994

1.0000
1.0000
1.0000
1.0000
1.0000
0.2059
0.5490
0.8159
0.9444
0.9873

1.0000
1.0000
1.0000
1.0000
1.0000
0.0874
0.3186
0.6042
0.8227
0.9383

1.0000
1.0000
1.0000
1.0000
1.0000
0.0352
0.1671
0.3980
0.6482
0.8358

1.0000
1.0000
1.0000
1.0000
1.0000
0.0134
0.0802
0.2361
0.4613
0.6865

0.9998
1.0000
1.0000
1.0000
1.0000
0.0047
0.0353
0.1268
0.2969
0.5155

0.9989
0.9999
1.0000
1.0000
1.0000
0.0016
0.0142
0.0617
0.1727
0.3519

0.9961
0.9994
0.9999
1.0000
1.0000
0.0005
0.0052
0.0271
0.0905
0.2173

0.9886
0.9978
0.9997
1.0000
1.0000
0.0001
0.0017
0.0107
0.0424
0.1204

0.9713
0.9935
0.9991
0.9999
1.0000
0.0000
0.0005
0.0037
0.0176
0.0592

15
15
15
15
15

5
6
7
8
9

0.9999
1.0000
1.0000
1.0000
1.0000

0.9978
0.9997
1.0000
1.0000
1.0000

0.9832
0.9964
0.9994
0.9999
1.0000

0.9389
0.9819
0.9958
0.9992
0.9999

0.8516
0.9434
0.9827
0.9958
0.9992

0.7216
0.8689
0.9500
0.9848
0.9963

0.5643
0.7548
0.8868
0.9578
0.9876

0.4032
0.6098
0.7869
0.9050
0.9662

0.2608
0.4522
0.6535
0.8182
0.9231

0.1509
0.3036
0.5000
0.6964
0.8491

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – distribution function

12

F (x) n x
15 10
15 11
15 12
15 13
15 14

0.05
1.0000
1.0000
1.0000
1.0000
1.0000

0.1
1.0000
1.0000
1.0000
1.0000
1.0000

0.15
1.0000
1.0000
1.0000
1.0000
1.0000

0.2
1.0000
1.0000
1.0000
1.0000
1.0000

0.25
0.9999
1.0000
1.0000
1.0000
1.0000

0.3
0.9993
0.9999
1.0000
1.0000
1.0000

0.35
0.9972
0.9995
0.9999
1.0000
1.0000

0.4
0.9907
0.9981
0.9997
1.0000
1.0000

0.45
0.9745
0.9937
0.9989
0.9999
1.0000

0.5
0.9408
0.9824
0.9963
0.9995
1.0000

15
16
16
16
16
16

15
0
1
2
3
4

1.0000
0.4401
0.8108
0.9571
0.9930
0.9991

1.0000
0.1853
0.5147
0.7892
0.9316
0.9830

1.0000
0.0743
0.2839
0.5614
0.7899
0.9209

1.0000
0.0281
0.1407
0.3518
0.5981
0.7982

1.0000
0.0100
0.0635
0.1971
0.4050
0.6302

1.0000
0.0033
0.0261
0.0994
0.2459
0.4499

1.0000
0.0010
0.0098
0.0451
0.1339
0.2892

1.0000
0.0003
0.0033
0.0183
0.0651
0.1666

1.0000
0.0001
0.0010
0.0066
0.0281
0.0853

1.0000
0.0000
0.0003
0.0021
0.0106
0.0384

16
16
16
16
16

5
6
7
8
9

0.9999
1.0000
1.0000
1.0000
1.0000

0.9967
0.9995
0.9999
1.0000
1.0000

0.9765
0.9944
0.9989
0.9998
1.0000

0.9183
0.9733
0.9930
0.9985
0.9998

0.8103
0.9204
0.9729
0.9925
0.9984

0.6598
0.8247
0.9256
0.9743
0.9929

0.4900
0.6881
0.8406
0.9329
0.9771

0.3288
0.5272
0.7161
0.8577
0.9417

0.1976
0.3660
0.5629
0.7441
0.8759

0.1051
0.2272
0.4018
0.5982
0.7728

16
16
16
16
16

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9997
1.0000
1.0000
1.0000
1.0000

0.9984
0.9997
1.0000
1.0000
1.0000

0.9938
0.9987
0.9998
1.0000
1.0000

0.9809
0.9951
0.9991
0.9999
1.0000

0.9514
0.9851
0.9965
0.9994
0.9999

0.8949
0.9616
0.9894
0.9979
0.9997

16
16
17
17
17
17
17

15
16
0
1
2
3
4

1.0000
1.0000
0.4181
0.7922
0.9497
0.9912
0.9988

1.0000
1.0000
0.1668
0.4818
0.7618
0.9174
0.9779

1.0000
1.0000
0.0631
0.2525
0.5198
0.7556
0.9013

1.0000
1.0000
0.0225
0.1182
0.3096
0.5489
0.7582

1.0000
1.0000
0.0075
0.0501
0.1637
0.3530
0.5739

1.0000
1.0000
0.0023
0.0193
0.0774
0.2019
0.3887

1.0000
1.0000
0.0007
0.0067
0.0327
0.1028
0.2348

1.0000
1.0000
0.0002
0.0021
0.0123
0.0464
0.1260

1.0000
1.0000
0.0000
0.0006
0.0041
0.0184
0.0596

1.0000
1.0000
0.0000
0.0001
0.0012
0.0064
0.0245

17
17
17
17
17

5
6
7
8
9

0.9999
1.0000
1.0000
1.0000
1.0000

0.9953
0.9992
0.9999
1.0000
1.0000

0.9681
0.9917
0.9983
0.9997
1.0000

0.8943
0.9623
0.9891
0.9974
0.9995

0.7653
0.8929
0.9598
0.9876
0.9969

0.5968
0.7752
0.8954
0.9597
0.9873

0.4197
0.6188
0.7872
0.9006
0.9617

0.2639
0.4478
0.6405
0.8011
0.9081

0.1471
0.2902
0.4743
0.6626
0.8166

0.0717
0.1662
0.3145
0.5000
0.6855

17
17
17
17
17

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9994
0.9999
1.0000
1.0000
1.0000

0.9968
0.9993
0.9999
1.0000
1.0000

0.9880
0.9970
0.9994
0.9999
1.0000

0.9652
0.9894
0.9975
0.9995
0.9999

0.9174
0.9699
0.9914
0.9981
0.9997

0.8338
0.9283
0.9755
0.9936
0.9988

17
17
17
18
18
18
18
18

15
16
17
0
1
2
3
4

1.0000
1.0000
1.0000
0.3972
0.7735
0.9419
0.9891
0.9985

1.0000
1.0000
1.0000
0.1501
0.4503
0.7338
0.9018
0.9718

1.0000
1.0000
1.0000
0.0536
0.2241
0.4797
0.7202
0.8794

1.0000
1.0000
1.0000
0.0180
0.0991
0.2713
0.5010
0.7164

1.0000
1.0000
1.0000
0.0056
0.0395
0.1353
0.3057
0.5187

1.0000
1.0000
1.0000
0.0016
0.0142
0.0600
0.1646
0.3327

1.0000
1.0000
1.0000
0.0004
0.0046
0.0236
0.0783
0.1886

1.0000
1.0000
1.0000
0.0001
0.0013
0.0082
0.0328
0.0942

1.0000
1.0000
1.0000
0.0000
0.0003
0.0025
0.0120
0.0411

0.9999
1.0000
1.0000
0.0000
0.0001
0.0007
0.0038
0.0154

18
18
18
18
18

5
6
7
8
9

0.9998
1.0000
1.0000
1.0000
1.0000

0.9936
0.9988
0.9998
1.0000
1.0000

0.9581
0.9882
0.9973
0.9995
0.9999

0.8671
0.9487
0.9837
0.9957
0.9991

0.7175
0.8610
0.9431
0.9807
0.9946

0.5344
0.7217
0.8593
0.9404
0.9790

0.3550
0.5491
0.7283
0.8609
0.9403

0.2088
0.3743
0.5634
0.7368
0.8653

0.1077
0.2258
0.3915
0.5778
0.7473

0.0481
0.1189
0.2403
0.4073
0.5927

18
18
18
18
18

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9998
1.0000
1.0000
1.0000
1.0000

0.9988
0.9998
1.0000
1.0000
1.0000

0.9939
0.9986
0.9997
1.0000
1.0000

0.9788
0.9938
0.9986
0.9997
1.0000

0.9424
0.9797
0.9942
0.9987
0.9998

0.8720
0.9463
0.9817
0.9951
0.9990

0.7597
0.8811
0.9519
0.9846
0.9962

18
18
18
18
19
19
19
19
19

15
16
17
18
0
1
2
3
4

1.0000
1.0000
1.0000
1.0000
0.3774
0.7547
0.9335
0.9868
0.9980

1.0000
1.0000
1.0000
1.0000
0.1351
0.4203
0.7054
0.8850
0.9648

1.0000
1.0000
1.0000
1.0000
0.0456
0.1985
0.4413
0.6841
0.8556

1.0000
1.0000
1.0000
1.0000
0.0144
0.0829
0.2369
0.4551
0.6733

1.0000
1.0000
1.0000
1.0000
0.0042
0.0310
0.1113
0.2631
0.4654

1.0000
1.0000
1.0000
1.0000
0.0011
0.0104
0.0462
0.1332
0.2822

1.0000
1.0000
1.0000
1.0000
0.0003
0.0031
0.0170
0.0591
0.1500

1.0000
1.0000
1.0000
1.0000
0.0001
0.0008
0.0055
0.0230
0.0696

0.9999
1.0000
1.0000
1.0000
0.0000
0.0002
0.0015
0.0077
0.0280

0.9993
0.9999
1.0000
1.0000
0.0000
0.0000
0.0004
0.0022
0.0096

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – distribution function

13

F (x) n x
19
5
19
6
19
7
19
8
19
9

0.05
0.9998
1.0000
1.0000
1.0000
1.0000

0.1
0.9914
0.9983
0.9997
1.0000
1.0000

0.15
0.9463
0.9837
0.9959
0.9992
0.9999

0.2
0.8369
0.9324
0.9767
0.9933
0.9984

0.25
0.6678
0.8251
0.9225
0.9713
0.9911

0.3
0.4739
0.6655
0.8180
0.9161
0.9674

0.35
0.2968
0.4812
0.6656
0.8145
0.9125

0.4
0.1629
0.3081
0.4878
0.6675
0.8139

0.45
0.0777
0.1727
0.3169
0.4940
0.6710

0.5
0.0318
0.0835
0.1796
0.3238
0.5000

19
19
19
19
19

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9997
1.0000
1.0000
1.0000
1.0000

0.9977
0.9995
0.9999
1.0000
1.0000

0.9895
0.9972
0.9994
0.9999
1.0000

0.9653
0.9886
0.9969
0.9993
0.9999

0.9115
0.9648
0.9884
0.9969
0.9994

0.8159
0.9129
0.9658
0.9891
0.9972

0.6762
0.8204
0.9165
0.9682
0.9904

19
19
19
19
19
20
20
20
20
20

15
16
17
18
19
0
1
2
3
4

1.0000
1.0000
1.0000
1.0000
1.0000
0.3585
0.7358
0.9245
0.9841
0.9974

1.0000
1.0000
1.0000
1.0000
1.0000
0.1216
0.3917
0.6769
0.8670
0.9568

1.0000
1.0000
1.0000
1.0000
1.0000
0.0388
0.1756
0.4049
0.6477
0.8298

1.0000
1.0000
1.0000
1.0000
1.0000
0.0115
0.0692
0.2061
0.4114
0.6296

1.0000
1.0000
1.0000
1.0000
1.0000
0.0032
0.0243
0.0913
0.2252
0.4148

1.0000
1.0000
1.0000
1.0000
1.0000
0.0008
0.0076
0.0355
0.1071
0.2375

1.0000
1.0000
1.0000
1.0000
1.0000
0.0002
0.0021
0.0121
0.0444
0.1182

0.9999
1.0000
1.0000
1.0000
1.0000
0.0000
0.0005
0.0036
0.0160
0.0510

0.9995
0.9999
1.0000
1.0000
1.0000
0.0000
0.0001
0.0009
0.0049
0.0189

0.9978
0.9996
1.0000
1.0000
1.0000
0.0000
0.0000
0.0002
0.0013
0.0059

20
20
20
20
20

5
6
7
8
9

0.9997
1.0000
1.0000
1.0000
1.0000

0.9887
0.9976
0.9996
0.9999
1.0000

0.9327
0.9781
0.9941
0.9987
0.9998

0.8042
0.9133
0.9679
0.9900
0.9974

0.6172
0.7858
0.8982
0.9591
0.9861

0.4164
0.6080
0.7723
0.8867
0.9520

0.2454
0.4166
0.6010
0.7624
0.8782

0.1256
0.2500
0.4159
0.5956
0.7553

0.0553
0.1299
0.2520
0.4143
0.5914

0.0207
0.0577
0.1316
0.2517
0.4119

20
20
20
20
20

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9994
0.9999
1.0000
1.0000
1.0000

0.9961
0.9991
0.9998
1.0000
1.0000

0.9829
0.9949
0.9987
0.9997
1.0000

0.9468
0.9804
0.9940
0.9985
0.9997

0.8725
0.9435
0.9790
0.9935
0.9984

0.7507
0.8692
0.9420
0.9786
0.9936

0.5881
0.7483
0.8684
0.9423
0.9793

20
20
20
20
20

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9997
1.0000
1.0000
1.0000
1.0000

0.9985
0.9997
1.0000
1.0000
1.0000

0.9941
0.9987
0.9998
1.0000
1.0000

20
21
21
21
21
21

20
0
1
2
3
4

1.0000
0.3406
0.7170
0.9151
0.9811
0.9968

1.0000
0.1094
0.3647
0.6484
0.8480
0.9478

1.0000
0.0329
0.1550
0.3705
0.6113
0.8025

1.0000
0.0092
0.0576
0.1787
0.3704
0.5860

1.0000
0.0024
0.0190
0.0745
0.1917
0.3674

1.0000
0.0006
0.0056
0.0271
0.0856
0.1984

1.0000
0.0001
0.0014
0.0086
0.0331
0.0924

1.0000
0.0000
0.0003
0.0024
0.0110
0.0370

1.0000
0.0000
0.0001
0.0006
0.0031
0.0126

1.0000
0.0000
0.0000
0.0001
0.0007
0.0036

21
21
21
21
21

5
6
7
8
9

0.9996
1.0000
1.0000
1.0000
1.0000

0.9856
0.9967
0.9994
0.9999
1.0000

0.9173
0.9713
0.9917
0.9980
0.9996

0.7693
0.8915
0.9569
0.9856
0.9959

0.5666
0.7436
0.8701
0.9439
0.9794

0.3627
0.5505
0.7230
0.8523
0.9324

0.2009
0.3567
0.5365
0.7059
0.8377

0.0957
0.2002
0.3495
0.5237
0.6914

0.0389
0.0964
0.1971
0.3413
0.5117

0.0133
0.0392
0.0946
0.1917
0.3318

21
21
21
21
21

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9990
0.9998
1.0000
1.0000
1.0000

0.9936
0.9983
0.9996
0.9999
1.0000

0.9736
0.9913
0.9976
0.9994
0.9999

0.9228
0.9687
0.9892
0.9969
0.9993

0.8256
0.9151
0.9648
0.9877
0.9964

0.6790
0.8159
0.9092
0.9621
0.9868

0.5000
0.6682
0.8083
0.9054
0.9608

21
21
21
21
21

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9992
0.9998
1.0000
1.0000
1.0000

0.9963
0.9992
0.9999
1.0000
1.0000

0.9867
0.9964
0.9993
0.9999
1.0000

21
21
22
22
22
22
22

20
21
0
1
2
3
4

1.0000
1.0000
0.3235
0.6982
0.9052
0.9778
0.9960

1.0000
1.0000
0.0985
0.3392
0.6200
0.8281
0.9379

1.0000
1.0000
0.0280
0.1367
0.3382
0.5752
0.7738

1.0000
1.0000
0.0074
0.0480
0.1545
0.3320
0.5429

1.0000
1.0000
0.0018
0.0149
0.0606
0.1624
0.3235

1.0000
1.0000
0.0004
0.0041
0.0207
0.0681
0.1645

1.0000
1.0000
0.0001
0.0010
0.0061
0.0245
0.0716

1.0000
1.0000
0.0000
0.0002
0.0016
0.0076
0.0266

1.0000
1.0000
0.0000
0.0000
0.0003
0.0020
0.0083

1.0000
1.0000
0.0000
0.0000
0.0001
0.0004
0.0022

22
22

5
6

0.9994
0.9999

0.9818
0.9956

0.9001
0.9632

0.7326
0.8670

0.5168
0.6994

0.3134
0.4942

0.1629
0.3022

0.0722
0.1584

0.0271
0.0705

0.0085
0.0262

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – distribution function

14

F (x) n x
22
7
22
8
22
9

0.05
1.0000
1.0000
1.0000

0.1
0.9991
0.9999
1.0000

0.15
0.9886
0.9970
0.9993

0.2
0.9439
0.9799
0.9939

0.25
0.8385
0.9254
0.9705

0.3
0.6713
0.8135
0.9084

0.35
0.4736
0.6466
0.7916

0.4
0.2898
0.4540
0.6244

0.45
0.1518
0.2764
0.4350

0.5
0.0669
0.1431
0.2617

22
22
22
22
22

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9984
0.9997
0.9999
1.0000
1.0000

0.9900
0.9971
0.9993
0.9999
1.0000

0.9613
0.9860
0.9957
0.9989
0.9998

0.8930
0.9526
0.9820
0.9942
0.9984

0.7720
0.8793
0.9449
0.9785
0.9930

0.6037
0.7543
0.8672
0.9383
0.9757

0.4159
0.5841
0.7383
0.8569
0.9331

22
22
22
22
22

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9997
0.9999
1.0000
1.0000
1.0000

0.9981
0.9996
0.9999
1.0000
1.0000

0.9920
0.9979
0.9995
0.9999
1.0000

0.9738
0.9915
0.9978
0.9996
0.9999

22
22
22
23
23
23
23
23

20
21
22
0
1
2
3
4

1.0000
1.0000
1.0000
0.3074
0.6794
0.8948
0.9742
0.9951

1.0000
1.0000
1.0000
0.0886
0.3151
0.5920
0.8073
0.9269

1.0000
1.0000
1.0000
0.0238
0.1204
0.3080
0.5396
0.7440

1.0000
1.0000
1.0000
0.0059
0.0398
0.1332
0.2965
0.5007

1.0000
1.0000
1.0000
0.0013
0.0116
0.0492
0.1370
0.2832

1.0000
1.0000
1.0000
0.0003
0.0030
0.0157
0.0538
0.1356

1.0000
1.0000
1.0000
0.0000
0.0007
0.0043
0.0181
0.0551

1.0000
1.0000
1.0000
0.0000
0.0001
0.0010
0.0052
0.0190

1.0000
1.0000
1.0000
0.0000
0.0000
0.0002
0.0012
0.0055

1.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0002
0.0013

23
23
23
23
23

5
6
7
8
9

0.9992
0.9999
1.0000
1.0000
1.0000

0.9774
0.9942
0.9988
0.9998
1.0000

0.8811
0.9537
0.9848
0.9958
0.9990

0.6947
0.8402
0.9285
0.9727
0.9911

0.4685
0.6537
0.8037
0.9037
0.9592

0.2688
0.4399
0.6181
0.7709
0.8799

0.1309
0.2534
0.4136
0.5860
0.7408

0.0540
0.1240
0.2373
0.3884
0.5562

0.0186
0.0510
0.1152
0.2203
0.3636

0.0053
0.0173
0.0466
0.1050
0.2024

23
23
23
23
23

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9998
1.0000
1.0000
1.0000
1.0000

0.9975
0.9994
0.9999
1.0000
1.0000

0.9851
0.9954
0.9988
0.9997
0.9999

0.9454
0.9786
0.9928
0.9979
0.9995

0.8575
0.9318
0.9717
0.9900
0.9970

0.7129
0.8364
0.9187
0.9651
0.9872

0.5278
0.6865
0.8164
0.9063
0.9589

0.3388
0.5000
0.6612
0.7976
0.8950

23
23
23
23
23

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9992
0.9998
1.0000
1.0000
1.0000

0.9960
0.9990
0.9998
1.0000
1.0000

0.9847
0.9952
0.9988
0.9998
1.0000

0.9534
0.9827
0.9947
0.9987
0.9998

23
23
23
23
24
24
24
24
24

20
21
22
23
0
1
2
3
4

1.0000
1.0000
1.0000
1.0000
0.2920
0.6608
0.8841
0.9702
0.9940

1.0000
1.0000
1.0000
1.0000
0.0798
0.2925
0.5643
0.7857
0.9149

1.0000
1.0000
1.0000
1.0000
0.0202
0.1059
0.2798
0.5049
0.7134

1.0000
1.0000
1.0000
1.0000
0.0047
0.0331
0.1145
0.2639
0.4599

1.0000
1.0000
1.0000
1.0000
0.0010
0.0090
0.0398
0.1150
0.2466

1.0000
1.0000
1.0000
1.0000
0.0002
0.0022
0.0119
0.0424
0.1111

1.0000
1.0000
1.0000
1.0000
0.0000
0.0005
0.0030
0.0133
0.0422

1.0000
1.0000
1.0000
1.0000
0.0000
0.0001
0.0007
0.0035
0.0134

1.0000
1.0000
1.0000
1.0000
0.0000
0.0000
0.0001
0.0008
0.0036

1.0000
1.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0001
0.0008

24
24
24
24
24

5
6
7
8
9

0.9990
0.9999
1.0000
1.0000
1.0000

0.9723
0.9925
0.9983
0.9997
0.9999

0.8606
0.9428
0.9801
0.9941
0.9985

0.6559
0.8111
0.9108
0.9638
0.9874

0.4222
0.6074
0.7662
0.8787
0.9453

0.2288
0.3886
0.5647
0.7250
0.8472

0.1044
0.2106
0.3575
0.5257
0.6866

0.0400
0.0960
0.1919
0.3279
0.4891

0.0127
0.0364
0.0863
0.1730
0.2991

0.0033
0.0113
0.0320
0.0758
0.1537

24
24
24
24
24

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9997
0.9999
1.0000
1.0000
1.0000

0.9962
0.9990
0.9998
1.0000
1.0000

0.9787
0.9928
0.9979
0.9995
0.9999

0.9258
0.9686
0.9885
0.9964
0.9990

0.8167
0.9058
0.9577
0.9836
0.9945

0.6502
0.7870
0.8857
0.9465
0.9783

0.4539
0.6151
0.7580
0.8659
0.9352

0.2706
0.4194
0.5806
0.7294
0.8463

24
24
24
24
24

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9998
1.0000
1.0000
1.0000
1.0000

0.9984
0.9996
0.9999
1.0000
1.0000

0.9925
0.9978
0.9995
0.9999
1.0000

0.9731
0.9905
0.9972
0.9993
0.9999

0.9242
0.9680
0.9887
0.9967
0.9992

24
24
24
24
24

20
21
22
23
24

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – distribution function

15

F (x) n x
25
0
25
1
25
2
25
3
25
4

0.05
0.2774
0.6424
0.8729
0.9659
0.9928

0.1
0.0718
0.2712
0.5371
0.7636
0.9020

0.15
0.0172
0.0931
0.2537
0.4711
0.6821

0.2
0.0038
0.0274
0.0982
0.2340
0.4207

0.25
0.0008
0.0070
0.0321
0.0962
0.2137

0.3
0.0001
0.0016
0.0090
0.0332
0.0905

0.35
0.0000
0.0003
0.0021
0.0097
0.0320

0.4
0.0000
0.0001
0.0004
0.0024
0.0095

0.45
0.0000
0.0000
0.0001
0.0005
0.0023

0.5
0.0000
0.0000
0.0000
0.0001
0.0005

25
25
25
25
25

5
6
7
8
9

0.9988
0.9998
1.0000
1.0000
1.0000

0.9666
0.9905
0.9977
0.9995
0.9999

0.8385
0.9305
0.9745
0.9920
0.9979

0.6167
0.7800
0.8909
0.9532
0.9827

0.3783
0.5611
0.7265
0.8506
0.9287

0.1935
0.3407
0.5118
0.6769
0.8106

0.0826
0.1734
0.3061
0.4668
0.6303

0.0294
0.0736
0.1536
0.2735
0.4246

0.0086
0.0258
0.0639
0.1340
0.2424

0.0020
0.0073
0.0216
0.0539
0.1148

25
25
25
25
25

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9995
0.9999
1.0000
1.0000
1.0000

0.9944
0.9985
0.9996
0.9999
1.0000

0.9703
0.9893
0.9966
0.9991
0.9998

0.9022
0.9558
0.9825
0.9940
0.9982

0.7712
0.8746
0.9396
0.9745
0.9907

0.5858
0.7323
0.8462
0.9222
0.9656

0.3843
0.5426
0.6937
0.8173
0.9040

0.2122
0.3450
0.5000
0.6550
0.7878

25
25
25
25
25

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9995
0.9999
1.0000
1.0000
1.0000

0.9971
0.9992
0.9998
1.0000
1.0000

0.9868
0.9957
0.9988
0.9997
0.9999

0.9560
0.9826
0.9942
0.9984
0.9996

0.8852
0.9461
0.9784
0.9927
0.9980

25
25
25
25
25

20
21
22
23
24

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9995
0.9999
1.0000
1.0000
1.0000

25
30
30
30
30
30

25
0
1
2
3
4

1.0000
0.2146
0.5535
0.8122
0.9392
0.9844

1.0000
0.0424
0.1837
0.4114
0.6474
0.8245

1.0000
0.0076
0.0480
0.1514
0.3217
0.5245

1.0000
0.0012
0.0105
0.0442
0.1227
0.2552

1.0000
0.0002
0.0020
0.0106
0.0374
0.0979

1.0000
0.0000
0.0003
0.0021
0.0093
0.0302

1.0000
0.0000
0.0000
0.0003
0.0019
0.0075

1.0000
0.0000
0.0000
0.0000
0.0003
0.0015

1.0000
0.0000
0.0000
0.0000
0.0000
0.0002

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

30
30
30
30
30

5
6
7
8
9

0.9967
0.9994
0.9999
1.0000
1.0000

0.9268
0.9742
0.9922
0.9980
0.9995

0.7106
0.8474
0.9302
0.9722
0.9903

0.4275
0.6070
0.7608
0.8713
0.9389

0.2026
0.3481
0.5143
0.6736
0.8034

0.0766
0.1595
0.2814
0.4315
0.5888

0.0233
0.0586
0.1238
0.2247
0.3575

0.0057
0.0172
0.0435
0.0940
0.1763

0.0011
0.0040
0.0121
0.0312
0.0694

0.0002
0.0007
0.0026
0.0081
0.0214

30
30
30
30
30

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9971
0.9992
0.9998
1.0000
1.0000

0.9744
0.9905
0.9969
0.9991
0.9998

0.8943
0.9493
0.9784
0.9918
0.9973

0.7304
0.8407
0.9155
0.9599
0.9831

0.5078
0.6548
0.7802
0.8737
0.9348

0.2915
0.4311
0.5785
0.7145
0.8246

0.1350
0.2327
0.3592
0.5025
0.6448

0.0494
0.1002
0.1808
0.2923
0.4278

30
30
30
30
30

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9992
0.9998
0.9999
1.0000
1.0000

0.9936
0.9979
0.9994
0.9998
1.0000

0.9699
0.9876
0.9955
0.9986
0.9996

0.9029
0.9519
0.9788
0.9917
0.9971

0.7691
0.8644
0.9286
0.9666
0.9862

0.5722
0.7077
0.8192
0.8998
0.9506

30
30
30
30
30

20
21
22
23
24

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9991
0.9998
1.0000
1.0000
1.0000

0.9950
0.9984
0.9996
0.9999
1.0000

0.9786
0.9919
0.9974
0.9993
0.9998

30
30
30
30
30

25
26
27
28
29

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

30
35
35
35
35
35

30
0
1
2
3
4

1.0000
0.1661
0.4720
0.7458
0.9042
0.9710

1.0000
0.0250
0.1224
0.3063
0.5310
0.7307

1.0000
0.0034
0.0243
0.0870
0.2088
0.3807

1.0000
0.0004
0.0040
0.0190
0.0605
0.1435

1.0000
0.0000
0.0005
0.0033
0.0136
0.0410

1.0000
0.0000
0.0001
0.0005
0.0024
0.0091

1.0000
0.0000
0.0000
0.0001
0.0003
0.0016

1.0000
0.0000
0.0000
0.0000
0.0000
0.0002

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

35
35
35

5
6
7

0.9927
0.9985
0.9997

0.8684
0.9448
0.9800

0.5689
0.7348
0.8562

0.2721
0.4328
0.5993

0.0976
0.1920
0.3223

0.0269
0.0650
0.1326

0.0058
0.0170
0.0419

0.0010
0.0034
0.0102

0.0001
0.0005
0.0019

0.0000
0.0001
0.0003

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – distribution function

16

F (x) n x
35
8
35
9

0.05
1.0000
1.0000

0.1
0.9937
0.9983

0.15
0.9311
0.9708

0.2
0.7450
0.8543

0.25
0.4743
0.6263

0.3
0.2341
0.3646

0.35
0.0890
0.1651

0.4
0.0260
0.0575

0.45
0.0057
0.0152

0.5
0.0009
0.0030

35
35
35
35
35

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

0.9996
0.9999
1.0000
1.0000
1.0000

0.9890
0.9963
0.9989
0.9997
0.9999

0.9253
0.9656
0.9858
0.9947
0.9982

0.7581
0.8579
0.9244
0.9637
0.9842

0.5100
0.6516
0.7729
0.8650
0.9269

0.2716
0.4019
0.5423
0.6760
0.7891

0.1123
0.1952
0.3057
0.4361
0.5728

0.0354
0.0729
0.1344
0.2233
0.3376

0.0083
0.0205
0.0448
0.0877
0.1553

35
35
35
35
35

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9995
0.9999
1.0000
1.0000
1.0000

0.9938
0.9978
0.9993
0.9998
0.9999

0.9641
0.9840
0.9936
0.9977
0.9992

0.8744
0.9318
0.9664
0.9850
0.9939

0.7003
0.8065
0.8857
0.9385
0.9700

0.4685
0.6024
0.7249
0.8251
0.8984

0.2498
0.3679
0.5000
0.6321
0.7502

35
35
35
35
35

20
21
22
23
24

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000
1.0000

0.9978
0.9993
0.9998
0.9999
1.0000

0.9867
0.9947
0.9981
0.9994
0.9998

0.9464
0.9745
0.9891
0.9958
0.9986

0.8447
0.9123
0.9552
0.9795
0.9917

35
35
35
35
35

25
26
27
28
29

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9996
0.9999
1.0000
1.0000
1.0000

0.9970
0.9991
0.9997
0.9999
1.0000

35
35
35
35
35

30
31
32
33
34

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

35
40
40
40
40
40

35
0
1
2
3
4

1.0000
0.1285
0.3991
0.6767
0.8619
0.9520

1.0000
0.0148
0.0805
0.2228
0.4231
0.6290

1.0000
0.0015
0.0121
0.0486
0.1302
0.2633

1.0000
0.0001
0.0015
0.0079
0.0285
0.0759

1.0000
0.0000
0.0001
0.0010
0.0047
0.0160

1.0000
0.0000
0.0000
0.0001
0.0006
0.0026

1.0000
0.0000
0.0000
0.0000
0.0001
0.0003

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

40
40
40
40
40

5
6
7
8
9

0.9861
0.9966
0.9993
0.9999
1.0000

0.7937
0.9005
0.9581
0.9845
0.9949

0.4325
0.6067
0.7559
0.8646
0.9328

0.1613
0.2859
0.4371
0.5931
0.7318

0.0433
0.0962
0.1820
0.2998
0.4395

0.0086
0.0238
0.0553
0.1110
0.1959

0.0013
0.0044
0.0124
0.0303
0.0644

0.0001
0.0006
0.0021
0.0061
0.0156

0.0000
0.0001
0.0002
0.0009
0.0027

0.0000
0.0000
0.0000
0.0001
0.0003

40
40
40
40
40

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

0.9985
0.9996
0.9999
1.0000
1.0000

0.9701
0.9880
0.9957
0.9986
0.9996

0.8392
0.9125
0.9568
0.9806
0.9921

0.5839
0.7151
0.8209
0.8968
0.9456

0.3087
0.4406
0.5772
0.7032
0.8074

0.1215
0.2053
0.3143
0.4408
0.5721

0.0352
0.0709
0.1285
0.2112
0.3174

0.0074
0.0179
0.0386
0.0751
0.1326

0.0011
0.0032
0.0083
0.0192
0.0403

40
40
40
40
40

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9971
0.9990
0.9997
0.9999
1.0000

0.9738
0.9884
0.9953
0.9983
0.9994

0.8849
0.9367
0.9680
0.9852
0.9937

0.6946
0.7978
0.8761
0.9301
0.9637

0.4402
0.5681
0.6885
0.7911
0.8702

0.2142
0.3185
0.4391
0.5651
0.6844

0.0769
0.1341
0.2148
0.3179
0.4373

40
40
40
40
40

20
21
22
23
24

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9998
1.0000
1.0000
1.0000
1.0000

0.9976
0.9991
0.9997
0.9999
1.0000

0.9827
0.9925
0.9970
0.9989
0.9996

0.9256
0.9608
0.9811
0.9917
0.9966

0.7870
0.8669
0.9233
0.9595
0.9804

0.5627
0.6821
0.7852
0.8659
0.9231

40
40
40
40
40

25
26
27
28
29

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9988
0.9996
0.9999
1.0000
1.0000

0.9914
0.9966
0.9988
0.9996
0.9999

0.9597
0.9808
0.9917
0.9968
0.9989

40
40
40
40
40

30
31
32
33
34

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9997
0.9999
1.0000
1.0000
1.0000

40
40

35
36

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – distribution function

17

F (x) n x
40 37
40 38
40 39

0.05
1.0000
1.0000
1.0000

0.1
1.0000
1.0000
1.0000

0.15
1.0000
1.0000
1.0000

0.2
1.0000
1.0000
1.0000

0.25
1.0000
1.0000
1.0000

0.3
1.0000
1.0000
1.0000

0.35
1.0000
1.0000
1.0000

0.4
1.0000
1.0000
1.0000

0.45
1.0000
1.0000
1.0000

0.5
1.0000
1.0000
1.0000

40
45
45
45
45
45

40
0
1
2
3
4

1.0000
0.0994
0.3350
0.6077
0.8134
0.9271

1.0000
0.0087
0.0524
0.1590
0.3289
0.5271

1.0000
0.0007
0.0060
0.0265
0.0785
0.1748

1.0000
0.0000
0.0005
0.0032
0.0129
0.0382

1.0000
0.0000
0.0000
0.0003
0.0016
0.0059

1.0000
0.0000
0.0000
0.0000
0.0001
0.0007

1.0000
0.0000
0.0000
0.0000
0.0000
0.0001

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

45
45
45
45
45

5
6
7
8
9

0.9761
0.9934
0.9984
0.9997
0.9999

0.7077
0.8415
0.9243
0.9680
0.9880

0.3142
0.4782
0.6394
0.7745
0.8726

0.0902
0.1768
0.2975
0.4407
0.5880

0.0179
0.0446
0.0941
0.1725
0.2800

0.0026
0.0080
0.0209
0.0471
0.0934

0.0003
0.0010
0.0033
0.0091
0.0220

0.0000
0.0001
0.0004
0.0012
0.0036

0.0000
0.0000
0.0000
0.0001
0.0004

0.0000
0.0000
0.0000
0.0000
0.0000

45
45
45
45
45

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

0.9960
0.9988
0.9997
0.9999
1.0000

0.9349
0.9698
0.9873
0.9952
0.9983

0.7205
0.8259
0.9005
0.9479
0.9750

0.4089
0.5457
0.6748
0.7841
0.8673

0.1647
0.2620
0.3802
0.5088
0.6347

0.0469
0.0896
0.1547
0.2437
0.3533

0.0094
0.0216
0.0446
0.0836
0.1430

0.0013
0.0036
0.0090
0.0201
0.0409

0.0001
0.0004
0.0012
0.0033
0.0080

45
45
45
45
45

15
16
17
18
19

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9995
0.9998
1.0000
1.0000
1.0000

0.9890
0.9956
0.9983
0.9994
0.9998

0.9247
0.9605
0.9809
0.9915
0.9965

0.7462
0.8358
0.9014
0.9451
0.9717

0.4752
0.5983
0.7113
0.8060
0.8785

0.2249
0.3272
0.4436
0.5643
0.6786

0.0762
0.1302
0.2056
0.3015
0.4131

0.0178
0.0362
0.0676
0.1163
0.1856

45
45
45
45
45

20
21
22
23
24

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9987
0.9995
0.9999
1.0000
1.0000

0.9865
0.9940
0.9976
0.9991
0.9997

0.9292
0.9618
0.9809
0.9911
0.9962

0.7777
0.8564
0.9135
0.9517
0.9750

0.5318
0.6474
0.7506
0.8350
0.8983

0.2757
0.3830
0.5000
0.6170
0.7243

45
45
45
45
45

25
26
27
28
29

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9985
0.9995
0.9998
0.9999
1.0000

0.9880
0.9947
0.9979
0.9992
0.9997

0.9418
0.9692
0.9850
0.9932
0.9972

0.8144
0.8837
0.9324
0.9638
0.9822

45
45
45
45
45

30
31
32
33
34

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9990
0.9996
0.9999
1.0000
1.0000

0.9920
0.9967
0.9988
0.9996
0.9999

45
45
45
45
45

35
36
37
38
39

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

45
45
45
45
45

40
41
42
43
44

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

45
50
50
50
50
50

45
0
1
2
3
4

1.0000
0.0769
0.2794
0.5405
0.7604
0.8964

1.0000
0.0052
0.0338
0.1117
0.2503
0.4312

1.0000
0.0003
0.0029
0.0142
0.0460
0.1121

1.0000
0.0000
0.0002
0.0013
0.0057
0.0185

1.0000
0.0000
0.0000
0.0001
0.0005
0.0021

1.0000
0.0000
0.0000
0.0000
0.0000
0.0002

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

1.0000
0.0000
0.0000
0.0000
0.0000
0.0000

50
50
50
50
50

5
6
7
8
9

0.9622
0.9882
0.9968
0.9992
0.9998

0.6161
0.7702
0.8779
0.9421
0.9755

0.2194
0.3613
0.5188
0.6681
0.7911

0.0480
0.1034
0.1904
0.3073
0.4437

0.0070
0.0194
0.0453
0.0916
0.1637

0.0007
0.0025
0.0073
0.0183
0.0402

0.0001
0.0002
0.0008
0.0025
0.0067

0.0000
0.0000
0.0001
0.0002
0.0008

0.0000
0.0000
0.0000
0.0000
0.0001

0.0000
0.0000
0.0000
0.0000
0.0000

50
50
50
50
50

10
11
12
13
14

1.0000
1.0000
1.0000
1.0000
1.0000

0.9906
0.9968
0.9990
0.9997
0.9999

0.8801
0.9372
0.9699
0.9868
0.9947

0.5836
0.7107
0.8139
0.8894
0.9393

0.2622
0.3816
0.5110
0.6370
0.7481

0.0789
0.1390
0.2229
0.3279
0.4468

0.0160
0.0342
0.0661
0.1163
0.1878

0.0022
0.0057
0.0133
0.0280
0.0540

0.0002
0.0006
0.0018
0.0045
0.0104

0.0000
0.0000
0.0002
0.0005
0.0013

´
CATOLICA-LISBON

p

Statistical Tables

Binomial Distribution – distribution function

18

F (x) n x
50 15
50 16
50 17
50 18
50 19

0.05
1.0000
1.0000
1.0000
1.0000
1.0000

0.1
1.0000
1.0000
1.0000
1.0000
1.0000

0.15
0.9981
0.9993
0.9998
0.9999
1.0000

0.2
0.9692
0.9856
0.9937
0.9975
0.9991

0.25
0.8369
0.9017
0.9449
0.9713
0.9861

0.3
0.5692
0.6839
0.7822
0.8594
0.9152

0.35
0.2801
0.3889
0.5060
0.6216
0.7264

0.4
0.0955
0.1561
0.2369
0.3356
0.4465

0.45
0.0220
0.0427
0.0765
0.1273
0.1974

0.5
0.0033
0.0077
0.0164
0.0325
0.0595

50
50
50
50
50

20
21
22
23
24

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9997
0.9999
1.0000
1.0000
1.0000

0.9937
0.9974
0.9990
0.9996
0.9999

0.9522
0.9749
0.9877
0.9944
0.9976

0.8139
0.8813
0.9290
0.9604
0.9793

0.5610
0.6701
0.7660
0.8438
0.9022

0.2862
0.3900
0.5019
0.6134
0.7160

0.1013
0.1611
0.2399
0.3359
0.4439

50
50
50
50
50

25
26
27
28
29

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9991
0.9997
0.9999
1.0000
1.0000

0.9900
0.9955
0.9981
0.9993
0.9997

0.9427
0.9686
0.9840
0.9924
0.9966

0.8034
0.8721
0.9220
0.9556
0.9765

0.5561
0.6641
0.7601
0.8389
0.8987

50
50
50
50
50

30
31
32
33
34

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9986
0.9995
0.9998
0.9999
1.0000

0.9884
0.9947
0.9978
0.9991
0.9997

0.9405
0.9675
0.9836
0.9923
0.9967

50
50
50
50
50

35
36
37
38
39

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9987
0.9995
0.9998
1.0000
1.0000

50
50
50
50
50

40
41
42
43
44

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

50
50
50
50
50

45
46
47
48
49

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

50

50

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

´
CATOLICA-LISBON

p

Statistical Tables

Hypergeometric Distribution

19

Hypergeometric Distribution
N1
x

N2 n−x f (x; n, p, N ) =
N
n
N
2
2
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6

n N1
1 1
1 1
1 1
1 1
2 1
2 1
2 2
2 2
1 1
1 1
2 1
2 1
2 2
2 2
2 2
3 1
3 1
3 2
3 2
3 3
3 3
1 1
1 1
2 1
2 1
2 2
2 2
2 2
3 1
3 1
3 2
3 2
3 2
3 3
3 3
3 3
4 1
4 1
4 2
4 2
4 3
4 3
4 4
4 4
1 1
1 1
2 1
2 1
2 2
2 2
2 2
3 1
3 1
3 2
3 2
3 2
3 3
3 3
3 3
3 3

x
0
1
0
1
0
1
1
2
0
1
0
1
0
1
2
0
1
1
2
2
3
0
1
0
1
0
1
2
0
1
0
1
2
1
2
3
0
1
1
2
2
3
3
4
0
1
0
1
0
1
2
0
1
0
1
2
0
1
2
3

´
CATOLICA-LISBON

F (x)
0.500000
1.000000
0.666667
1.000000
0.333333
1.000000
0.666667
1.000000
0.750000
1.000000
0.500000
1.000000
0.166667
0.833333
1.000000
0.250000
1.000000
0.500000
1.000000
0.750000
1.000000
0.800000
1.000000
0.600000
1.000000
0.300000
0.900000
1.000000
0.400000
1.000000
0.100000
0.700000
1.000000
0.300000
0.900000
1.000000
0.200000
1.000000
0.400000
1.000000
0.600000
1.000000
0.800000
1.000000
0.833333
1.000000
0.666667
1.000000
0.400000
0.933333
1.000000
0.500000
1.000000
0.200000
0.800000
1.000000
0.050000
0.500000
0.950000
1.000000

f (x)
0.500000
0.500000
0.666667
0.333333
0.333333
0.666667
0.666667
0.333333
0.750000
0.250000
0.500000
0.500000
0.166667
0.666667
0.166667
0.250000
0.750000
0.500000
0.500000
0.750000
0.250000
0.800000
0.200000
0.600000
0.400000
0.300000
0.600000
0.100000
0.400000
0.600000
0.100000
0.600000
0.300000
0.300000
0.600000
0.100000
0.200000
0.800000
0.400000
0.600000
0.600000
0.400000
0.800000
0.200000
0.833333
0.166667
0.666667
0.333333
0.400000
0.533333
0.066667
0.500000
0.500000
0.200000
0.600000
0.200000
0.050000
0.450000
0.450000
0.050000

N
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7

n N1
4 1
4 1
4 2
4 2
4 2
4 3
4 3
4 3
4 4
4 4
4 4
5 1
5 1
5 2
5 2
5 3
5 3
5 4
5 4
5 5
5 5
1 1
1 1
2 1
2 1
2 2
2 2
2 2
3 1
3 1
3 2
3 2
3 2
3 3
3 3
3 3
3 3
4 1
4 1
4 2
4 2
4 2
4 3
4 3
4 3
4 3
4 4
4 4
4 4
4 4
5 1
5 1
5 2
5 2
5 2
5 3
5 3
5 3
5 4
5 4

x
0
1
0
1
2
1
2
3
2
3
4
0
1
1
2
2
3
3
4
4
5
0
1
0
1
0
1
2
0
1
0
1
2
0
1
2
3
0
1
0
1
2
0
1
2
3
1
2
3
4
0
1
0
1
2
1
2
3
2
3

F (x)
0.333333
1.000000
0.066667
0.600000
1.000000
0.200000
0.800000
1.000000
0.400000
0.933333
1.000000
0.166667
1.000000
0.333333
1.000000
0.500000
1.000000
0.666667
1.000000
0.833333
1.000000
0.857143
1.000000
0.714286
1.000000
0.476190
0.952381
1.000000
0.571429
1.000000
0.285714
0.857143
1.000000
0.114286
0.628571
0.971429
1.000000
0.428571
1.000000
0.142857
0.714286
1.000000
0.028571
0.371429
0.885714
1.000000
0.114286
0.628571
0.971429
1.000000
0.285714
1.000000
0.047619
0.523810
1.000000
0.142857
0.714286
1.000000
0.285714
0.857143

with p = N1 /N

f (x)
0.333333
0.666667
0.066667
0.533333
0.400000
0.200000
0.600000
0.200000
0.400000
0.533333
0.066667
0.166667
0.833333
0.333333
0.666667
0.500000
0.500000
0.666667
0.333333
0.833333
0.166667
0.857143
0.142857
0.714286
0.285714
0.476190
0.476190
0.047619
0.571429
0.428571
0.285714
0.571429
0.142857
0.114286
0.514286
0.342857
0.028571
0.428571
0.571429
0.142857
0.571429
0.285714
0.028571
0.342857
0.514286
0.114286
0.114286
0.514286
0.342857
0.028571
0.285714
0.714286
0.047619
0.476190
0.476190
0.142857
0.571429
0.285714
0.285714
0.571429

N
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8

n N1
5 4
5 5
5 5
5 5
6 1
6 1
6 2
6 2
6 3
6 3
6 4
6 4
6 5
6 5
6 6
6 6
1 1
1 1
2 1
2 1
2 2
2 2
2 2
3 1
3 1
3 2
3 2
3 2
3 3
3 3
3 3
3 3
4 1
4 1
4 2
4 2
4 2
4 3
4 3
4 3
4 3
4 4
4 4
4 4
4 4
4 4
5 1
5 1
5 2
5 2
5 2
5 3
5 3
5 3
5 3
5 4
5 4
5 4
5 4
5 5

x
4
3
4
5
0
1
1
2
2
3
3
4
4
5
5
6
0
1
0
1
0
1
2
0
1
0
1
2
0
1
2
3
0
1
0
1
2
0
1
2
3
0
1
2
3
4
0
1
0
1
2
0
1
2
3
1
2
3
4
2

F (x)
1.000000
0.476190
0.952381
1.000000
0.142857
1.000000
0.285714
1.000000
0.428571
1.000000
0.571429
1.000000
0.714286
1.000000
0.857143
1.000000
0.875000
1.000000
0.750000
1.000000
0.535714
0.964286
1.000000
0.625000
1.000000
0.357143
0.892857
1.000000
0.178571
0.714286
0.982143
1.000000
0.500000
1.000000
0.214286
0.785714
1.000000
0.071429
0.500000
0.928571
1.000000
0.014286
0.242857
0.757143
0.985714
1.000000
0.375000
1.000000
0.107143
0.642857
1.000000
0.017857
0.285714
0.821429
1.000000
0.071429
0.500000
0.928571
1.000000
0.178571

f (x)
0.142857
0.476190
0.476190
0.047619
0.142857
0.857143
0.285714
0.714286
0.428571
0.571429
0.571429
0.428571
0.714286
0.285714
0.857143
0.142857
0.875000
0.125000
0.750000
0.250000
0.535714
0.428571
0.035714
0.625000
0.375000
0.357143
0.535714
0.107143
0.178571
0.535714
0.267857
0.017857
0.500000
0.500000
0.214286
0.571429
0.214286
0.071429
0.428571
0.428571
0.071429
0.014286
0.228571
0.514286
0.228571
0.014286
0.375000
0.625000
0.107143
0.535714
0.357143
0.017857
0.267857
0.535714
0.178571
0.071429
0.428571
0.428571
0.071429
0.178571

Statistical Tables

Hypergeometric Distribution

N
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9

n N1
5 5
5 5
5 5
6 1
6 1
6 2
6 2
6 2
6 3
6 3
6 3
6 4
6 4
6 4
6 5
6 5
6 5
6 6
6 6
6 6
7 1
7 1
7 2
7 2
7 3
7 3
7 4
7 4
7 5
7 5
7 6
7 6
7 7
7 7
1 1
1 1
2 1
2 1
2 2
2 2
2 2
3 1
3 1
3 2
3 2
3 2
3 3
3 3
3 3
3 3
4 1
4 1
4 2
4 2
4 2
4 3
4 3
4 3
4 3
4 4
4 4
4 4
4 4
4 4
5 1
5 1
5 2

x
3
4
5
0
1
0
1
2
1
2
3
2
3
4
3
4
5
4
5
6
0
1
1
2
2
3
3
4
4
5
5
6
6
7
0
1
0
1
0
1
2
0
1
0
1
2
0
1
2
3
0
1
0
1
2
0
1
2
3
0
1
2
3
4
0
1
0

F (x)
0.714286
0.982143
1.000000
0.250000
1.000000
0.035714
0.464286
1.000000
0.107143
0.642857
1.000000
0.214286
0.785714
1.000000
0.357143
0.892857
1.000000
0.535714
0.964286
1.000000
0.125000
1.000000
0.250000
1.000000
0.375000
1.000000
0.500000
1.000000
0.625000
1.000000
0.750000
1.000000
0.875000
1.000000
0.888889
1.000000
0.777778
1.000000
0.583333
0.972222
1.000000
0.666667
1.000000
0.416667
0.916667
1.000000
0.238095
0.773810
0.988095
1.000000
0.555556
1.000000
0.277778
0.833333
1.000000
0.119048
0.595238
0.952381
1.000000
0.039683
0.357143
0.833333
0.992063
1.000000
0.444444
1.000000
0.166667

´
CATOLICA-LISBON

20

f (x)
0.535714
0.267857
0.017857
0.250000
0.750000
0.035714
0.428571
0.535714
0.107143
0.535714
0.357143
0.214286
0.571429
0.214286
0.357143
0.535714
0.107143
0.535714
0.428571
0.035714
0.125000
0.875000
0.250000
0.750000
0.375000
0.625000
0.500000
0.500000
0.625000
0.375000
0.750000
0.250000
0.875000
0.125000
0.888889
0.111111
0.777778
0.222222
0.583333
0.388889
0.027778
0.666667
0.333333
0.416667
0.500000
0.083333
0.238095
0.535714
0.214286
0.011905
0.555556
0.444444
0.277778
0.555556
0.166667
0.119048
0.476190
0.357143
0.047619
0.039683
0.317460
0.476190
0.158730
0.007937
0.444444
0.555556
0.166667

N
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9

n N1
5 2
5 2
5 3
5 3
5 3
5 3
5 4
5 4
5 4
5 4
5 4
5 5
5 5
5 5
5 5
5 5
6 1
6 1
6 2
6 2
6 2
6 3
6 3
6 3
6 3
6 4
6 4
6 4
6 4
6 5
6 5
6 5
6 5
6 6
6 6
6 6
6 6
7 1
7 1
7 2
7 2
7 2
7 3
7 3
7 3
7 4
7 4
7 4
7 5
7 5
7 5
7 6
7 6
7 6
7 7
7 7
7 7
8 1
8 1
8 2
8 2
8 3
8 3
8 4
8 4
8 5
8 5

x
1
2
0
1
2
3
0
1
2
3
4
1
2
3
4
5
0
1
0
1
2
0
1
2
3
1
2
3
4
2
3
4
5
3
4
5
6
0
1
0
1
2
1
2
3
2
3
4
3
4
5
4
5
6
5
6
7
0
1
1
2
2
3
3
4
4
5

F (x)
0.722222
1.000000
0.047619
0.404762
0.880952
1.000000
0.007937
0.166667
0.642857
0.960317
1.000000
0.039683
0.357143
0.833333
0.992063
1.000000
0.333333
1.000000
0.083333
0.583333
1.000000
0.011905
0.226190
0.761905
1.000000
0.047619
0.404762
0.880952
1.000000
0.119048
0.595238
0.952381
1.000000
0.238095
0.773810
0.988095
1.000000
0.222222
1.000000
0.027778
0.416667
1.000000
0.083333
0.583333
1.000000
0.166667
0.722222
1.000000
0.277778
0.833333
1.000000
0.416667
0.916667
1.000000
0.583333
0.972222
1.000000
0.111111
1.000000
0.222222
1.000000
0.333333
1.000000
0.444444
1.000000
0.555556
1.000000

f (x)
0.555556
0.277778
0.047619
0.357143
0.476190
0.119048
0.007937
0.158730
0.476190
0.317460
0.039683
0.039683
0.317460
0.476190
0.158730
0.007937
0.333333
0.666667
0.083333
0.500000
0.416667
0.011905
0.214286
0.535714
0.238095
0.047619
0.357143
0.476190
0.119048
0.119048
0.476190
0.357143
0.047619
0.238095
0.535714
0.214286
0.011905
0.222222
0.777778
0.027778
0.388889
0.583333
0.083333
0.500000
0.416667
0.166667
0.555556
0.277778
0.277778
0.555556
0.166667
0.416667
0.500000
0.083333
0.583333
0.388889
0.027778
0.111111
0.888889
0.222222
0.777778
0.333333
0.666667
0.444444
0.555556
0.555556
0.444444

N
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10

n N1
8 6
8 6
8 7
8 7
8 8
8 8
1 1
1 1
2 1
2 1
2 2
2 2
2 2
3 1
3 1
3 2
3 2
3 2
3 3
3 3
3 3
3 3
4 1
4 1
4 2
4 2
4 2
4 3
4 3
4 3
4 3
4 4
4 4
4 4
4 4
4 4
5 1
5 1
5 2
5 2
5 2
5 3
5 3
5 3
5 3
5 4
5 4
5 4
5 4
5 4
5 5
5 5
5 5
5 5
5 5
5 5
6 1
6 1
6 2
6 2
6 2
6 3
6 3
6 3
6 3
6 4
6 4

x
5
6
6
7
7
8
0
1
0
1
0
1
2
0
1
0
1
2
0
1
2
3
0
1
0
1
2
0
1
2
3
0
1
2
3
4
0
1
0
1
2
0
1
2
3
0
1
2
3
4
0
1
2
3
4
5
0
1
0
1
2
0
1
2
3
0
1

F (x)
0.666667
1.000000
0.777778
1.000000
0.888889
1.000000
0.900000
1.000000
0.800000
1.000000
0.622222
0.977778
1.000000
0.700000
1.000000
0.466667
0.933333
1.000000
0.291667
0.816667
0.991667
1.000000
0.600000
1.000000
0.333333
0.866667
1.000000
0.166667
0.666667
0.966667
1.000000
0.071429
0.452381
0.880952
0.995238
1.000000
0.500000
1.000000
0.222222
0.777778
1.000000
0.083333
0.500000
0.916667
1.000000
0.023810
0.261905
0.738095
0.976190
1.000000
0.003968
0.103175
0.500000
0.896825
0.996032
1.000000
0.400000
1.000000
0.133333
0.666667
1.000000
0.033333
0.333333
0.833333
1.000000
0.004762
0.119048

f (x)
0.666667
0.333333
0.777778
0.222222
0.888889
0.111111
0.900000
0.100000
0.800000
0.200000
0.622222
0.355556
0.022222
0.700000
0.300000
0.466667
0.466667
0.066667
0.291667
0.525000
0.175000
0.008333
0.600000
0.400000
0.333333
0.533333
0.133333
0.166667
0.500000
0.300000
0.033333
0.071429
0.380952
0.428571
0.114286
0.004762
0.500000
0.500000
0.222222
0.555556
0.222222
0.083333
0.416667
0.416667
0.083333
0.023810
0.238095
0.476190
0.238095
0.023810
0.003968
0.099206
0.396825
0.396825
0.099206
0.003968
0.400000
0.600000
0.133333
0.533333
0.333333
0.033333
0.300000
0.500000
0.166667
0.004762
0.114286

Statistical Tables

Hypergeometric Distribution

N
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10

n N1
6 4
6 4
6 4
6 5
6 5
6 5
6 5
6 5
6 6
6 6
6 6
6 6
6 6
7 1
7 1
7 2
7 2
7 2
7 3
7 3
7 3
7 3
7 4
7 4
7 4
7 4
7 5

x
2
3
4
1
2
3
4
5
2
3
4
5
6
0
1
0
1
2
0
1
2
3
1
2
3
4
2

F (x)
0.547619
0.928571
1.000000
0.023810
0.261905
0.738095
0.976190
1.000000
0.071429
0.452381
0.880952
0.995238
1.000000
0.300000
1.000000
0.066667
0.533333
1.000000
0.008333
0.183333
0.708333
1.000000
0.033333
0.333333
0.833333
1.000000
0.083333

´
CATOLICA-LISBON

21

f (x)
0.428571
0.380952
0.071429
0.023810
0.238095
0.476190
0.238095
0.023810
0.071429
0.380952
0.428571
0.114286
0.004762
0.300000
0.700000
0.066667
0.466667
0.466667
0.008333
0.175000
0.525000
0.291667
0.033333
0.300000
0.500000
0.166667
0.083333

N
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10

n N1
7 5
7 5
7 5
7 6
7 6
7 6
7 6
7 7
7 7
7 7
7 7
8 1
8 1
8 2
8 2
8 2
8 3
8 3
8 3
8 4
8 4
8 4
8 5
8 5
8 5
8 6
8 6

x
3
4
5
3
4
5
6
4
5
6
7
0
1
0
1
2
1
2
3
2
3
4
3
4
5
4
5

F (x)
0.500000
0.916667
1.000000
0.166667
0.666667
0.966667
1.000000
0.291667
0.816667
0.991667
1.000000
0.200000
1.000000
0.022222
0.377778
1.000000
0.066667
0.533333
1.000000
0.133333
0.666667
1.000000
0.222222
0.777778
1.000000
0.333333
0.866667

f (x)
0.416667
0.416667
0.083333
0.166667
0.500000
0.300000
0.033333
0.291667
0.525000
0.175000
0.008333
0.200000
0.800000
0.022222
0.355556
0.622222
0.066667
0.466667
0.466667
0.133333
0.533333
0.333333
0.222222
0.555556
0.222222
0.333333
0.533333

N
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10

n N1
8 6
8 7
8 7
8 7
8 8
8 8
8 8
9 1
9 1
9 2
9 2
9 3
9 3
9 4
9 4
9 5
9 5
9 6
9 6
9 7
9 7
9 8
9 8
9 9
9 9

x
6
5
6
7
6
7
8
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9

F (x)
1.000000
0.466667
0.933333
1.000000
0.622222
0.977778
1.000000
0.100000
1.000000
0.200000
1.000000
0.300000
1.000000
0.400000
1.000000
0.500000
1.000000
0.600000
1.000000
0.700000
1.000000
0.800000
1.000000
0.900000
1.000000

f (x)
0.133333
0.466667
0.466667
0.066667
0.622222
0.355556
0.022222
0.100000
0.900000
0.200000
0.800000
0.300000
0.700000
0.400000
0.600000
0.500000
0.500000
0.600000
0.400000
0.700000
0.300000
0.800000
0.200000
0.900000
0.100000

Statistical Tables

Poisson Distribution – probability function

22

Poisson Distribution – f(x) f (x; λ) = f (x) x 0
1
2
3
4

e−λ λx x! λ

0.1
0.9048
0.0905
0.0045
0.0002
0.0000

0.2
0.8187
0.1637
0.0164
0.0011
0.0001

0.3
0.7408
0.2222
0.0333
0.0033
0.0003

0.4
0.6703
0.2681
0.0536
0.0072
0.0007

0.5
0.6065
0.3033
0.0758
0.0126
0.0016

0.6
0.5488
0.3293
0.0988
0.0198
0.0030

0.7
0.4966
0.3476
0.1217
0.0284
0.0050

0.8
0.4493
0.3595
0.1438
0.0383
0.0077

0.9
0.4066
0.3659
0.1647
0.0494
0.0111

1.0
0.3679
0.3679
0.1839
0.0613
0.0153

0.0000
0.0000
0.0000

0.0000
0.0000
0.0000

0.0000
0.0000
0.0000

0.0001
0.0000
0.0000

0.0002
0.0000
0.0000

0.0004
0.0000
0.0000

0.0007
0.0001
0.0000

0.0012
0.0002
0.0000

0.0020
0.0003
0.0000

0.0031
0.0005
0.0001

1.1
0.3329
0.3662
0.2014
0.0738
0.0203

1.2
0.3012
0.3614
0.2169
0.0867
0.0260

1.3
0.2725
0.3543
0.2303
0.0998
0.0324

1.4
0.2466
0.3452
0.2417
0.1128
0.0395

1.5
0.2231
0.3347
0.2510
0.1255
0.0471

1.6
0.2019
0.3230
0.2584
0.1378
0.0551

1.7
0.1827
0.3106
0.2640
0.1496
0.0636

1.8
0.1653
0.2975
0.2678
0.1607
0.0723

1.9
0.1496
0.2842
0.2700
0.1710
0.0812

2.0
0.1353
0.2707
0.2707
0.1804
0.0902

0.0045
0.0008
0.0001
0.0000
0.0000

0.0062
0.0012
0.0002
0.0000
0.0000

0.0084
0.0018
0.0003
0.0001
0.0000

0.0111
0.0026
0.0005
0.0001
0.0000

0.0141
0.0035
0.0008
0.0001
0.0000

0.0176
0.0047
0.0011
0.0002
0.0000

0.0216
0.0061
0.0015
0.0003
0.0001

0.0260
0.0078
0.0020
0.0005
0.0001

0.0309
0.0098
0.0027
0.0006
0.0001

0.0361
0.0120
0.0034
0.0009
0.0002

2.1
0.1225
0.2572
0.2700
0.1890
0.0992

2.2
0.1108
0.2438
0.2681
0.1966
0.1082

2.3
0.1003
0.2306
0.2652
0.2033
0.1169

2.4
0.0907
0.2177
0.2613
0.2090
0.1254

2.5
0.0821
0.2052
0.2565
0.2138
0.1336

2.6
0.0743
0.1931
0.2510
0.2176
0.1414

2.7
0.0672
0.1815
0.2450
0.2205
0.1488

2.8
0.0608
0.1703
0.2384
0.2225
0.1557

2.9
0.0550
0.1596
0.2314
0.2237
0.1622

3.0
0.0498
0.1494
0.2240
0.2240
0.1680

5
6
7
8
9

0.0417
0.0146
0.0044
0.0011
0.0003

0.0476
0.0174
0.0055
0.0015
0.0004

0.0538
0.0206
0.0068
0.0019
0.0005

0.0602
0.0241
0.0083
0.0025
0.0007

0.0668
0.0278
0.0099
0.0031
0.0009

0.0735
0.0319
0.0118
0.0038
0.0011

0.0804
0.0362
0.0139
0.0047
0.0014

0.0872
0.0407
0.0163
0.0057
0.0018

0.0940
0.0455
0.0188
0.0068
0.0022

0.1008
0.0504
0.0216
0.0081
0.0027

10
11
12

0.0001
0.0000
0.0000

0.0001
0.0000
0.0000

0.0001
0.0000
0.0000

0.0002
0.0000
0.0000

0.0002
0.0000
0.0000

0.0003
0.0001
0.0000

0.0004
0.0001
0.0000

0.0005
0.0001
0.0000

0.0006
0.0002
0.0000

0.0008
0.0002
0.0001

f (x) x 0
1
2
3
4

3.1
0.0450
0.1397
0.2165
0.2237
0.1733

3.2
0.0408
0.1304
0.2087
0.2226
0.1781

3.3
0.0369
0.1217
0.2008
0.2209
0.1823

3.4
0.0334
0.1135
0.1929
0.2186
0.1858

3.5
0.0302
0.1057
0.1850
0.2158
0.1888

3.6
0.0273
0.0984
0.1771
0.2125
0.1912

3.7
0.0247
0.0915
0.1692
0.2087
0.1931

3.8
0.0224
0.0850
0.1615
0.2046
0.1944

3.9
0.0202
0.0789
0.1539
0.2001
0.1951

4.0
0.0183
0.0733
0.1465
0.1954
0.1954

5
6
7
8
9

0.1075
0.0555
0.0246
0.0095
0.0033

0.1140
0.0608
0.0278
0.0111
0.0040

0.1203
0.0662
0.0312
0.0129
0.0047

0.1264
0.0716
0.0348
0.0148
0.0056

0.1322
0.0771
0.0385
0.0169
0.0066

0.1377
0.0826
0.0425
0.0191
0.0076

0.1429
0.0881
0.0466
0.0215
0.0089

0.1477
0.0936
0.0508
0.0241
0.0102

0.1522
0.0989
0.0551
0.0269
0.0116

0.1563
0.1042
0.0595
0.0298
0.0132

10
11
12
13
14

0.0010
0.0003
0.0001
0.0000
0.0000

0.0013
0.0004
0.0001
0.0000
0.0000

0.0016
0.0005
0.0001
0.0000
0.0000

0.0019
0.0006
0.0002
0.0000
0.0000

0.0023
0.0007
0.0002
0.0001
0.0000

0.0028
0.0009
0.0003
0.0001
0.0000

0.0033
0.0011
0.0003
0.0001
0.0000

0.0039
0.0013
0.0004
0.0001
0.0000

0.0045
0.0016
0.0005
0.0002
0.0000

0.0053
0.0019
0.0006
0.0002
0.0001

5
6
7 f (x) x 0
1
2
3
4
5
6
7
8
9
f (x) x 0
1
2
3
4

´
CATOLICA-LISBON

λ

λ

λ

Statistical Tables

Poisson Distribution – probability function

f (x) x 0
1
2
3
4

23

λ
4.1
0.0166
0.0679
0.1393
0.1904
0.1951

4.2
0.0150
0.0630
0.1323
0.1852
0.1944

4.3
0.0136
0.0583
0.1254
0.1798
0.1933

4.4
0.0123
0.0540
0.1188
0.1743
0.1917

4.5
0.0111
0.0500
0.1125
0.1687
0.1898

4.6
0.0101
0.0462
0.1063
0.1631
0.1875

4.7
0.0091
0.0427
0.1005
0.1574
0.1849

4.8
0.0082
0.0395
0.0948
0.1517
0.1820

4.9
0.0074
0.0365
0.0894
0.1460
0.1789

5.0
0.0067
0.0337
0.0842
0.1404
0.1755

5
6
7
8
9

0.1600
0.1093
0.0640
0.0328
0.0150

0.1633
0.1143
0.0686
0.0360
0.0168

0.1662
0.1191
0.0732
0.0393
0.0188

0.1687
0.1237
0.0778
0.0428
0.0209

0.1708
0.1281
0.0824
0.0463
0.0232

0.1725
0.1323
0.0869
0.0500
0.0255

0.1738
0.1362
0.0914
0.0537
0.0281

0.1747
0.1398
0.0959
0.0575
0.0307

0.1753
0.1432
0.1002
0.0614
0.0334

0.1755
0.1462
0.1044
0.0653
0.0363

10
11
12
13
14

0.0061
0.0023
0.0008
0.0002
0.0001

0.0071
0.0027
0.0009
0.0003
0.0001

0.0081
0.0032
0.0011
0.0004
0.0001

0.0092
0.0037
0.0013
0.0005
0.0001

0.0104
0.0043
0.0016
0.0006
0.0002

0.0118
0.0049
0.0019
0.0007
0.0002

0.0132
0.0056
0.0022
0.0008
0.0003

0.0147
0.0064
0.0026
0.0009
0.0003

0.0164
0.0073
0.0030
0.0011
0.0004

0.0181
0.0082
0.0034
0.0013
0.0005

15

0.0000

0.0000

0.0000

0.0000

0.0001

0.0001

0.0001

0.0001

0.0001

0.0002

f (x) x 0
1
2
3
4

5.1
0.0061
0.0311
0.0793
0.1348
0.1719

5.2
0.0055
0.0287
0.0746
0.1293
0.1681

5.3
0.0050
0.0265
0.0701
0.1239
0.1641

5.4
0.0045
0.0244
0.0659
0.1185
0.1600

5.5
0.0041
0.0225
0.0618
0.1133
0.1558

5.6
0.0037
0.0207
0.0580
0.1082
0.1515

5.7
0.0033
0.0191
0.0544
0.1033
0.1472

5.8
0.0030
0.0176
0.0509
0.0985
0.1428

5.9
0.0027
0.0162
0.0477
0.0938
0.1383

6.0
0.0025
0.0149
0.0446
0.0892
0.1339

5
6
7
8
9

0.1753
0.1490
0.1086
0.0692
0.0392

0.1748
0.1515
0.1125
0.0731
0.0423

0.1740
0.1537
0.1163
0.0771
0.0454

0.1728
0.1555
0.1200
0.0810
0.0486

0.1714
0.1571
0.1234
0.0849
0.0519

0.1697
0.1584
0.1267
0.0887
0.0552

0.1678
0.1594
0.1298
0.0925
0.0586

0.1656
0.1601
0.1326
0.0962
0.0620

0.1632
0.1605
0.1353
0.0998
0.0654

0.1606
0.1606
0.1377
0.1033
0.0688

10
11
12
13
14

0.0200
0.0093
0.0039
0.0015
0.0006

0.0220
0.0104
0.0045
0.0018
0.0007

0.0241
0.0116
0.0051
0.0021
0.0008

0.0262
0.0129
0.0058
0.0024
0.0009

0.0285
0.0143
0.0065
0.0028
0.0011

0.0309
0.0157
0.0073
0.0032
0.0013

0.0334
0.0173
0.0082
0.0036
0.0015

0.0359
0.0190
0.0092
0.0041
0.0017

0.0386
0.0207
0.0102
0.0046
0.0019

0.0413
0.0225
0.0113
0.0052
0.0022

15
16
17

0.0002
0.0001
0.0000

0.0002
0.0001
0.0000

0.0003
0.0001
0.0000

0.0003
0.0001
0.0000

0.0004
0.0001
0.0000

0.0005
0.0002
0.0001

0.0006
0.0002
0.0001

0.0007
0.0002
0.0001

0.0008
0.0003
0.0001

0.0009
0.0003
0.0001

f (x) x 0
1
2
3
4

6.1
0.0022
0.0137
0.0417
0.0848
0.1294

6.2
0.0020
0.0126
0.0390
0.0806
0.1249

6.3
0.0018
0.0116
0.0364
0.0765
0.1205

6.4
0.0017
0.0106
0.0340
0.0726
0.1162

6.5
0.0015
0.0098
0.0318
0.0688
0.1118

6.6
0.0014
0.0090
0.0296
0.0652
0.1076

6.7
0.0012
0.0082
0.0276
0.0617
0.1034

6.8
0.0011
0.0076
0.0258
0.0584
0.0992

6.9
0.0010
0.0070
0.0240
0.0552
0.0952

7.0
0.0009
0.0064
0.0223
0.0521
0.0912

5
6
7
8
9

0.1579
0.1605
0.1399
0.1066
0.0723

0.1549
0.1601
0.1418
0.1099
0.0757

0.1519
0.1595
0.1435
0.1130
0.0791

0.1487
0.1586
0.1450
0.1160
0.0825

0.1454
0.1575
0.1462
0.1188
0.0858

0.1420
0.1562
0.1472
0.1215
0.0891

0.1385
0.1546
0.1480
0.1240
0.0923

0.1349
0.1529
0.1486
0.1263
0.0954

0.1314
0.1511
0.1489
0.1284
0.0985

0.1277
0.1490
0.1490
0.1304
0.1014

10
11
12
13
14

0.0441
0.0244
0.0124
0.0058
0.0025

0.0469
0.0265
0.0137
0.0065
0.0029

0.0498
0.0285
0.0150
0.0073
0.0033

0.0528
0.0307
0.0164
0.0081
0.0037

0.0558
0.0330
0.0179
0.0089
0.0041

0.0588
0.0353
0.0194
0.0099
0.0046

0.0618
0.0377
0.0210
0.0108
0.0052

0.0649
0.0401
0.0227
0.0119
0.0058

0.0679
0.0426
0.0245
0.0130
0.0064

0.0710
0.0452
0.0263
0.0142
0.0071

15
16
17
18
19

0.0010
0.0004
0.0001
0.0000
0.0000

0.0012
0.0005
0.0002
0.0001
0.0000

0.0014
0.0005
0.0002
0.0001
0.0000

0.0016
0.0006
0.0002
0.0001
0.0000

0.0018
0.0007
0.0003
0.0001
0.0000

0.0020
0.0008
0.0003
0.0001
0.0000

0.0023
0.0010
0.0004
0.0001
0.0001

0.0026
0.0011
0.0004
0.0002
0.0001

0.0029
0.0013
0.0005
0.0002
0.0001

0.0033
0.0014
0.0006
0.0002
0.0001

´
CATOLICA-LISBON

λ

λ

Statistical Tables

Poisson Distribution – probability function

f (x) x 0
1
2
3
4

24

λ
7.1
0.0008
0.0059
0.0208
0.0492
0.0874

7.2
0.0007
0.0054
0.0194
0.0464
0.0836

7.3
0.0007
0.0049
0.0180
0.0438
0.0799

7.4
0.0006
0.0045
0.0167
0.0413
0.0764

7.5
0.0006
0.0041
0.0156
0.0389
0.0729

7.6
0.0005
0.0038
0.0145
0.0366
0.0696

7.7
0.0005
0.0035
0.0134
0.0345
0.0663

7.8
0.0004
0.0032
0.0125
0.0324
0.0632

7.9
0.0004
0.0029
0.0116
0.0305
0.0602

8.0
0.0003
0.0027
0.0107
0.0286
0.0573

5
6
7
8
9

0.1241
0.1468
0.1489
0.1321
0.1042

0.1204
0.1445
0.1486
0.1337
0.1070

0.1167
0.1420
0.1481
0.1351
0.1096

0.1130
0.1394
0.1474
0.1363
0.1121

0.1094
0.1367
0.1465
0.1373
0.1144

0.1057
0.1339
0.1454
0.1381
0.1167

0.1021
0.1311
0.1442
0.1388
0.1187

0.0986
0.1282
0.1428
0.1392
0.1207

0.0951
0.1252
0.1413
0.1395
0.1224

0.0916
0.1221
0.1396
0.1396
0.1241

10
11
12
13
14

0.0740
0.0478
0.0283
0.0154
0.0078

0.0770
0.0504
0.0303
0.0168
0.0086

0.0800
0.0531
0.0323
0.0181
0.0095

0.0829
0.0558
0.0344
0.0196
0.0104

0.0858
0.0585
0.0366
0.0211
0.0113

0.0887
0.0613
0.0388
0.0227
0.0123

0.0914
0.0640
0.0411
0.0243
0.0134

0.0941
0.0667
0.0434
0.0260
0.0145

0.0967
0.0695
0.0457
0.0278
0.0157

0.0993
0.0722
0.0481
0.0296
0.0169

15
16
17
18
19

0.0037
0.0016
0.0007
0.0003
0.0001

0.0041
0.0019
0.0008
0.0003
0.0001

0.0046
0.0021
0.0009
0.0004
0.0001

0.0051
0.0024
0.0010
0.0004
0.0002

0.0057
0.0026
0.0012
0.0005
0.0002

0.0062
0.0030
0.0013
0.0006
0.0002

0.0069
0.0033
0.0015
0.0006
0.0003

0.0075
0.0037
0.0017
0.0007
0.0003

0.0083
0.0041
0.0019
0.0008
0.0003

0.0090
0.0045
0.0021
0.0009
0.0004

20
21

0.0000
0.0000

0.0000
0.0000

0.0001
0.0000

0.0001
0.0000

0.0001
0.0000

0.0001
0.0000

0.0001
0.0000

0.0001
0.0000

0.0001
0.0001

0.0002
0.0001

f (x) x 0
1
2
3
4

8.1
0.0003
0.0025
0.0100
0.0269
0.0544

8.2
0.0003
0.0023
0.0092
0.0252
0.0517

8.3
0.0002
0.0021
0.0086
0.0237
0.0491

8.4
0.0002
0.0019
0.0079
0.0222
0.0466

8.5
0.0002
0.0017
0.0074
0.0208
0.0443

8.6
0.0002
0.0016
0.0068
0.0195
0.0420

8.7
0.0002
0.0014
0.0063
0.0183
0.0398

8.8
0.0002
0.0013
0.0058
0.0171
0.0377

8.9
0.0001
0.0012
0.0054
0.0160
0.0357

9.0
0.0001
0.0011
0.0050
0.0150
0.0337

5
6
7
8
9

0.0882
0.1191
0.1378
0.1395
0.1256

0.0849
0.1160
0.1358
0.1392
0.1269

0.0816
0.1128
0.1338
0.1388
0.1280

0.0784
0.1097
0.1317
0.1382
0.1290

0.0752
0.1066
0.1294
0.1375
0.1299

0.0722
0.1034
0.1271
0.1366
0.1306

0.0692
0.1003
0.1247
0.1356
0.1311

0.0663
0.0972
0.1222
0.1344
0.1315

0.0635
0.0941
0.1197
0.1332
0.1317

0.0607
0.0911
0.1171
0.1318
0.1318

10
11
12
13
14

0.1017
0.0749
0.0505
0.0315
0.0182

0.1040
0.0776
0.0530
0.0334
0.0196

0.1063
0.0802
0.0555
0.0354
0.0210

0.1084
0.0828
0.0579
0.0374
0.0225

0.1104
0.0853
0.0604
0.0395
0.0240

0.1123
0.0878
0.0629
0.0416
0.0256

0.1140
0.0902
0.0654
0.0438
0.0272

0.1157
0.0925
0.0679
0.0459
0.0289

0.1172
0.0948
0.0703
0.0481
0.0306

0.1186
0.0970
0.0728
0.0504
0.0324

15
16
17
18
19

0.0098
0.0050
0.0024
0.0011
0.0005

0.0107
0.0055
0.0026
0.0012
0.0005

0.0116
0.0060
0.0029
0.0014
0.0006

0.0126
0.0066
0.0033
0.0015
0.0007

0.0136
0.0072
0.0036
0.0017
0.0008

0.0147
0.0079
0.0040
0.0019
0.0009

0.0158
0.0086
0.0044
0.0021
0.0010

0.0169
0.0093
0.0048
0.0024
0.0011

0.0182
0.0101
0.0053
0.0026
0.0012

0.0194
0.0109
0.0058
0.0029
0.0014

20
21
22

0.0002
0.0001
0.0000

0.0002
0.0001
0.0000

0.0002
0.0001
0.0000

0.0003
0.0001
0.0000

0.0003
0.0001
0.0001

0.0004
0.0002
0.0001

0.0004
0.0002
0.0001

0.0005
0.0002
0.0001

0.0005
0.0002
0.0001

0.0006
0.0003
0.0001

´
CATOLICA-LISBON

λ

Statistical Tables

Poisson Distribution – probability function

f (x) x 0
1
2
3
4

25

λ
9.1
0.0001
0.0010
0.0046
0.0140
0.0319

9.2
0.0001
0.0009
0.0043
0.0131
0.0302

9.3
0.0001
0.0009
0.0040
0.0123
0.0285

9.4
0.0001
0.0008
0.0037
0.0115
0.0269

9.5
0.0001
0.0007
0.0034
0.0107
0.0254

9.6
0.0001
0.0007
0.0031
0.0100
0.0240

9.7
0.0001
0.0006
0.0029
0.0093
0.0226

9.8
0.0001
0.0005
0.0027
0.0087
0.0213

9.9
0.0001
0.0005
0.0025
0.0081
0.0201

10
0.0000
0.0005
0.0023
0.0076
0.0189

5
6
7
8
9

0.0581
0.0881
0.1145
0.1302
0.1317

0.0555
0.0851
0.1118
0.1286
0.1315

0.0530
0.0822
0.1091
0.1269
0.1311

0.0506
0.0793
0.1064
0.1251
0.1306

0.0483
0.0764
0.1037
0.1232
0.1300

0.0460
0.0736
0.1010
0.1212
0.1293

0.0439
0.0709
0.0982
0.1191
0.1284

0.0418
0.0682
0.0955
0.1170
0.1274

0.0398
0.0656
0.0928
0.1148
0.1263

0.0378
0.0631
0.0901
0.1126
0.1251

10
11
12
13
14

0.1198
0.0991
0.0752
0.0526
0.0342

0.1210
0.1012
0.0776
0.0549
0.0361

0.1219
0.1031
0.0799
0.0572
0.0380

0.1228
0.1049
0.0822
0.0594
0.0399

0.1235
0.1067
0.0844
0.0617
0.0419

0.1241
0.1083
0.0866
0.0640
0.0439

0.1245
0.1098
0.0888
0.0662
0.0459

0.1249
0.1112
0.0908
0.0685
0.0479

0.1250
0.1125
0.0928
0.0707
0.0500

0.1251
0.1137
0.0948
0.0729
0.0521

15
16
17
18
19

0.0208
0.0118
0.0063
0.0032
0.0015

0.0221
0.0127
0.0069
0.0035
0.0017

0.0235
0.0137
0.0075
0.0039
0.0019

0.0250
0.0147
0.0081
0.0042
0.0021

0.0265
0.0157
0.0088
0.0046
0.0023

0.0281
0.0168
0.0095
0.0051
0.0026

0.0297
0.0180
0.0103
0.0055
0.0028

0.0313
0.0192
0.0111
0.0060
0.0031

0.0330
0.0204
0.0119
0.0065
0.0034

0.0347
0.0217
0.0128
0.0071
0.0037

20
21
22
23
24

0.0007
0.0003
0.0001
0.0000
0.0000

0.0008
0.0003
0.0001
0.0001
0.0000

0.0009
0.0004
0.0002
0.0001
0.0000

0.0010
0.0004
0.0002
0.0001
0.0000

0.0011
0.0005
0.0002
0.0001
0.0000

0.0012
0.0006
0.0002
0.0001
0.0000

0.0014
0.0006
0.0003
0.0001
0.0000

0.0015
0.0007
0.0003
0.0001
0.0001

0.0017
0.0008
0.0004
0.0002
0.0001

0.0019
0.0009
0.0004
0.0002
0.0001

´
CATOLICA-LISBON

Statistical Tables

Poisson Distribution – probability function

f (x) x 0
1
2
3
4

26

λ
11
0.0000
0.0002
0.0010
0.0037
0.0102

12
0.0000
0.0001
0.0004
0.0018
0.0053

13
0.0000
0.0000
0.0002
0.0008
0.0027

14
0.0000
0.0000
0.0001
0.0004
0.0013

15
0.0000
0.0000
0.0000
0.0002
0.0006

16
0.0000
0.0000
0.0000
0.0001
0.0003

17
0.0000
0.0000
0.0000
0.0000
0.0001

18
0.0000
0.0000
0.0000
0.0000
0.0001

19
0.0000
0.0000
0.0000
0.0000
0.0000

20
0.0000
0.0000
0.0000
0.0000
0.0000

5
6
7
8
9

0.0224
0.0411
0.0646
0.0888
0.1085

0.0127
0.0255
0.0437
0.0655
0.0874

0.0070
0.0152
0.0281
0.0457
0.0661

0.0037
0.0087
0.0174
0.0304
0.0473

0.0019
0.0048
0.0104
0.0194
0.0324

0.0010
0.0026
0.0060
0.0120
0.0213

0.0005
0.0014
0.0034
0.0072
0.0135

0.0002
0.0007
0.0019
0.0042
0.0083

0.0001
0.0004
0.0010
0.0024
0.0050

0.0001
0.0002
0.0005
0.0013
0.0029

10
11
12
13
14

0.1194
0.1194
0.1094
0.0926
0.0728

0.1048
0.1144
0.1144
0.1056
0.0905

0.0859
0.1015
0.1099
0.1099
0.1021

0.0663
0.0844
0.0984
0.1060
0.1060

0.0486
0.0663
0.0829
0.0956
0.1024

0.0341
0.0496
0.0661
0.0814
0.0930

0.0230
0.0355
0.0504
0.0658
0.0800

0.0150
0.0245
0.0368
0.0509
0.0655

0.0095
0.0164
0.0259
0.0378
0.0514

0.0058
0.0106
0.0176
0.0271
0.0387

15
16
17
18
19

0.0534
0.0367
0.0237
0.0145
0.0084

0.0724
0.0543
0.0383
0.0255
0.0161

0.0885
0.0719
0.0550
0.0397
0.0272

0.0989
0.0866
0.0713
0.0554
0.0409

0.1024
0.0960
0.0847
0.0706
0.0557

0.0992
0.0992
0.0934
0.0830
0.0699

0.0906
0.0963
0.0963
0.0909
0.0814

0.0786
0.0884
0.0936
0.0936
0.0887

0.0650
0.0772
0.0863
0.0911
0.0911

0.0516
0.0646
0.0760
0.0844
0.0888

20
21
22
23
24

0.0046
0.0024
0.0012
0.0006
0.0003

0.0097
0.0055
0.0030
0.0016
0.0008

0.0177
0.0109
0.0065
0.0037
0.0020

0.0286
0.0191
0.0121
0.0074
0.0043

0.0418
0.0299
0.0204
0.0133
0.0083

0.0559
0.0426
0.0310
0.0216
0.0144

0.0692
0.0560
0.0433
0.0320
0.0226

0.0798
0.0684
0.0560
0.0438
0.0328

0.0866
0.0783
0.0676
0.0559
0.0442

0.0888
0.0846
0.0769
0.0669
0.0557

25
26
27
28
29

0.0001
0.0000
0.0000
0.0000
0.0000

0.0004
0.0002
0.0001
0.0000
0.0000

0.0010
0.0005
0.0002
0.0001
0.0001

0.0024
0.0013
0.0007
0.0003
0.0002

0.0050
0.0029
0.0016
0.0009
0.0004

0.0092
0.0057
0.0034
0.0019
0.0011

0.0154
0.0101
0.0063
0.0038
0.0023

0.0237
0.0164
0.0109
0.0070
0.0044

0.0336
0.0246
0.0173
0.0117
0.0077

0.0446
0.0343
0.0254
0.0181
0.0125

30
31
32
33
34

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0000
0.0000
0.0000
0.0000

0.0002
0.0001
0.0001
0.0000
0.0000

0.0006
0.0003
0.0001
0.0001
0.0000

0.0013
0.0007
0.0004
0.0002
0.0001

0.0026
0.0015
0.0009
0.0005
0.0002

0.0049
0.0030
0.0018
0.0010
0.0006

0.0083
0.0054
0.0034
0.0020
0.0012

35
36
37
38
39

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000

0.0001
0.0001
0.0000
0.0000
0.0000

0.0003
0.0002
0.0001
0.0000
0.0000

0.0007
0.0004
0.0002
0.0001
0.0001

40

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

´
CATOLICA-LISBON

Statistical Tables

Poisson Distribution – distribution function

27

Poisson Distribution – F(x)
F (x) x 0
1
2
3
4

λ
0.1
0.9048
0.9953
0.9998
1.0000
1.0000

0.2
0.8187
0.9825
0.9989
0.9999
1.0000

0.3
0.7408
0.9631
0.9964
0.9997
1.0000

0.4
0.6703
0.9384
0.9921
0.9992
0.9999

0.5
0.6065
0.9098
0.9856
0.9982
0.9998

0.6
0.5488
0.8781
0.9769
0.9966
0.9996

0.7
0.4966
0.8442
0.9659
0.9942
0.9992

0.8
0.4493
0.8088
0.9526
0.9909
0.9986

0.9
0.4066
0.7725
0.9371
0.9865
0.9977

1.0
0.3679
0.7358
0.9197
0.9810
0.9963

1.0000
1.0000
1.0000

1.0000
1.0000
1.0000

1.0000
1.0000
1.0000

1.0000
1.0000
1.0000

1.0000
1.0000
1.0000

1.0000
1.0000
1.0000

0.9999
1.0000
1.0000

0.9998
1.0000
1.0000

0.9997
1.0000
1.0000

0.9994
0.9999
1.0000

1.1
0.3329
0.6990
0.9004
0.9743
0.9946

1.2
0.3012
0.6626
0.8795
0.9662
0.9923

1.3
0.2725
0.6268
0.8571
0.9569
0.9893

1.4
0.2466
0.5918
0.8335
0.9463
0.9857

1.5
0.2231
0.5578
0.8088
0.9344
0.9814

1.6
0.2019
0.5249
0.7834
0.9212
0.9763

1.7
0.1827
0.4932
0.7572
0.9068
0.9704

1.8
0.1653
0.4628
0.7306
0.8913
0.9636

1.9
0.1496
0.4337
0.7037
0.8747
0.9559

2.0
0.1353
0.4060
0.6767
0.8571
0.9473

0.9990
0.9999
1.0000
1.0000
1.0000

0.9985
0.9997
1.0000
1.0000
1.0000

0.9978
0.9996
0.9999
1.0000
1.0000

0.9968
0.9994
0.9999
1.0000
1.0000

0.9955
0.9991
0.9998
1.0000
1.0000

0.9940
0.9987
0.9997
1.0000
1.0000

0.9920
0.9981
0.9996
0.9999
1.0000

0.9896
0.9974
0.9994
0.9999
1.0000

0.9868
0.9966
0.9992
0.9998
1.0000

0.9834
0.9955
0.9989
0.9998
1.0000

2.1
0.1225
0.3796
0.6496
0.8386
0.9379

2.2
0.1108
0.3546
0.6227
0.8194
0.9275

2.3
0.1003
0.3309
0.5960
0.7993
0.9162

2.4
0.0907
0.3084
0.5697
0.7787
0.9041

2.5
0.0821
0.2873
0.5438
0.7576
0.8912

2.6
0.0743
0.2674
0.5184
0.7360
0.8774

2.7
0.0672
0.2487
0.4936
0.7141
0.8629

2.8
0.0608
0.2311
0.4695
0.6919
0.8477

2.9
0.0550
0.2146
0.4460
0.6696
0.8318

3.0
0.0498
0.1991
0.4232
0.6472
0.8153

5
6
7
8
9

0.9796
0.9941
0.9985
0.9997
0.9999

0.9751
0.9925
0.9980
0.9995
0.9999

0.9700
0.9906
0.9974
0.9994
0.9999

0.9643
0.9884
0.9967
0.9991
0.9998

0.9580
0.9858
0.9958
0.9989
0.9997

0.9510
0.9828
0.9947
0.9985
0.9996

0.9433
0.9794
0.9934
0.9981
0.9995

0.9349
0.9756
0.9919
0.9976
0.9993

0.9258
0.9713
0.9901
0.9969
0.9991

0.9161
0.9665
0.9881
0.9962
0.9989

10
11
12

1.0000
1.0000
1.0000

1.0000
1.0000
1.0000

1.0000
1.0000
1.0000

1.0000
1.0000
1.0000

0.9999
1.0000
1.0000

0.9999
1.0000
1.0000

0.9999
1.0000
1.0000

0.9998
1.0000
1.0000

0.9998
0.9999
1.0000

0.9997
0.9999
1.0000

F (x) x 0
1
2
3
4

3.1
0.0450
0.1847
0.4012
0.6248
0.7982

3.2
0.0408
0.1712
0.3799
0.6025
0.7806

3.3
0.0369
0.1586
0.3594
0.5803
0.7626

3.4
0.0334
0.1468
0.3397
0.5584
0.7442

3.5
0.0302
0.1359
0.3208
0.5366
0.7254

3.6
0.0273
0.1257
0.3027
0.5152
0.7064

3.7
0.0247
0.1162
0.2854
0.4942
0.6872

3.8
0.0224
0.1074
0.2689
0.4735
0.6678

3.9
0.0202
0.0992
0.2531
0.4532
0.6484

4.0
0.0183
0.0916
0.2381
0.4335
0.6288

5
6
7
8
9

0.9057
0.9612
0.9858
0.9953
0.9986

0.8946
0.9554
0.9832
0.9943
0.9982

0.8829
0.9490
0.9802
0.9931
0.9978

0.8705
0.9421
0.9769
0.9917
0.9973

0.8576
0.9347
0.9733
0.9901
0.9967

0.8441
0.9267
0.9692
0.9883
0.9960

0.8301
0.9182
0.9648
0.9863
0.9952

0.8156
0.9091
0.9599
0.9840
0.9942

0.8006
0.8995
0.9546
0.9815
0.9931

0.7851
0.8893
0.9489
0.9786
0.9919

10
11
12
13
14

0.9996
0.9999
1.0000
1.0000
1.0000

0.9995
0.9999
1.0000
1.0000
1.0000

0.9994
0.9998
1.0000
1.0000
1.0000

0.9992
0.9998
0.9999
1.0000
1.0000

0.9990
0.9997
0.9999
1.0000
1.0000

0.9987
0.9996
0.9999
1.0000
1.0000

0.9984
0.9995
0.9999
1.0000
1.0000

0.9981
0.9994
0.9998
1.0000
1.0000

0.9977
0.9993
0.9998
0.9999
1.0000

0.9972
0.9991
0.9997
0.9999
1.0000

5
6
7
F (x) x 0
1
2
3
4
5
6
7
8
9
F (x) x 0
1
2
3
4

´
CATOLICA-LISBON

λ

λ

λ

Statistical Tables

Poisson Distribution – distribution function

F (x) x 0
1
2
3
4

28

λ
4.1
0.0166
0.0845
0.2238
0.4142
0.6093

4.2
0.0150
0.0780
0.2102
0.3954
0.5898

4.3
0.0136
0.0719
0.1974
0.3772
0.5704

4.4
0.0123
0.0663
0.1851
0.3594
0.5512

4.5
0.0111
0.0611
0.1736
0.3423
0.5321

4.6
0.0101
0.0563
0.1626
0.3257
0.5132

4.7
0.0091
0.0518
0.1523
0.3097
0.4946

4.8
0.0082
0.0477
0.1425
0.2942
0.4763

4.9
0.0074
0.0439
0.1333
0.2793
0.4582

5.0
0.0067
0.0404
0.1247
0.2650
0.4405

5
6
7
8
9

0.7693
0.8786
0.9427
0.9755
0.9905

0.7531
0.8675
0.9361
0.9721
0.9889

0.7367
0.8558
0.9290
0.9683
0.9871

0.7199
0.8436
0.9214
0.9642
0.9851

0.7029
0.8311
0.9134
0.9597
0.9829

0.6858
0.8180
0.9049
0.9549
0.9805

0.6684
0.8046
0.8960
0.9497
0.9778

0.6510
0.7908
0.8867
0.9442
0.9749

0.6335
0.7767
0.8769
0.9382
0.9717

0.6160
0.7622
0.8666
0.9319
0.9682

10
11
12
13
14

0.9966
0.9989
0.9997
0.9999
1.0000

0.9959
0.9986
0.9996
0.9999
1.0000

0.9952
0.9983
0.9995
0.9998
1.0000

0.9943
0.9980
0.9993
0.9998
0.9999

0.9933
0.9976
0.9992
0.9997
0.9999

0.9922
0.9971
0.9990
0.9997
0.9999

0.9910
0.9966
0.9988
0.9996
0.9999

0.9896
0.9960
0.9986
0.9995
0.9999

0.9880
0.9953
0.9983
0.9994
0.9998

0.9863
0.9945
0.9980
0.9993
0.9998

15
16

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

0.9999
1.0000

0.9999
1.0000

F (x) x 0
1
2
3
4

5.1
0.0061
0.0372
0.1165
0.2513
0.4231

5.2
0.0055
0.0342
0.1088
0.2381
0.4061

5.3
0.0050
0.0314
0.1016
0.2254
0.3895

5.4
0.0045
0.0289
0.0948
0.2133
0.3733

5.5
0.0041
0.0266
0.0884
0.2017
0.3575

5.6
0.0037
0.0244
0.0824
0.1906
0.3422

5.7
0.0033
0.0224
0.0768
0.1800
0.3272

5.8
0.0030
0.0206
0.0715
0.1700
0.3127

5.9
0.0027
0.0189
0.0666
0.1604
0.2987

6.0
0.0025
0.0174
0.0620
0.1512
0.2851

5
6
7
8
9

0.5984
0.7474
0.8560
0.9252
0.9644

0.5809
0.7324
0.8449
0.9181
0.9603

0.5635
0.7171
0.8335
0.9106
0.9559

0.5461
0.7017
0.8217
0.9027
0.9512

0.5289
0.6860
0.8095
0.8944
0.9462

0.5119
0.6703
0.7970
0.8857
0.9409

0.4950
0.6544
0.7841
0.8766
0.9352

0.4783
0.6384
0.7710
0.8672
0.9292

0.4619
0.6224
0.7576
0.8574
0.9228

0.4457
0.6063
0.7440
0.8472
0.9161

10
11
12
13
14

0.9844
0.9937
0.9976
0.9992
0.9997

0.9823
0.9927
0.9972
0.9990
0.9997

0.9800
0.9916
0.9967
0.9988
0.9996

0.9775
0.9904
0.9962
0.9986
0.9995

0.9747
0.9890
0.9955
0.9983
0.9994

0.9718
0.9875
0.9949
0.9980
0.9993

0.9686
0.9859
0.9941
0.9977
0.9991

0.9651
0.9841
0.9932
0.9973
0.9990

0.9614
0.9821
0.9922
0.9969
0.9988

0.9574
0.9799
0.9912
0.9964
0.9986

15
16
17
18

0.9999
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000

0.9997
0.9999
1.0000
1.0000

0.9996
0.9999
1.0000
1.0000

0.9996
0.9999
1.0000
1.0000

0.9995
0.9998
0.9999
1.0000

F (x) x 0
1
2
3
4

6.1
0.0022
0.0159
0.0577
0.1425
0.2719

6.2
0.0020
0.0146
0.0536
0.1342
0.2592

6.3
0.0018
0.0134
0.0498
0.1264
0.2469

6.4
0.0017
0.0123
0.0463
0.1189
0.2351

6.5
0.0015
0.0113
0.0430
0.1118
0.2237

6.6
0.0014
0.0103
0.0400
0.1052
0.2127

6.7
0.0012
0.0095
0.0371
0.0988
0.2022

6.8
0.0011
0.0087
0.0344
0.0928
0.1920

6.9
0.0010
0.0080
0.0320
0.0871
0.1823

7.0
0.0009
0.0073
0.0296
0.0818
0.1730

5
6
7
8
9

0.4298
0.5902
0.7301
0.8367
0.9090

0.4141
0.5742
0.7160
0.8259
0.9016

0.3988
0.5582
0.7017
0.8148
0.8939

0.3837
0.5423
0.6873
0.8033
0.8858

0.3690
0.5265
0.6728
0.7916
0.8774

0.3547
0.5108
0.6581
0.7796
0.8686

0.3406
0.4953
0.6433
0.7673
0.8596

0.3270
0.4799
0.6285
0.7548
0.8502

0.3137
0.4647
0.6136
0.7420
0.8405

0.3007
0.4497
0.5987
0.7291
0.8305

10
11
12
13
14

0.9531
0.9776
0.9900
0.9958
0.9984

0.9486
0.9750
0.9887
0.9952
0.9981

0.9437
0.9723
0.9873
0.9945
0.9978

0.9386
0.9693
0.9857
0.9937
0.9974

0.9332
0.9661
0.9840
0.9929
0.9970

0.9274
0.9627
0.9821
0.9920
0.9966

0.9214
0.9591
0.9801
0.9909
0.9961

0.9151
0.9552
0.9779
0.9898
0.9956

0.9084
0.9510
0.9755
0.9885
0.9950

0.9015
0.9467
0.9730
0.9872
0.9943

15
16
17
18
19

0.9994
0.9998
0.9999
1.0000
1.0000

0.9993
0.9997
0.9999
1.0000
1.0000

0.9992
0.9997
0.9999
1.0000
1.0000

0.9990
0.9996
0.9999
1.0000
1.0000

0.9988
0.9996
0.9998
0.9999
1.0000

0.9986
0.9995
0.9998
0.9999
1.0000

0.9984
0.9994
0.9998
0.9999
1.0000

0.9982
0.9993
0.9997
0.9999
1.0000

0.9979
0.9992
0.9997
0.9999
1.0000

0.9976
0.9990
0.9996
0.9999
1.0000

´
CATOLICA-LISBON

λ

λ

Statistical Tables

Poisson Distribution – distribution function

F (x) x 0
1
2
3
4

29

λ
7.1
0.0008
0.0067
0.0275
0.0767
0.1641

7.2
0.0007
0.0061
0.0255
0.0719
0.1555

7.3
0.0007
0.0056
0.0236
0.0674
0.1473

7.4
0.0006
0.0051
0.0219
0.0632
0.1395

7.5
0.0006
0.0047
0.0203
0.0591
0.1321

7.6
0.0005
0.0043
0.0188
0.0554
0.1249

7.7
0.0005
0.0039
0.0174
0.0518
0.1181

7.8
0.0004
0.0036
0.0161
0.0485
0.1117

7.9
0.0004
0.0033
0.0149
0.0453
0.1055

8.0
0.0003
0.0030
0.0138
0.0424
0.0996

5
6
7
8
9

0.2881
0.4349
0.5838
0.7160
0.8202

0.2759
0.4204
0.5689
0.7027
0.8096

0.2640
0.4060
0.5541
0.6892
0.7988

0.2526
0.3920
0.5393
0.6757
0.7877

0.2414
0.3782
0.5246
0.6620
0.7764

0.2307
0.3646
0.5100
0.6482
0.7649

0.2203
0.3514
0.4956
0.6343
0.7531

0.2103
0.3384
0.4812
0.6204
0.7411

0.2006
0.3257
0.4670
0.6065
0.7290

0.1912
0.3134
0.4530
0.5925
0.7166

10
11
12
13
14

0.8942
0.9420
0.9703
0.9857
0.9935

0.8867
0.9371
0.9673
0.9841
0.9927

0.8788
0.9319
0.9642
0.9824
0.9918

0.8707
0.9265
0.9609
0.9805
0.9908

0.8622
0.9208
0.9573
0.9784
0.9897

0.8535
0.9148
0.9536
0.9762
0.9886

0.8445
0.9085
0.9496
0.9739
0.9873

0.8352
0.9020
0.9454
0.9714
0.9859

0.8257
0.8952
0.9409
0.9687
0.9844

0.8159
0.8881
0.9362
0.9658
0.9827

15
16
17
18
19

0.9972
0.9989
0.9996
0.9998
0.9999

0.9969
0.9987
0.9995
0.9998
0.9999

0.9964
0.9985
0.9994
0.9998
0.9999

0.9959
0.9983
0.9993
0.9997
0.9999

0.9954
0.9980
0.9992
0.9997
0.9999

0.9948
0.9978
0.9991
0.9996
0.9999

0.9941
0.9974
0.9989
0.9996
0.9998

0.9934
0.9971
0.9988
0.9995
0.9998

0.9926
0.9967
0.9986
0.9994
0.9998

0.9918
0.9963
0.9984
0.9993
0.9997

20
21

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

1.0000
1.0000

0.9999
1.0000

0.9999
1.0000

0.9999
1.0000

0.9999
1.0000

F (x) x 0
1
2
3
4

8.1
0.0003
0.0028
0.0127
0.0396
0.0940

8.2
0.0003
0.0025
0.0118
0.0370
0.0887

8.3
0.0002
0.0023
0.0109
0.0346
0.0837

8.4
0.0002
0.0021
0.0100
0.0323
0.0789

8.5
0.0002
0.0019
0.0093
0.0301
0.0744

8.6
0.0002
0.0018
0.0086
0.0281
0.0701

8.7
0.0002
0.0016
0.0079
0.0262
0.0660

8.8
0.0002
0.0015
0.0073
0.0244
0.0621

8.9
0.0001
0.0014
0.0068
0.0228
0.0584

9.0
0.0001
0.0012
0.0062
0.0212
0.0550

5
6
7
8
9

0.1822
0.3013
0.4391
0.5786
0.7041

0.1736
0.2896
0.4254
0.5647
0.6915

0.1653
0.2781
0.4119
0.5507
0.6788

0.1573
0.2670
0.3987
0.5369
0.6659

0.1496
0.2562
0.3856
0.5231
0.6530

0.1422
0.2457
0.3728
0.5094
0.6400

0.1352
0.2355
0.3602
0.4958
0.6269

0.1284
0.2256
0.3478
0.4823
0.6137

0.1219
0.2160
0.3357
0.4689
0.6006

0.1157
0.2068
0.3239
0.4557
0.5874

10
11
12
13
14

0.8058
0.8807
0.9313
0.9628
0.9810

0.7955
0.8731
0.9261
0.9595
0.9791

0.7850
0.8652
0.9207
0.9561
0.9771

0.7743
0.8571
0.9150
0.9524
0.9749

0.7634
0.8487
0.9091
0.9486
0.9726

0.7522
0.8400
0.9029
0.9445
0.9701

0.7409
0.8311
0.8965
0.9403
0.9675

0.7294
0.8220
0.8898
0.9358
0.9647

0.7178
0.8126
0.8829
0.9311
0.9617

0.7060
0.8030
0.8758
0.9261
0.9585

15
16
17
18
19

0.9908
0.9958
0.9982
0.9992
0.9997

0.9898
0.9953
0.9979
0.9991
0.9997

0.9887
0.9947
0.9977
0.9990
0.9996

0.9875
0.9941
0.9973
0.9989
0.9995

0.9862
0.9934
0.9970
0.9987
0.9995

0.9848
0.9926
0.9966
0.9985
0.9994

0.9832
0.9918
0.9962
0.9983
0.9993

0.9816
0.9909
0.9957
0.9981
0.9992

0.9798
0.9899
0.9952
0.9978
0.9991

0.9780
0.9889
0.9947
0.9976
0.9989

20
21
22
23

0.9999
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000

0.9997
0.9999
1.0000
1.0000

0.9997
0.9999
1.0000
1.0000

0.9996
0.9998
0.9999
1.0000

0.9996
0.9998
0.9999
1.0000

´
CATOLICA-LISBON

λ

Statistical Tables

Poisson Distribution – distribution function

F (x) x 0
1
2
3
4

30

λ
9.1
0.0001
0.0011
0.0058
0.0198
0.0517

9.2
0.0001
0.0010
0.0053
0.0184
0.0486

9.3
0.0001
0.0009
0.0049
0.0172
0.0456

9.4
0.0001
0.0009
0.0045
0.0160
0.0429

9.5
0.0001
0.0008
0.0042
0.0149
0.0403

9.6
0.0001
0.0007
0.0038
0.0138
0.0378

9.7
0.0001
0.0007
0.0035
0.0129
0.0355

9.8
0.0001
0.0006
0.0033
0.0120
0.0333

9.9
0.0001
0.0005
0.0030
0.0111
0.0312

10
0.0000
0.0005
0.0028
0.0103
0.0293

5
6
7
8
9

0.1098
0.1978
0.3123
0.4426
0.5742

0.1041
0.1892
0.3010
0.4296
0.5611

0.0986
0.1808
0.2900
0.4168
0.5479

0.0935
0.1727
0.2792
0.4042
0.5349

0.0885
0.1649
0.2687
0.3918
0.5218

0.0838
0.1574
0.2584
0.3796
0.5089

0.0793
0.1502
0.2485
0.3676
0.4960

0.0750
0.1433
0.2388
0.3558
0.4832

0.0710
0.1366
0.2294
0.3442
0.4705

0.0671
0.1301
0.2202
0.3328
0.4579

10
11
12
13
14

0.6941
0.7932
0.8684
0.9210
0.9552

0.6820
0.7832
0.8607
0.9156
0.9517

0.6699
0.7730
0.8529
0.9100
0.9480

0.6576
0.7626
0.8448
0.9042
0.9441

0.6453
0.7520
0.8364
0.8981
0.9400

0.6329
0.7412
0.8279
0.8919
0.9357

0.6205
0.7303
0.8191
0.8853
0.9312

0.6080
0.7193
0.8101
0.8786
0.9265

0.5955
0.7081
0.8009
0.8716
0.9216

0.5830
0.6968
0.7916
0.8645
0.9165

15
16
17
18
19

0.9760
0.9878
0.9941
0.9973
0.9988

0.9738
0.9865
0.9934
0.9969
0.9986

0.9715
0.9852
0.9927
0.9966
0.9985

0.9691
0.9838
0.9919
0.9962
0.9983

0.9665
0.9823
0.9911
0.9957
0.9980

0.9638
0.9806
0.9902
0.9952
0.9978

0.9609
0.9789
0.9892
0.9947
0.9975

0.9579
0.9770
0.9881
0.9941
0.9972

0.9546
0.9751
0.9870
0.9935
0.9969

0.9513
0.9730
0.9857
0.9928
0.9965

20
21
22
23
24

0.9995
0.9998
0.9999
1.0000
1.0000

0.9994
0.9998
0.9999
1.0000
1.0000

0.9993
0.9997
0.9999
1.0000
1.0000

0.9992
0.9997
0.9999
1.0000
1.0000

0.9991
0.9996
0.9999
0.9999
1.0000

0.9990
0.9996
0.9998
0.9999
1.0000

0.9989
0.9995
0.9998
0.9999
1.0000

0.9987
0.9995
0.9998
0.9999
1.0000

0.9986
0.9994
0.9997
0.9999
1.0000

0.9984
0.9993
0.9997
0.9999
1.0000

´
CATOLICA-LISBON

Statistical Tables

Poisson Distribution – distribution function

F (x) x 0
1
2
3
4

31

λ
11
0.0000
0.0002
0.0012
0.0049
0.0151

12
0.0000
0.0001
0.0005
0.0023
0.0076

13
0.0000
0.0000
0.0002
0.0011
0.0037

14
0.0000
0.0000
0.0001
0.0005
0.0018

15
0.0000
0.0000
0.0000
0.0002
0.0009

16
0.0000
0.0000
0.0000
0.0001
0.0004

17
0.0000
0.0000
0.0000
0.0000
0.0002

18
0.0000
0.0000
0.0000
0.0000
0.0001

19
0.0000
0.0000
0.0000
0.0000
0.0000

20
0.0000
0.0000
0.0000
0.0000
0.0000

5
6
7
8
9

0.0375
0.0786
0.1432
0.2320
0.3405

0.0203
0.0458
0.0895
0.1550
0.2424

0.0107
0.0259
0.0540
0.0998
0.1658

0.0055
0.0142
0.0316
0.0621
0.1094

0.0028
0.0076
0.0180
0.0374
0.0699

0.0014
0.0040
0.0100
0.0220
0.0433

0.0007
0.0021
0.0054
0.0126
0.0261

0.0003
0.0010
0.0029
0.0071
0.0154

0.0002
0.0005
0.0015
0.0039
0.0089

0.0001
0.0003
0.0008
0.0021
0.0050

10
11
12
13
14

0.4599
0.5793
0.6887
0.7813
0.8540

0.3472
0.4616
0.5760
0.6815
0.7720

0.2517
0.3532
0.4631
0.5730
0.6751

0.1757
0.2600
0.3585
0.4644
0.5704

0.1185
0.1848
0.2676
0.3632
0.4657

0.0774
0.1270
0.1931
0.2745
0.3675

0.0491
0.0847
0.1350
0.2009
0.2808

0.0304
0.0549
0.0917
0.1426
0.2081

0.0183
0.0347
0.0606
0.0984
0.1497

0.0108
0.0214
0.0390
0.0661
0.1049

15
16
17
18
19

0.9074
0.9441
0.9678
0.9823
0.9907

0.8444
0.8987
0.9370
0.9626
0.9787

0.7636
0.8355
0.8905
0.9302
0.9573

0.6694
0.7559
0.8272
0.8826
0.9235

0.5681
0.6641
0.7489
0.8195
0.8752

0.4667
0.5660
0.6593
0.7423
0.8122

0.3715
0.4677
0.5640
0.6550
0.7363

0.2867
0.3751
0.4686
0.5622
0.6509

0.2148
0.2920
0.3784
0.4695
0.5606

0.1565
0.2211
0.2970
0.3814
0.4703

20
21
22
23
24

0.9953
0.9977
0.9990
0.9995
0.9998

0.9884
0.9939
0.9970
0.9985
0.9993

0.9750
0.9859
0.9924
0.9960
0.9980

0.9521
0.9712
0.9833
0.9907
0.9950

0.9170
0.9469
0.9673
0.9805
0.9888

0.8682
0.9108
0.9418
0.9633
0.9777

0.8055
0.8615
0.9047
0.9367
0.9594

0.7307
0.7991
0.8551
0.8989
0.9317

0.6472
0.7255
0.7931
0.8490
0.8933

0.5591
0.6437
0.7206
0.7875
0.8432

25
26
27
28
29

0.9999
1.0000
1.0000
1.0000
1.0000

0.9997
0.9999
0.9999
1.0000
1.0000

0.9990
0.9995
0.9998
0.9999
1.0000

0.9974
0.9987
0.9994
0.9997
0.9999

0.9938
0.9967
0.9983
0.9991
0.9996

0.9869
0.9925
0.9959
0.9978
0.9989

0.9748
0.9848
0.9912
0.9950
0.9973

0.9554
0.9718
0.9827
0.9897
0.9941

0.9269
0.9514
0.9687
0.9805
0.9882

0.8878
0.9221
0.9475
0.9657
0.9782

30
31
32
33
34

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
1.0000
1.0000
1.0000
1.0000

0.9998
0.9999
1.0000
1.0000
1.0000

0.9994
0.9997
0.9999
0.9999
1.0000

0.9986
0.9993
0.9996
0.9998
0.9999

0.9967
0.9982
0.9990
0.9995
0.9998

0.9930
0.9960
0.9978
0.9988
0.9994

0.9865
0.9919
0.9953
0.9973
0.9985

35
36
37
38
39

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

1.0000
1.0000
1.0000
1.0000
1.0000

0.9999
0.9999
1.0000
1.0000
1.0000

0.9997
0.9998
0.9999
1.0000
1.0000

0.9992
0.9996
0.9998
0.9999
0.9999

40

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

´
CATOLICA-LISBON

Statistical Tables

Normal distribution

32

Normal distribution (standardized) z Φ(z) =
−∞

t2
1
√ e− 2 dt


z
0
0.1
0.2
0.3
0.4

0.00
0.5000
0.5398
0.5793
0.6179
0.6554

0.01
0.5040
0.5438
0.5832
0.6217
0.6591

0.02
0.5080
0.5478
0.5871
0.6255
0.6628

0.03
0.5120
0.5517
0.5910
0.6293
0.6664

0.04
0.5160
0.5557
0.5948
0.6331
0.6700

0.05
0.5199
0.5596
0.5987
0.6368
0.6736

0.06
0.5239
0.5636
0.6026
0.6406
0.6772

0.07
0.5279
0.5675
0.6064
0.6443
0.6808

0.08
0.5319
0.5714
0.6103
0.6480
0.6844

0.09
0.5359
0.5753
0.6141
0.6517
0.6879

0.5
0.6
0.7
0.8
0.9

0.6915
0.7257
0.7580
0.7881
0.8159

0.6950
0.7291
0.7611
0.7910
0.8186

0.6985
0.7324
0.7642
0.7939
0.8212

0.7019
0.7357
0.7673
0.7967
0.8238

0.7054
0.7389
0.7704
0.7995
0.8264

0.7088
0.7422
0.7734
0.8023
0.8289

0.7123
0.7454
0.7764
0.8051
0.8315

0.7157
0.7486
0.7794
0.8078
0.8340

0.7190
0.7517
0.7823
0.8106
0.8365

0.7224
0.7549
0.7852
0.8133
0.8389

1
1.1
1.2
1.3
1.4

0.8413
0.8643
0.8849
0.9032
0.9192

0.8438
0.8665
0.8869
0.9049
0.9207

0.8461
0.8686
0.8888
0.9066
0.9222

0.8485
0.8708
0.8907
0.9082
0.9236

0.8508
0.8729
0.8925
0.9099
0.9251

0.8531
0.8749
0.8944
0.9115
0.9265

0.8554
0.8770
0.8962
0.9131
0.9279

0.8577
0.8790
0.8980
0.9147
0.9292

0.8599
0.8810
0.8997
0.9162
0.9306

0.8621
0.8830
0.9015
0.9177
0.9319

1.5
1.6
1.7
1.8
1.9

0.9332
0.9452
0.9554
0.9641
0.9713

0.9345
0.9463
0.9564
0.9649
0.9719

0.9357
0.9474
0.9573
0.9656
0.9726

0.9370
0.9484
0.9582
0.9664
0.9732

0.9382
0.9495
0.9591
0.9671
0.9738

0.9394
0.9505
0.9599
0.9678
0.9744

0.9406
0.9515
0.9608
0.9686
0.9750

0.9418
0.9525
0.9616
0.9693
0.9756

0.9429
0.9535
0.9625
0.9699
0.9761

0.9441
0.9545
0.9633
0.9706
0.9767

2
2.1
2.2
2.3
2.4

0.9772
0.9821
0.9861
0.9893
0.9918

0.9778
0.9826
0.9864
0.9896
0.9920

0.9783
0.9830
0.9868
0.9898
0.9922

0.9788
0.9834
0.9871
0.9901
0.9925

0.9793
0.9838
0.9875
0.9904
0.9927

0.9798
0.9842
0.9878
0.9906
0.9929

0.9803
0.9846
0.9881
0.9909
0.9931

0.9808
0.9850
0.9884
0.9911
0.9932

0.9812
0.9854
0.9887
0.9913
0.9934

0.9817
0.9857
0.9890
0.9916
0.9936

2.5
2.6
2.7
2.8
2.9

0.9938
0.9953
0.9965
0.9974
0.9981

0.9940
0.9955
0.9966
0.9975
0.9982

0.9941
0.9956
0.9967
0.9976
0.9982

0.9943
0.9957
0.9968
0.9977
0.9983

0.9945
0.9959
0.9969
0.9977
0.9984

0.9946
0.9960
0.9970
0.9978
0.9984

0.9948
0.9961
0.9971
0.9979
0.9985

0.9949
0.9962
0.9972
0.9979
0.9985

0.9951
0.9963
0.9973
0.9980
0.9986

0.9952
0.9964
0.9974
0.9981
0.9986

3
3.1
3.2
3.3
3.4

0.9987
0.9990
0.9993
0.9995
0.9997

0.9987
0.9991
0.9993
0.9995
0.9997

0.9987
0.9991
0.9994
0.9995
0.9997

0.9988
0.9991
0.9994
0.9996
0.9997

0.9988
0.9992
0.9994
0.9996
0.9997

0.9989
0.9992
0.9994
0.9996
0.9997

0.9989
0.9992
0.9994
0.9996
0.9997

0.9989
0.9992
0.9995
0.9996
0.9997

0.9990
0.9993
0.9995
0.9996
0.9997

0.9990
0.9993
0.9995
0.9997
0.9998

Φ(z)
0.0001
0.0005
0.001

z
−3.719
−3.291
−3.090

Φ(z)
0.05
0.10
0.15

z
−1.645
−1.282
−1.036

0.005
0.010
0.025

−2.576
−2.326
−1.960

0.20
0.25
0.30

−0.8416
−0.6745
−0.5244

´
CATOLICA-LISBON

Φ(z) z 0.35 −0.3853
0.40 −0.2533
0.45 −0.1257
0.50
0.000
0.55
0.1257
0.60
0.2533
0.65
0.3853

Φ(z) z 0.70 0.5244
0.75 0.6745
0.80 0.8416

Φ(z)
0.975
0.990
0.995

z
1.960
2.326
2.576

0.85
0.90
0.95

0.999
0.9995
0.9999

3.090
3.291
3.719

1.036
1.282
1.645

Statistical Tables

χ2 distribution

33

χ2 distribution

0.010
0.000157
0.0201
0.115
0.297
0.554

0.025
0.000982
0.0506
0.216
0.484
0.831

0.05
0.00393
0.103
0.352
0.711
1.145

0.100
0.0158
0.211
0.584
1.064
1.610

0.250
0.102
0.575
1.213
1.923
2.675

F (x)
0.500
0.455
1.386
2.366
3.357
4.351

0.750
1.323
2.773
4.108
5.385
6.626

0.900
2.706
4.605
6.251
7.779
9.236

0.950
3.841
5.991
7.815
9.488
11.071

0.975
5.024
7.378
9.348
11.143
12.833

0.990
6.635
9.210
11.345
13.277
15.086

0.995
7.879
10.597
12.838
14.860
16.750

0.676
0.989
1.344
1.735
2.156

0.872
1.239
1.647
2.088
2.558

1.237
1.690
2.180
2.700
3.247

1.635
2.167
2.733
3.325
3.940

2.204
2.833
3.490
4.168
4.865

3.455
4.255
5.071
5.899
6.737

5.348
6.346
7.344
8.343
9.342

7.841
9.037
10.219
11.389
12.549

10.645
12.017
13.362
14.684
15.987

12.592
14.067
15.507
16.919
18.307

14.449
16.013
17.535
19.023
20.483

16.812
18.475
20.090
21.666
23.209

18.548
20.278
21.955
23.589
25.188

11
12
13
14
15

2.603
3.074
3.565
4.075
4.601

3.053
3.571
4.107
4.660
5.229

3.816
4.404
5.009
5.629
6.262

4.575
5.226
5.892
6.571
7.261

5.578
6.304
7.042
7.790
8.547

7.584
8.438
9.299
10.17
11.04

10.341
11.340
12.340
13.339
14.339

13.701
14.845
15.984
17.117
18.245

17.275
18.549
19.812
21.064
22.307

19.675
21.026
22.362
23.685
24.996

21.920
23.337
24.736
26.119
27.488

24.725
26.217
27.688
29.141
30.578

26.757
28.300
29.820
31.319
32.801

16
17
18
19
20

5.142
5.697
6.265
6.844
7.434

5.812
6.408
7.015
7.633
8.260

6.908
7.564
8.231
8.907
9.591

7.962
8.672
9.390
10.12
10.85

9.312
10.09
10.86
11.65
12.44

11.91
12.79
13.68
14.56
15.45

15.338
16.338
17.338
18.338
19.337

19.369
20.489
21.605
22.718
23.828

23.542
24.769
25.989
27.204
28.412

26.296
27.587
28.869
30.144
31.410

28.845
30.191
31.526
32.852
34.170

32.000
33.409
34.805
36.191
37.566

34.267
35.719
37.157
38.582
39.997

21
22
23
24
25

8.034
8.643
9.260
9.886
10.520

8.897
9.542
10.20
10.86
11.524

10.28
10.98
11.69
12.40
13.120

11.59
12.34
13.09
13.85
14.611

13.24
14.04
14.85
15.66
16.473

16.34
17.24
18.14
19.04
19.939

20.337
21.337
22.337
23.337
24.337

24.935
26.039
27.141
28.241
29.339

29.615
30.813
32.007
33.196
34.382

32.671
33.924
35.173
36.415
37.653

35.479
36.781
38.076
39.364
40.647

38.932
40.289
41.638
42.980
44.314

41.401
42.796
44.181
45.559
46.928

26
27
28
29
30

11.160
11.808
12.461
13.121
13.787

12.198
12.879
13.565
14.257
14.954

13.844
14.573
15.308
16.047
16.791

15.379
16.151
16.928
17.708
18.493

17.292
18.114
18.939
19.768
20.599

20.843
21.749
22.657
23.567
24.478

25.337
26.336
27.336
28.336
29.336

30.435
31.528
32.621
33.711
34.800

35.563
36.741
37.916
39.088
40.256

38.885
40.113
41.337
42.557
43.773

41.923
43.195
44.461
45.722
46.979

45.642
46.963
48.278
49.588
50.892

48.290
49.645
50.993
52.336
53.672

40
50
60
90

20.707
27.991
35.534
59.196

22.164
29.707
37.485
61.754

24.433
32.357
40.482
65.647

26.509
34.764
43.188
69.126

29.051
37.689
46.459
73.291

33.660
42.942
52.294
80.625

39.335
49.335
59.335
89.334

45.616
56.334
66.981
98.650

51.805
63.167
74.397
107.565

55.758
67.505
79.082
113.145

59.342
71.420
83.298
118.136

63.691
76.154
88.379
124.116

66.766
79.490
91.952
128.299

r
1
2
3
4
5

0.005
0.0000393
0.0100
0.072
0.207
0.412

6
7
8
9
10

´
CATOLICA-LISBON

Statistical Tables

Student’s t distribution

34

Student’s t distribution r 1
2
3
4
5

0.60
0.325
0.289
0.277
0.271
0.267

0.75
1.000
0.816
0.765
0.741
0.727

0.90
3.078
1.886
1.638
1.533
1.476

F (x)
0.95
0.975
6.314 12.706
2.920
4.303
2.353
3.182
2.132
2.776
2.015
2.571

6
7
8
9
10

0.265
0.263
0.262
0.261
0.260

0.718
0.711
0.706
0.703
0.700

1.440
1.415
1.397
1.383
1.372

1.943
1.895
1.860
1.833
1.812

11
12
13
14
15

0.260
0.259
0.259
0.258
0.258

0.697
0.695
0.694
0.692
0.691

1.363
1.356
1.350
1.345
1.341

16
17
18
19
20

0.258
0.257
0.257
0.257
0.257

0.690
0.689
0.688
0.688
0.687

21
22
23
24
25

0.257
0.256
0.256
0.256
0.256

26
27
28
29
30
40
50
60
120


´
CATOLICA-LISBON

0.99
31.821
6.965
4.541
3.747
3.365

0.995
63.657
9.925
5.841
4.604
4.032

0.9995
636.619
31.599
12.924
8.610
6.869

2.447
2.365
2.306
2.262
2.228

3.143
2.998
2.896
2.821
2.764

3.707
3.499
3.355
3.250
3.169

5.959
5.408
5.041
4.781
4.587

1.796
1.782
1.771
1.761
1.753

2.201
2.179
2.160
2.145
2.131

2.718
2.681
2.650
2.624
2.602

3.106
3.055
3.012
2.977
2.947

4.437
4.318
4.221
4.140
4.073

1.337
1.333
1.330
1.328
1.325

1.746
1.740
1.734
1.729
1.725

2.120
2.110
2.101
2.093
2.086

2.583
2.567
2.552
2.539
2.528

2.921
2.898
2.878
2.861
2.845

4.015
3.965
3.922
3.883
3.850

0.686
0.686
0.685
0.685
0.684

1.323
1.321
1.319
1.318
1.316

1.721
1.717
1.714
1.711
1.708

2.080
2.074
2.069
2.064
2.060

2.518
2.508
2.500
2.492
2.485

2.831
2.819
2.807
2.797
2.787

3.819
3.792
3.768
3.745
3.725

0.256
0.256
0.256
0.256
0.256

0.684
0.684
0.683
0.683
0.683

1.315
1.314
1.313
1.311
1.310

1.706
1.703
1.701
1.699
1.697

2.056
2.052
2.048
2.045
2.042

2.479
2.473
2.467
2.462
2.457

2.779
2.771
2.763
2.756
2.750

3.707
3.690
3.674
3.659
3.646

0.255
0.255
0.254
0.254
0.253

0.681
0.679
0.679
0.677
0.674

1.303
1.299
1.296
1.289
1.282

1.684
1.676
1.671
1.658
1.645

2.021
2.009
2.000
1.980
1.960

2.423
2.403
2.390
2.358
2.326

2.704
2.678
2.660
2.617
2.576

3.551
3.496
3.460
3.373
3.291

Statistical Tables

1
39.86
8.53
5.54
4.54

3.29
3.23
3.18
3.14
3.10

3.07
3.05
3.03
3.01
2.99

2.97
2.96
2.95
2.94
2.93

2.92
2.91
2.90
2.89
2.89

2.88
2.84
2.79
2.75
2.71

5
6
7
8
9

10
11
12
13
14

15
16
17
18
19

20
21
22
23
24

25
26
27
28
29

30
40
60
120


´
CATOLICA-LISBON

r2

4.06
3.78
3.59
3.46
3.36

F =0.90
1
2
3
4

Snedcor’s F distribution

2.49
2.44
2.39
2.35
2.30

2.53
2.52
2.51
2.50
2.50

2.59
2.57
2.56
2.55
2.54

2.70
2.67
2.64
2.62
2.61

2.92
2.86
2.81
2.76
2.73

3.78
3.46
3.26
3.11
3.01

2
49.50
9.00
5.46
4.32

2.28
2.23
2.18
2.13
2.08

2.32
2.31
2.30
2.29
2.28

2.38
2.36
2.35
2.34
2.33

2.49
2.46
2.44
2.42
2.40

2.73
2.66
2.61
2.56
2.52

3.62
3.29
3.07
2.92
2.81

3
53.59
9.16
5.39
4.19

2.14
2.09
2.04
1.99
1.94

2.18
2.17
2.17
2.16
2.15

2.25
2.23
2.22
2.21
2.19

2.36
2.33
2.31
2.29
2.27

2.61
2.54
2.48
2.43
2.39

3.52
3.18
2.96
2.81
2.69

4
55.83
9.24
5.34
4.11

2.05
2.00
1.95
1.90
1.85

2.09
2.08
2.07
2.06
2.06

2.16
2.14
2.13
2.11
2.10

2.27
2.24
2.22
2.20
2.18

2.52
2.45
2.39
2.35
2.31

3.45
3.11
2.88
2.73
2.61

5
57.24
9.29
5.31
4.05

1.98
1.93
1.87
1.82
1.77

2.02
2.01
2.00
2.00
1.99

2.09
2.08
2.06
2.05
2.04

2.21
2.18
2.15
2.13
2.11

2.46
2.39
2.33
2.28
2.24

3.40
3.05
2.83
2.67
2.55

6
58.20
9.33
5.28
4.01

1.93
1.87
1.82
1.77
1.72

1.97
1.96
1.95
1.94
1.93

2.04
2.02
2.01
1.99
1.98

2.16
2.13
2.10
2.08
2.06

2.41
2.34
2.28
2.23
2.19

3.37
3.01
2.78
2.62
2.51

7
58.91
9.35
5.27
3.98

1.88
1.83
1.77
1.72
1.67

1.93
1.92
1.91
1.90
1.89

2.00
1.98
1.97
1.95
1.94

2.12
2.09
2.06
2.04
2.02

2.38
2.30
2.24
2.20
2.15

3.34
2.98
2.75
2.59
2.47

8
59.44
9.37
5.25
3.95

1.85
1.79
1.74
1.68
1.63

1.89
1.88
1.87
1.87
1.86

1.96
1.95
1.93
1.92
1.91

2.09
2.06
2.03
2.00
1.98

2.35
2.27
2.21
2.16
2.12

3.32
2.96
2.72
2.56
2.44

9
59.86
9.38
5.24
3.94

1.82
1.76
1.71
1.65
1.60

1.87
1.86
1.85
1.84
1.83

1.94
1.92
1.90
1.89
1.88

2.06
2.03
2.00
1.98
1.96

2.32
2.25
2.19
2.14
2.10

3.30
2.94
2.70
2.54
2.42

r1
10
60.19
9.39
5.23
3.92

1.77
1.71
1.66
1.60
1.55

1.82
1.81
1.80
1.79
1.78

1.89
1.87
1.86
1.84
1.83

2.02
1.99
1.96
1.93
1.91

2.28
2.21
2.15
2.10
2.05

3.27
2.90
2.67
2.50
2.38

12
60.71
9.41
5.22
3.90

1.72
1.66
1.60
1.55
1.49

1.77
1.76
1.75
1.74
1.73

1.84
1.83
1.81
1.80
1.78

1.97
1.94
1.91
1.89
1.86

2.24
2.17
2.10
2.05
2.01

3.24
2.87
2.63
2.46
2.34

15
61.22
9.42
5.20
3.87

Snedcor’s F distribution

1.67
1.61
1.54
1.48
1.42

1.72
1.71
1.70
1.69
1.68

1.79
1.78
1.76
1.74
1.73

1.92
1.89
1.86
1.84
1.81

2.20
2.12
2.06
2.01
1.96

3.21
2.84
2.59
2.42
2.30

20
61.74
9.44
5.18
3.84

1.64
1.57
1.51
1.45
1.38

1.69
1.68
1.67
1.66
1.65

1.77
1.75
1.73
1.72
1.70

1.90
1.87
1.84
1.81
1.79

2.18
2.10
2.04
1.98
1.94

3.19
2.82
2.58
2.40
2.28

1.61
1.54
1.48
1.41
1.34

1.66
1.65
1.64
1.63
1.62

1.74
1.72
1.70
1.69
1.67

1.87
1.84
1.81
1.78
1.76

2.16
2.08
2.01
1.96
1.91

3.17
2.80
2.56
2.38
2.25

1.57
1.51
1.44
1.37
1.30

1.63
1.61
1.60
1.59
1.58

1.71
1.69
1.67
1.66
1.64

1.85
1.81
1.78
1.75
1.73

2.13
2.05
1.99
1.93
1.89

3.16
2.78
2.54
2.36
2.23

24
30
40
62.00 62.26 62.53
9.45
9.46
9.47
5.18
5.17
5.16
3.83
3.82
3.80

1.54
1.47
1.40
1.32
1.24

1.59
1.58
1.57
1.56
1.55

1.68
1.66
1.64
1.62
1.61

1.82
1.78
1.75
1.72
1.70

2.11
2.03
1.96
1.90
1.86

3.14
2.76
2.51
2.34
2.21

60
62.79
9.47
5.15
3.79

1.50
1.42
1.35
1.26
1.17

1.56
1.54
1.53
1.52
1.51

1.64
1.62
1.60
1.59
1.57

1.79
1.75
1.72
1.69
1.67

2.08
2.00
1.93
1.88
1.83

3.12
2.74
2.49
2.32
2.18

120
63.06
9.48
5.14
3.78

1.46
1.38
1.29
1.19
1.00

1.52
1.50
1.49
1.48
1.47

1.61
1.59
1.57
1.55
1.53

1.76
1.72
1.69
1.66
1.63

2.06
1.97
1.90
1.88
1.80

3.10
2.72
2.47
2.29
2.16


63.33
9.49
5.13
3.76

Statistical Tables

35

1
161.4
18.51
10.13
7.71

4.96
4.84
4.75
4.67
4.60

4.54
4.49
4.45
4.41
4.38

4.35
4.32
4.30
4.28
4.26

4.24
4.23
4.21
4.20
4.18

4.17
4.08
4.00
3.92
3.84

5
6
7
8
9

10
11
12
13
14

15
16
17
18
19

20
21
22
23
24

25
26
27
28
29

30
40
60
120


´
CATOLICA-LISBON

r2

6.61
5.99
5.59
5.32
5.12

F =0.95
1
2
3
4

Snedcor’s F distribution

3.32
3.23
3.15
3.07
3.00

3.39
3.37
3.35
3.34
3.33

3.49
3.47
3.44
3.42
3.40

3.68
3.63
3.59
3.55
3.52

4.10
3.98
3.89
3.81
3.74

5.79
5.14
4.74
4.46
4.26

2
199.5
19.00
9.55
6.94

2.92
2.84
2.76
2.68
2.60

2.99
2.98
2.96
2.95
2.93

3.10
3.07
3.05
3.03
3.01

3.29
3.24
3.20
3.16
3.13

3.71
3.59
3.49
3.41
3.34

5.41
4.76
4.35
4.07
3.86

3
215.7
19.16
9.28
6.59

2.69
2.61
2.53
2.45
2.37

2.76
2.74
2.73
2.71
2.70

2.87
2.84
2.82
2.80
2.78

3.06
3.01
2.96
2.93
2.90

3.48
3.36
3.26
3.18
3.11

5.19
4.53
4.12
3.84
3.63

4
224.6
19.25
9.12
6.39

2.53
2.45
2.37
2.29
2.21

2.60
2.59
2.57
2.56
2.55

2.71
2.68
2.66
2.64
2.62

2.90
2.85
2.81
2.77
2.74

3.33
3.20
3.11
3.03
2.96

5.05
4.39
3.97
3.69
3.48

5
230.2
19.30
9.01
6.26

2.42
2.34
2.25
2.18
2.10

2.49
2.47
2.46
2.45
2.43

2.60
2.57
2.55
2.53
2.51

2.79
2.74
2.70
2.66
2.63

3.22
3.09
3.00
2.92
2.85

4.95
4.28
3.87
3.58
3.37

6
234.0
19.33
8.94
6.16

2.33
2.25
2.17
2.09
2.01

2.40
2.39
2.37
2.36
2.35

2.51
2.49
2.46
2.44
2.42

2.71
2.66
2.61
2.58
2.54

3.14
3.01
2.91
2.83
2.76

4.88
4.21
3.79
3.50
3.29

7
236.8
19.35
8.89
6.09

2.27
2.18
2.10
2.02
1.94

2.34
2.32
2.31
2.29
2.28

2.45
2.42
2.40
2.37
2.36

2.64
2.59
2.55
2.51
2.48

3.07
2.95
2.85
2.77
2.70

4.82
4.15
3.73
3.44
3.23

8
238.9
19.37
8.85
6.04

2.21
2.12
2.04
1.96
1.88

2.28
2.27
2.25
2.24
2.22

2.39
2.37
2.34
2.32
2.30

2.59
2.54
2.49
2.46
2.42

3.02
2.90
2.80
2.71
2.65

4.77
4.10
3.68
3.39
3.18

9
240.5
19.38
8.81
6.00

2.16
2.08
1.99
1.91
1.83

2.24
2.22
2.20
2.19
2.18

2.35
2.32
2.30
2.27
2.25

2.54
2.49
2.45
2.41
2.38

2.98
2.85
2.75
2.67
2.60

4.74
4.06
3.64
3.35
3.14

r1
10
241.9
19.40
8.79
5.96

2.09
2.00
1.92
1.83
1.75

2.16
2.15
2.13
2.12
2.10

2.28
2.25
2.23
2.20
2.18

2.48
2.42
2.38
2.34
2.31

2.91
2.79
2.69
2.60
2.53

4.68
4.00
3.57
3.28
3.07

12
243.9
19.41
8.74
5.91

2.01
1.92
1.84
1.75
1.67

2.09
2.07
2.06
2.04
2.03

2.20
2.18
2.15
2.13
2.11

2.40
2.35
2.31
2.27
2.23

2.85
2.72
2.62
2.53
2.46

4.62
3.94
3.51
3.22
3.01

15
245.9
19.43
8.70
5.86

1.93
1.84
1.75
1.66
1.57

2.01
1.99
1.97
1.96
1.94

2.12
2.10
2.07
2.05
2.03

2.33
2.28
2.23
2.19
2.16

2.77
2.65
2.54
2.46
2.39

4.56
3.87
3.44
3.15
2.94

20
248.0
19.45
8.66
5.80

1.89
1.79
1.70
1.61
1.52

1.96
1.95
1.93
1.91
1.90

2.08
2.05
2.03
2.01
1.98

2.29
2.24
2.19
2.15
2.11

2.74
2.61
2.51
2.42
2.35

4.53
3.84
3.41
3.12
2.90

1.84
1.74
1.65
1.55
1.46

1.92
1.90
1.88
1.87
1.85

2.04
2.01
1.98
1.96
1.94

2.25
2.19
2.15
2.11
2.07

2.70
2.57
2.47
2.38
2.31

4.50
3.81
3.38
3.08
2.86

1.79
1.69
1.59
1.50
1.39

1.87
1.85
1.84
1.82
1.81

1.99
1.96
1.94
1.91
1.89

2.20
2.15
2.10
2.06
2.03

2.66
2.53
2.43
2.34
2.27

4.46
3.77
3.34
3.04
2.83

24
30
40
249.1 250.1 251.1
19.45 19.46 19.47
8.64
8.62
8.59
5.77
5.75
5.72

1.74
1.64
1.53
1.43
1.32

1.82
1.80
1.79
1.77
1.75

1.95
1.92
1.89
1.86
1.84

2.16
2.11
2.06
2.02
1.98

2.62
2.49
2.38
2.30
2.22

4.43
3.74
3.30
3.01
2.79

60
252.2
19.48
8.57
5.69

1.68
1.58
1.47
1.35
1.22

1.77
1.75
1.73
1.71
1.70

1.90
1.87
1.84
1.81
1.79

2.11
2.06
2.01
1.97
1.93

2.58
2.45
2.34
2.25
2.18

4.40
3.70
3.27
2.97
2.75

120
253.3
19.49
8.55
5.66

1.62
1.51
1.39
1.25
1.00

1.71
1.69
1.67
1.65
1.64

1.84
1.81
1.78
1.76
1.73

2.07
2.01
1.96
1.92
1.88

2.54
2.40
2.30
2.21
2.13

4.36
3.67
3.23
2.93
2.71


254.3
19.50
8.53
5.63

Statistical Tables

36

´
CATOLICA-LISBON

r2

10.01
8.81
8.07
7.57
7.21

6.94
6.72
6.55
6.41
6.30

6.20
6.12
6.04
5.98
5.92

5.87
5.83
5.79
5.75
5.72

5.69
5.66
5.63
5.61
5.59

5.57
5.42
5.29
5.15
5.02

10
11
12
13
14

15
16
17
18
19

20
21
22
23
24

25
26
27
28
29

30
40
60
120


1
647.8
38.51
17.44
12.22

5
6
7
8
9

F =0.975
1
2
3
4

Snedcor’s F distribution

4.18
4.05
3.93
3.80
3.69

4.29
4.27
4.24
4.22
4.20

4.46
4.42
4.38
4.35
4.32

4.77
4.69
4.62
4.56
4.51

5.46
5.26
5.10
4.97
4.86

8.43
7.26
6.54
6.06
5.71

2
799.5
39.00
16.04
10.65

3.59
3.46
3.34
3.23
3.12

3.69
3.67
3.65
3.63
3.61

3.86
3.82
3.78
3.75
3.72

4.15
4.08
4.01
3.95
3.90

4.83
4.63
4.47
4.35
4.24

7.76
6.60
5.89
5.42
5.08

3
864.2
39.17
15.44
9.98

3.25
3.13
3.01
2.89
2.79

3.35
3.33
3.31
3.29
3.27

3.51
3.48
3.44
3.41
3.38

3.80
3.73
3.66
3.61
3.56

4.47
4.28
4.12
4.00
3.89

7.39
6.23
5.52
5.05
4.72

4
899.6
39.25
15.10
9.60

3.03
2.90
2.79
2.67
2.57

3.13
3.10
3.08
3.06
3.04

3.29
3.25
3.22
3.18
3.15

3.58
3.50
3.44
3.38
3.33

4.24
4.04
3.89
3.77
3.66

7.15
5.99
5.29
4.82
4.48

5
921.8
39.30
14.88
9.36

2.87
2.74
2.63
2.52
2.41

2.97
2.94
2.92
2.90
2.88

3.13
3.09
3.05
3.02
2.99

3.41
3.34
3.28
3.22
3.17

4.07
3.88
3.73
3.60
3.50

6.98
5.82
5.12
4.65
4.32

6
937.1
39.33
14.73
9.20

2.75
2.62
2.51
2.39
2.29

2.85
2.82
2.80
2.78
2.76

3.01
2.97
2.93
2.90
2.87

3.29
3.22
3.16
3.10
3.05

3.95
3.76
3.61
3.48
3.38

6.85
5.70
4.99
4.53
4.20

7
948.2
39.36
14.62
9.07

2.65
2.53
2.41
2.30
2.19

2.75
2.73
2.71
2.69
2.67

2.91
2.87
2.84
2.81
2.78

3.20
3.12
3.06
3.01
2.96

3.85
3.66
3.51
3.39
3.29

6.76
5.60
4.90
4.43
4.10

8
956.7
39.37
14.54
8.98

2.57
2.45
2.33
2.22
2.11

2.68
2.65
2.63
2.61
2.59

2.84
2.80
2.76
2.73
2.70

3.12
3.05
2.98
2.93
2.88

3.78
3.59
3.44
3.31
3.21

6.68
5.52
4.82
4.36
4.03

9
963.3
39.39
14.47
8.90

2.51
2.39
2.27
2.16
2.05

2.61
2.59
2.57
2.55
2.53

2.77
2.73
2.70
2.67
2.64

3.06
2.99
2.92
2.87
2.82

3.72
3.53
3.37
3.25
3.15

6.62
5.46
4.76
4.30
3.96

r1
10
968.6
39.40
14.42
8.84

2.41
2.29
2.17
2.05
1.94

2.51
2.49
2.47
2.45
2.43

2.68
2.64
2.60
2.57
2.54

2.96
2.89
2.82
2.77
2.72

3.62
3.43
3.28
3.15
3.05

6.52
5.37
4.67
4.20
3.87

12
976.7
39.41
14.34
8.75

2.31
2.18
2.06
1.94
1.83

2.41
2.39
2.36
2.34
2.32

2.57
2.53
2.50
2.47
2.44

2.86
2.79
2.72
2.67
2.62

3.52
3.33
3.18
3.05
2.95

6.43
5.27
4.57
4.10
3.77

15
984.9
39.43
14.25
8.66

2.20
2.07
1.94
1.82
1.71

2.30
2.28
2.25
2.23
2.21

2.46
2.42
2.39
2.36
2.33

2.76
2.68
2.62
2.56
2.51

3.42
3.23
3.07
2.95
2.84

6.33
5.17
4.47
4.00
3.67

20
993.1
39.45
14.17
8.56

2.14
2.01
1.88
1.76
1.64

2.24
2.22
2.19
2.17
2.15

2.41
2.37
2.33
2.30
2.27

2.70
2.63
2.56
2.50
2.45

3.37
3.17
3.02
2.89
2.79

6.28
5.12
4.41
3.95
3.61

2.07
1.94
1.82
1.69
1.57

2.18
2.16
2.13
2.11
2.09

2.35
2.31
2.27
2.24
2.21

2.64
2.57
2.50
2.44
2.39

3.31
3.12
2.96
2.84
2.73

6.23
5.07
4.36
3.89
3.56

2.01
1.88
1.74
1.61
1.48

2.12
2.09
2.07
2.05
2.03

2.29
2.25
2.21
2.18
2.15

2.59
2.51
2.44
2.38
2.33

3.26
3.06
2.91
2.78
2.67

6.18
5.01
4.31
3.84
3.51

24
30
40
997.2 1001 1006
39.46 39.46 39.47
14.12 14.08 14.04
8.51
8.46
8.41

1.94
1.80
1.67
1.53
1.39

2.05
2.03
2.00
1.98
1.96

2.22
2.18
2.14
2.11
2.08

2.52
2.45
2.38
2.32
2.27

3.20
3.00
2.85
2.72
2.61

6.12
4.96
4.25
3.78
3.45

60
1010
39.48
13.99
8.36

1.87
1.72
1.58
1.43
1.27

1.98
1.95
1.93
1.91
1.89

2.16
2.11
2.08
2.04
2.01

2.46
2.38
2.32
2.26
2.20

3.14
2.94
2.79
2.66
2.55

6.07
4.90
4.20
3.73
3.39

120
1014
39.49
13.95
8.31

1.79
1.64
1.48
1.31
1.00

1.91
1.88
1.85
1.83
1.81

2.09
2.04
2.00
1.97
1.94

2.40
2.32
2.25
2.19
2.13

3.08
2.88
2.72
2.60
2.49

6.02
4.85
4.14
3.67
3.33


1018
39.50
13.90
8.26

Statistical Tables

37

1
4052
98.50
34.12
21.20

10.04
9.65
9.33
9.07
8.86

8.68
8.53
8.40
8.29
8.18

8.10
8.02
7.95
7.88
7.82

7.77
7.72
7.68
7.64
7.60

7.56
7.31
7.08
6.85
6.63

5
6
7
8
9

10
11
12
13
14

15
16
17
18
19

20
21
22
23
24

25
26
27
28
29

30
40
60
120


´
CATOLICA-LISBON

r2

16.26
13.75
12.25
11.26
10.56

F =0.99
1
2
3
4

Snedcor’s F distribution

5.39
5.18
4.98
4.79
4.61

5.57
5.53
5.49
5.45
5.42

5.85
5.78
5.72
5.66
5.61

6.36
6.23
6.11
6.01
5.93

7.56
7.21
6.93
6.70
6.51

13.27
10.92
9.55
8.65
8.02

2
4999
99.00
30.82
18.00

4.51
4.31
4.13
3.95
3.78

4.68
4.64
4.60
4.57
4.54

4.94
4.87
4.82
4.76
4.72

5.42
5.29
5.18
5.09
5.01

6.55
6.22
5.95
5.74
5.56

12.06
9.78
8.45
7.59
6.99

3
5403
99.17
29.46
16.69

4.02
3.83
3.65
3.48
3.32

4.18
4.14
4.11
4.07
4.04

4.43
4.37
4.31
4.26
4.22

4.89
4.77
4.67
4.58
4.50

5.99
5.67
5.41
5.21
5.04

11.39
9.15
7.85
7.01
6.42

4
5625
99.25
28.71
15.98

3.70
3.51
3.34
3.17
3.02

3.85
3.82
3.78
3.75
3.73

4.10
4.04
3.99
3.94
3.90

4.56
4.44
4.34
4.25
4.17

5.64
5.32
5.06
4.86
4.69

10.97
8.75
7.46
6.63
6.06

5
5764
99.30
28.24
15.52

3.47
3.29
3.12
2.96
2.80

3.63
3.59
3.56
3.53
3.50

3.87
3.81
3.76
3.71
3.67

4.32
4.20
4.10
4.01
3.94

5.39
5.07
4.82
4.62
4.46

10.67
8.47
7.19
6.37
5.80

6
5859
99.33
27.91
15.21

3.30
3.12
2.95
2.79
2.64

3.46
3.42
3.39
3.36
3.33

3.70
3.64
3.59
3.54
3.50

4.14
4.03
3.93
3.84
3.77

5.20
4.89
4.64
4.44
4.28

10.46
8.26
6.99
6.18
5.61

7
5928
99.36
27.67
14.98

3.17
2.99
2.82
2.66
2.51

3.32
3.29
3.26
3.23
3.20

3.56
3.51
3.45
3.41
3.36

4.00
3.89
3.79
3.71
3.63

5.06
4.74
4.50
4.30
4.14

10.29
8.10
6.84
6.03
5.47

8
5981
99.37
27.49
14.80

3.07
2.89
2.72
2.56
2.41

3.22
3.18
3.15
3.12
3.09

3.46
3.40
3.35
3.30
3.26

3.89
3.78
3.68
3.60
3.52

4.94
4.63
4.39
4.19
4.03

10.16
7.98
6.72
5.91
5.35

9
6022
99.39
27.35
14.66

2.98
2.80
2.63
2.47
2.32

3.13
3.09
3.06
3.03
3.00

3.37
3.31
3.26
3.21
3.17

3.80
3.69
3.59
3.51
3.43

4.85
4.54
4.30
4.10
3.94

10.05
7.87
6.62
5.81
5.26

r1
10
6056
99.40
27.23
14.55

2.84
2.66
2.50
2.34
2.18

2.99
2.96
2.93
2.90
2.87

3.23
3.17
3.12
3.07
3.03

3.67
3.55
3.46
3.37
3.30

4.71
4.40
4.16
3.96
3.80

9.89
7.72
6.47
5.67
5.11

12
6106
99.42
27.05
14.37

2.70
2.52
2.35
2.19
2.04

2.85
2.81
2.78
2.75
2.73

3.09
3.03
2.98
2.93
2.89

3.52
3.41
3.31
3.23
3.15

4.56
4.25
4.01
3.82
3.66

9.72
7.56
6.31
5.52
4.96

15
6157
99.43
26.87
14.20

2.55
2.37
2.20
2.03
1.88

2.70
2.66
2.63
2.60
2.57

2.94
2.88
2.83
2.78
2.74

3.37
3.26
3.16
3.08
3.00

4.41
4.10
3.86
3.66
3.51

9.55
7.40
6.16
5.36
4.81

20
6209
99.45
26.69
14.02

2.47
2.29
2.12
1.95
1.79

2.62
2.58
2.55
2.52
2.49

2.86
2.80
2.75
2.70
2.66

3.29
3.18
3.08
3.00
2.92

4.33
4.02
3.78
3.59
3.43

9.47
7.31
6.07
5.28
4.73

24
6235
99.46
26.60
13.93

2.39
2.20
2.03
1.86
1.70

2.54
2.50
2.47
2.44
2.41

2.78
2.72
2.67
2.62
2.58

3.21
3.10
3.00
2.92
2.84

4.25
3.94
3.70
3.51
3.35

9.38
7.23
5.99
5.20
4.65

30
6261
99.47
26.50
13.84

2.30
2.11
1.94
1.76
1.59

2.45
2.42
2.38
2.35
2.33

2.69
2.64
2.58
2.54
2.49

3.13
3.02
2.92
2.84
2.76

4.17
3.86
3.62
3.43
3.27

9.29
7.14
5.91
5.12
4.57

40
6287
99.47
26.41
13.75

2.21
2.02
1.84
1.66
1.47

2.36
2.33
2.29
2.26
2.23

2.61
2.55
2.50
2.45
2.40

3.05
2.93
2.83
2.75
2.67

4.08
3.78
3.54
3.34
3.18

9.20
7.06
5.82
5.03
4.48

60
6313
99.48
26.32
13.65

2.11
1.92
1.73
1.53
1.32

2.27
2.23
2.20
2.17
2.14

2.52
2.46
2.40
2.35
2.31

2.96
2.84
2.75
2.66
2.58

4.00
3.69
3.45
3.25
3.09

9.11
6.97
5.74
4.95
4.40

120
6339
99.49
26.22
13.56

2.01
1.80
1.60
1.38
1.00

2.17
2.13
2.10
2.06
2.03

2.42
2.36
2.31
2.26
2.21

2.87
2.75
2.65
2.57
2.49

3.91
3.60
3.36
3.17
3.00

9.02
6.88
5.65
4.86
4.31


6366
99.50
26.13
13.46

Statistical Tables

38

5.82
5.73
5.65
5.58
5.52

5.24
4.98
4.73
4.50
4.28

9.48
9.41
9.34
9.28
9.23

25
26
27
28
29

6.99
6.89
6.81
6.73
6.66

6.48
6.30
6.16
6.03
5.92

30
9.18
6.35
40
8.83
6.07
60
8.49
5.79
120
8.18
5.54

7.88
5.30
∗ multiplicar por 10

9.94
9.83
9.73
9.63
9.55

20
21
22
23
24

7.70
7.51
7.35
7.21
7.09

8.08
7.60
7.23
6.93
6.68

16.53
12.92
10.88
9.60
8.72

3
2161∗
199.2
47.47
24.26

5.46
5.41
5.36
5.32
5.28

10.80
10.58
10.38
10.22
10.07

15
16
17
18
19

9.43
8.91
8.51
8.19
7.92

18.31
14.54
12.40
11.04
10.11

2
2000∗
199.0
49.80
26.28

6.60
6.54
6.49
6.44
6.40

12.83
12.23
11.75
11.37
11.06

10
11
12
13
14

´
CATOLICA-LISBON

r2

22.78
18.63
16.24
14.69
13.61

5
6
7
8
9

F =0.995
1
1 1621∗
2
198.5
3
55.55
4
31.33

Snedcor’s F distribution

4.62
4.37
4.14
3.92
3.72

4.84
4.79
4.74
4.70
4.66

5.17
5.09
5.02
4.95
4.89

5.80
5.64
5.50
5.37
5.27

7.34
6.88
6.52
6.23
6.00

15.56
12.03
10.05
8.81
7.96

4
2250∗
199.2
46.19
23.15

4.23
3.99
3.76
3.55
3.35

4.43
4.38
4.34
4.30
4.26

4.76
4.68
4.61
4.54
4.49

5.37
5.21
5.07
4.96
4.85

6.87
6.42
6.07
5.79
5.56

14.94
11.46
9.52
8.30
7.47

5
2306∗
199.3
45.39
22.46

3.95
3.71
3.49
3.28
3.09

4.15
4.10
4.06
4.02
3.98

4.47
4.39
4.32
4.26
4.20

5.07
4.91
4.78
4.66
4.56

6.54
6.10
5.76
5.48
5.26

14.51
11.07
9.16
7.95
7.13

6
2344∗
199.3
44.84
21.97

3.74
3.51
3.29
3.09
2.90

3.94
3.89
3.85
3.81
3.77

4.26
4.18
4.11
4.05
3.99

4.85
4.69
4.56
4.44
4.34

6.30
5.86
5.52
5.25
5.03

14.20
10.79
8.89
7.69
6.88

7
2371∗
199.4
44.43
21.62

3.58
3.35
3.13
2.93
2.74

3.78
3.73
3.69
3.65
3.61

4.09
4.01
3.94
3.88
3.83

4.67
4.52
4.39
4.28
4.18

6.12
5.68
5.35
5.08
4.86

13.96
10.57
8.68
7.50
6.69

8
2393∗
199.4
44.13
21.35

3.45
3.22
3.01
2.81
2.62

3.64
3.60
3.56
3.52
3.48

3.96
3.88
3.81
3.75
3.69

4.54
4.38
4.25
4.14
4.04

5.97
5.54
5.20
4.94
4.72

13.77
10.39
8.51
7.34
6.54

9
2409∗
199.4
43.88
21.14

3.34
3.12
2.90
2.71
2.52

3.54
3.49
3.45
3.41
3.38

3.85
3.77
3.70
3.64
3.59

4.42
4.27
4.14
4.03
3.93

5.85
5.42
5.09
4.82
4.60

13.62
10.25
8.38
7.21
6.42

r1
10
2422∗
199.4
43.69
20.97

3.18
2.95
2.74
2.54
2.36

3.37
3.33
3.28
3.25
3.21

3.68
3.60
3.54
3.47
3.42

4.25
4.10
3.97
3.86
3.76

5.66
5.24
4.91
4.64
4.43

13.38
10.03
8.18
7.01
6.23

12
2443∗
199.4
43.39
20.70

3.01
2.78
2.57
2.37
2.19

3.20
3.15
3.11
3.07
3.04

3.50
3.43
3.36
3.30
3.25

4.07
3.92
3.79
3.68
3.59

5.47
5.05
4.72
4.46
4.25

13.15
9.81
7.97
6.81
6.03

15
2463∗
199.4
43.08
20.44

2.82
2.60
2.39
2.19
2.00

3.01
2.97
2.93
2.89
2.86

3.32
3.24
3.18
3.12
3.06

3.88
3.73
3.61
3.50
3.40

5.27
4.86
4.53
4.27
4.06

12.90
9.59
7.75
6.61
5.83

20
2484∗
199.4
42.78
20.17

2.73
2.50
2.29
2.09
1.90

2.92
2.87
2.83
2.79
2.76

3.22
3.15
3.08
3.02
2.97

3.79
3.64
3.51
3.40
3.31

5.17
4.76
4.43
4.17
3.96

12.78
9.47
7.64
6.50
5.73

24
2494∗
199.5
42.62
20.03

2.63
2.40
2.19
1.98
1.79

2.82
2.77
2.73
2.69
2.66

3.12
3.05
2.98
2.92
2.87

3.69
3.54
3.41
3.30
3.21

5.07
4.65
4.33
4.07
3.86

12.66
9.36
7.53
6.40
5.62

30
2504∗
199.5
42.47
19.89

2.52
2.30
2.08
1.87
1.67

2.72
2.67
2.63
2.59
2.56

3.02
2.95
2.88
2.82
2.77

3.58
3.44
3.31
3.20
3.11

4.97
4.55
4.23
3.97
3.76

12.53
9.24
7.42
6.29
5.52

40
2515∗
199.5
42.31
19.75

2.42
2.18
1.96
1.75
1.53

2.61
2.56
2.52
2.48
2.45

2.92
2.84
2.77
2.71
2.66

3.48
3.33
3.21
3.10
3.00

4.86
4.45
4.12
3.87
3.66

12.40
9.12
7.31
6.18
5.41

60
2525∗
199.5
42.15
19.61

2.30
2.06
1.83
1.61
1.36

2.50
2.45
2.41
2.37
2.33

2.81
2.73
2.66
2.60
2.55

3.37
3.22
3.10
2.99
2.89

4.75
4.34
4.01
3.76
3.55

12.27
9.00
7.19
6.06
5.30

120
2536∗
199.5
41.99
19.47

Statistical Tables

2.18
1.93
1.69
1.43
1.00

2.38
2.33
2.25
2.29
2.24

2.69
2.61
2.55
2.48
2.43

3.26
3.11
2.98
2.87
2.78

4.64
4.23
3.90
3.65
3.44

12.14
8.88
7.08
5.95
5.19


2547∗
199.5
41.83
19.32

39

8.10
7.94
7.80
7.67
7.55

7.05
6.59
6.17
5.78
5.42

13.88
13.74
13.61
13.50
13.39

25
26
27
28
29

9.95
9.77
9.61
9.47
9.34

9.34
9.01
8.73
8.49
8.28

30 13.29
8.77
40 12.61
8.25
60 11.97
7.77
120 11.38
7.32

10.83
6.91
∗ multiplicar por 100

14.82
14.59
14.38
14.20
14.03

20
21
22
23
24

11.34
10.97
10.66
10.39
10.16

12.55
11.56
10.80
10.21
9.73

33.20
23.70
18.77
15.83
13.90

3
5404∗
999.2
141.1
56.18

7.45
7.36
7.27
7.19
7.12

16.59
16.12
15.72
15.38
15.08

15
16
17
18
19

14.91
13.81
12.97
12.31
11.78

37.12
27.00
21.69
18.49
16.39

2
5000∗
999.0
148.5
61.25

9.22
9.12
9.02
8.93
8.85

21.04
19.69
18.64
17.82
17.14

10
11
12
13
14

´
CATOLICA-LISBON

r2

47.18
35.51
29.25
25.41
22.86

5
6
7
8
9

F =0.999
1
1
4053∗
2
998.5
3
167.0
4
74.14

Snedcor’s F distribution

6.12
5.70
5.31
4.95
4.62

6.49
6.41
6.33
6.25
6.19

7.10
6.95
6.81
6.70
6.59

8.25
7.94
7.68
7.46
7.27

11.28
10.35
9.63
9.07
8.62

31.09
21.92
17.20
14.39
12.56

4
5625∗
999.2
137.1
53.44

5.53
5.13
4.76
4.42
4.10

5.89
5.80
5.73
5.66
5.59

6.46
6.32
6.19
6.08
5.98

7.57
7.27
7.02
6.81
6.62

10.48
9.58
8.89
8.35
7.92

29.75
20.80
16.21
13.48
11.71

5
5764∗
999.3
134.6
51.71

5.12
4.73
4.37
4.04
3.74

5.46
5.38
5.31
5.24
5.18

6.02
5.88
5.76
5.65
5.55

7.09
6.80
6.56
6.35
6.18

9.93
9.05
8.38
7.86
7.44

28.83
20.03
15.52
12.86
11.13

6
5859∗
999.3
132.8
50.53

4.82
4.44
4.09
3.77
3.47

5.15
5.07
5.00
4.93
4.87

5.69
5.56
5.44
5.33
5.23

6.74
6.46
6.22
6.02
5.85

9.52
8.66
8.00
7.49
7.08

28.16
19.46
15.02
12.40
10.70

7
5929
999.4
131.6
49.66

4.58
4.21
3.86
3.55
3.27

4.91
4.83
4.76
4.69
4.64

5.44
5.31
5.19
5.09
4.99

6.47
6.19
5.96
5.76
5.59

9.20
8.35
7.71
7.21
6.80

27.65
19.03
14.63
12.05
10.37

8
5981∗
999.4
130.6
49.00

4.39
4.02
3.69
3.38
3.10

4.71
4.64
4.57
4.50
4.45

5.24
5.11
4.99
4.89
4.80

6.26
5.98
5.75
5.56
5.39

8.96
8.12
7.48
6.98
6.58

27.24
18.69
14.33
11.77
10.11

9
6023∗
999.4
129.9
48.47

4.24
3.87
3.54
3.24
2.96

4.56
4.48
4.41
4.35
4.29

5.08
4.95
4.83
4.73
4.64

6.08
5.81
5.58
5.39
5.22

8.75
7.92
7.29
6.80
6.40

26.92
18.41
14.08
11.54
9.89

r1
10
6056∗
999.4
129.2
48.05

4.00
3.64
3.32
3.02
2.74

4.31
4.24
4.17
4.11
4.05

4.82
4.70
4.58
4.48
4.39

5.81
5.55
5.32
5.13
4.97

8.45
7.63
7.00
6.52
6.13

26.42
17.99
13.71
11.19
9.57

12
6107∗
999.4
128.3
47.41

3.75
3.40
3.08
2.78
2.51

4.06
3.99
3.92
3.86
3.80

4.56
4.44
4.33
4.23
4.14

5.54
5.27
5.05
4.87
4.70

8.13
7.32
6.71
6.23
5.85

25.91
17.56
13.32
10.84
9.24

15
6158∗
999.4
127.4
46.76

3.49
3.14
2.83
2.53
2.27

3.79
3.72
3.66
3.60
3.54

4.29
4.17
4.06
3.96
3.87

5.25
4.99
4.78
4.59
4.43

7.80
7.01
6.40
5.93
5.56

25.39
17.12
12.93
10.48
8.90

20
6209∗
999.4
126.4
46.10

3.36
3.01
2.69
2.40
2.13

3.66
3.59
3.52
3.46
3.41

4.15
4.03
3.92
3.82
3.74

5.10
4.85
4.63
4.45
4.29

7.64
6.85
6.25
5.78
5.41

25.13
16.90
12.73
10.30
8.72

24
6235∗
999.5
125.9
45.77

3.22
2.87
2.55
2.26
1.99

3.52
3.44
3.38
3.32
3.27

4.00
3.88
3.78
3.68
3.59

4.95
4.70
4.48
4.30
4.14

7.47
6.68
6.09
5.63
5.25

24.87
16.67
12.53
10.11
8.55

30
6261∗
999.5
125.4
45.43

3.07
2.73
2.41
2.11
1.84

3.37
3.30
3.23
3.18
3.12

3.86
3.74
3.63
3.53
3.45

4.80
4.54
4.33
4.15
3.99

7.30
6.52
5.93
5.47
5.10

24.60
16.44
12.33
9.92
8.37

40
6287∗
999.5
125.0
45.09

2.92
2.57
2.25
1.95
1.66

3.22
3.15
3.08
3.02
2.97

3.70
3.58
3.48
3.38
3.29

4.64
4.39
4.18
4.00
3.84

7.12
6.35
5.76
5.30
4.94

24.33
16.21
12.12
9.73
8.19

60
6313∗
999.5
124.5
44.75

2.76
2.41
2.08
1.77
1.45

3.06
2.99
2.92
2.86
2.81

3.54
3.42
3.32
3.22
3.14

4.47
4.23
4.02
3.84
3.68

6.94
6.18
5.59
5.14
4.77

24.06
15.98
11.91
9.53
8.00

120
6340∗
999.5
124.0
44.40

Statistical Tables

2.59
2.23
1.89
1.54
1.00

2.89
2.82
2.75
2.69
2.64

3.38
3.26
3.15
3.05
2.97

4.31
4.05
3.85
3.67
3.51

6.76
6.00
5.42
4.97
4.69

23.79
15.75
11.79
15.75
7.81


6366∗
999.3
123.46
44.05

40

Durbin-Watson Statistic

41

Durbin-Watson Statistic α = 5% n 15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
45
50
55
60
65
70
75
80
85
90
95
100

k =1 dL dU
1.08 1.36
1.10 1.37
1.13 1.38
1.16 1.39
1.18 1.40
1.20 1.41
1.22 1.42
1.24 1.43
1.26 1.44
1.27 1.45
1.29 1.45
1.30 1.46
1.32 1.47
1.33 1.48
1.34 1.48
1.35 1.49
1.36 1.50
1.37 1.50
1.38 1.51
1.39 1.51
1.40 1.52
1.41 1.52
1.42 1.53
1.43 1.54
1.43 1.54
1.44 1.54
1.48 1.57
1.50 1.59
1.53 1.60
1.55 1.62
1.57 1.63
1.58 1.64
1.60 1.65
1.61 1.66
1.62 1.67
1.63 1.68
1.64 1.69
1.65 1.69

k =2 dL dU
0.95 1.54
0.98 1.54
1.02 1.54
1.05 1.53
1.08 1.53
1.10 1.54
1.13 1.54
1.15 1.54
1.17 1.54
1.19 1.55
1.21 1.55
1.22 1.55
1.24 1.56
1.26 1.56
1.27 1.56
1.28 1.57
1.30 1.57
1.31 1.57
1.32 1.58
1.33 1.58
1.34 1.58
1.35 1.59
1.36 1.59
1.37 1.59
1.38 1.60
1.39 1.60
1.43 1.62
1.46 1.63
1.49 1.64
1.51 1.65
1.54 1.66
1.55 1.67
1.57 1.68
1.59 1.69
1.60 1.70
1.61 1.70
1.62 1.71
1.63 1.72

k =3 dL dU
0.82 1.75
0.86 1.73
0.90 1.71
0.93 1.69
0.97 1.68
1.00 1.68
1.03 1.67
1.05 1.66
1.08 1.66
1.10 1.66
1.12 1.66
1.14 1.65
1.16 1.65
1.18 1.65
1.20 1.65
1.21 1.65
1.23 1.65
1.24 1.65
1.26 1.65
1.27 1.65
1.28 1.65
1.29 1.65
1.31 1.66
1.32 1.66
1.33 1.66
1.34 1.66
1.38 1.67
1.42 1.67
1.45 1.68
1.48 1.69
1.50 1.70
1.52 1.70
1.54 1.71
1.56 1.72
1.57 1.72
1.59 1.73
1.60 1.73
1.61 1.74

k =4 dL dU
0.69 1.97
0.74 1.93
0.78 1.90
0.82 1.87
0.86 1.85
0.90 1.83
0.93 1.81
0.96 1.80
0.99 1.79
1.01 1.78
1.04 1.77
1.06 1.76
1.08 1.76
1.10 1.75
1.12 1.74
1.14 1.74
1.16 1.74
1.18 1.73
1.19 1.73
1.21 1.73
1.22 1.73
1.24 1.73
1.25 1.72
1.26 1.72
1.27 1.72
1.29 1.72
1.34 1.72
1.38 1.72
1.41 1.72
1.44 1.73
1.47 1.73
1.49 1.74
1.51 1.74
1.53 1.74
1.55 1.75
1.57 1.75
1.58 1.75
1.59 1.76

k =5 dL dU
0.56 2.21
0.62 2.15
0.67 2.10
0.71 2.06
0.75 2.02
0.79 1.99
0.83 1.96
0.86 1.94
0.90 1.92
0.93 1.90
0.95 1.89
0.98 1.88
1.01 1.86
1.03 1.85
1.05 1.84
1.07 1.83
1.09 1.83
1.11 1.82
1.13 1.81
1.15 1.81
1.16 1.80
1.18 1.80
1.19 1.80
1.21 1.79
1.22 1.79
1.23 1.79
1.29 1.78
1.34 1.77
1.38 1.77
1.41 1.77
1.44 1.77
1.46 1.77
1.49 1.77
1.51 1.77
1.52 1.77
1.54 1.78
1.56 1.78
1.57 1.78

k : number of explanatory variables, excluding the constant term.

´
CATOLICA-LISBON

Statistical Tables

Durbin-Watson Statistic

42

α = 2.5% n 15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
45
50
55
60
65
70
75
80
85
90
95
100

k =1 dL dU
0.95 1.23
0.98 1.24
1.01 1.25
1.03 1.26
1.06 1.28
1.08 1.28
1.10 1.30
1.12 1.31
1.14 1.32
1.16 1.33
1.18 1.34
1.19 1.35
1.21 1.36
1.22 1.37
1.24 1.38
1.25 1.38
1.26 1.39
1.27 1.40
1.28 1.41
1.29 1.41
1.30 1.42
1.31 1.43
1.32 1.43
1.33 1.44
1.34 1.44
1.35 1.45
1.39 1.48
1.42 1.50
1.45 1.52
1.47 1.54
1.49 1.55
1.51 1.57
1.53 1.58
1.54 1.59
1.56 1.60
1.57 1.61
1.58 1.62
1.59 1.63

k =2 dL dU
0.83 1.40
0.86 1.40
0.90 1.40
0.93 1.40
0.96 1.41
0.99 1.41
1.01 1.41
1.04 1.42
1.06 1.42
1.08 1.43
1.10 1.43
1.12 1.44
1.13 1.44
1.15 1.45
1.17 1.45
1.18 1.46
1.20 1.47
1.21 1.47
1.22 1.48
1.24 1.48
1.25 1.48
1.26 1.49
1.27 1.49
1.28 1.50
1.29 1.50
1.30 1.51
1.34 1.53
1.38 1.54
1.41 1.56
1.44 1.57
1.46 1.59
1.48 1.60
1.50 1.61
1.52 1.62
1.53 1.63
1.55 1.64
1.56 1.65
1.57 1.65

k =3 dL dU
0.71 1.61
0.75 1.59
0.79 1.58
0.82 1.56
0.86 1.55
0.89 1.55
0.92 1.54
0.95 1.54
0.97 1.54
1.00 1.54
1.02 1.54
1.04 1.54
1.06 1.54
1.08 1.54
1.10 1.54
1.12 1.54
1.13 1.55
1.15 1.55
1.16 1.55
1.17 1.55
1.19 1.55
1.20 1.56
1.21 1.56
1.23 1.56
1.24 1.56
1.25 1.57
1.30 1.58
1.34 1.59
1.37 1.60
1.40 1.61
1.43 1.62
1.45 1.63
1.47 1.64
1.49 1.65
1.51 1.65
1.53 1.66
1.54 1.67
1.55 1.67

k =4 dL dU
0.59 1.84
0.64 1.80
0.68 1.77
0.72 1.74
0.76 1.72
0.79 1.70
0.83 1.69
0.86 1.68
0.89 1.67
0.91 1.66
0.94 1.65
0.96 1.65
0.99 1.64
1.01 1.64
1.03 1.63
1.05 1.63
1.07 1.63
1.08 1.63
1.10 1.63
1.12 1.63
1.13 1.63
1.15 1.63
1.16 1.62
1.17 1.62
1.19 1.63
1.20 1.63
1.25 1.63
1.30 1.64
1.33 1.64
1.37 1.65
1.40 1.66
1.42 1.66
1.45 1.67
1.47 1.67
1.49 1.68
1.50 1.69
1.52 1.69
1.53 1.70

k =5 dL dU
0.48 2.09
0.53 2.03
0.57 1.98
0.62 1.93
0.66 1.90
0.70 1.87
0.73 1.84
0.77 1.82
0.80 1.80
0.83 1.79
0.86 1.77
0.88 1.76
0.91 1.75
0.93 1.74
0.96 1.73
0.98 1.73
1.00 1.72
1.02 1.71
1.04 1.71
1.06 1.70
1.07 1.70
1.09 1.70
1.10 1.70
1.12 1.70
1.13 1.69
1.15 1.69
1.21 1.69
1.26 1.69
1.30 1.69
1.33 1.69
1.36 1.69
1.39 1.70
1.42 1.70
1.44 1.70
1.46 1.71
1.48 1.71
1.50 1.71
1.51 1.72

k : number of explanatory variables, excluding the constant term.

´
CATOLICA-LISBON

Statistical Tables

Durbin-Watson Statistic

43

α = 1% n 15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
45
50
55
60
65
70
75
80
85
90
95
100

k =1 dL dU
0.81 1.07
0.84 1.09
0.87 1.10
0.90 1.12
0.93 1.13
0.95 1.15
0.97 1.16
1.00 1.17
1.02 1.19
1.04 1.20
1.05 1.21
1.07 1.22
1.09 1.23
1.10 1.24
1.12 1.25
1.13 1.26
1.15 1.27
1.16 1.28
1.17 1.29
1.18 1.30
1.19 1.31
1.21 1.32
1.22 1.32
1.23 1.33
1.24 1.34
1.25 1.34
1.29 1.38
1.32 1.40
1.36 1.43
1.38 1.45
1.41 1.47
1.43 1.49
1.45 1.50
1.47 1.52
1.48 1.53
1.50 1.54
1.51 1.55
1.52 1.56

k =2 dL dU
0.70 1.25
0.74 1.25
0.77 1.25
0.80 1.26
0.83 1.26
0.86 1.27
0.89 1.27
0.91 1.28
0.94 1.29
0.96 1.30
0.98 1.30
1.00 1.31
1.02 1.32
1.04 1.32
1.05 1.33
1.07 1.34
1.08 1.34
1.10 1.35
1.11 1.36
1.13 1.36
1.14 1.37
1.15 1.38
1.16 1.38
1.18 1.39
1.19 1.39
1.20 1.40
1.24 1.42
1.28 1.45
1.32 1.47
1.35 1.48
1.38 1.50
1.40 1.52
1.42 1.53
1.44 1.54
1.46 1.55
1.47 1.56
1.49 1.57
1.50 1.58

k =3 dL dU
0.59 1.46
0.63 1.44
0.67 1.43
0.71 1.42
0.74 1.41
0.77 1.41
0.80 1.41
0.83 1.40
0.86 1.40
0.88 1.41
0.90 1.41
0.93 1.41
0.95 1.41
0.97 1.41
0.99 1.42
1.01 1.42
1.02 1.42
1.04 1.43
1.05 1.43
1.07 1.43
1.08 1.44
1.10 1.44
1.11 1.45
1.12 1.45
1.14 1.45
1.15 1.46
1.20 1.48
1.24 1.49
1.28 1.51
1.32 1.52
1.35 1.53
1.37 1.55
1.39 1.56
1.42 1.57
1.43 1.58
1.45 1.59
1.47 1.60
1.48 1.60

k =4 dL dU
0.49 1.70
0.53 1.66
0.57 1.63
0.61 1.60
0.65 1.58
0.68 1.57
0.72 1.55
0.75 1.54
0.77 1.53
0.80 1.53
0.83 1.52
0.85 1.52
0.88 1.51
0.90 1.51
0.92 1.51
0.94 1.51
0.96 1.51
0.98 1.51
1.00 1.51
1.01 1.51
1.03 1.51
1.04 1.51
1.06 1.51
1.07 1.52
1.09 1.52
1.10 1.52
1.16 1.53
1.20 1.54
1.25 1.55
1.28 1.56
1.31 1.57
1.34 1.58
1.37 1.59
1.39 1.60
1.41 1.60
1.43 1.61
1.45 1.62
1.46 1.63

k =5 dL dU
0.39 1.96
0.44 1.91
0.48 1.85
0.52 1.80
0.56 1.77
0.60 1.74
0.63 1.71
0.66 1.69
0.70 1.67
0.72 1.66
0.75 1.65
0.78 1.64
0.81 1.63
0.83 1.62
0.85 1.61
0.88 1.61
0.90 1.60
0.92 1.60
0.94 1.59
0.95 1.59
0.97 1.59
0.99 1.59
1.00 1.59
1.02 1.58
1.03 1.58
1.05 1.58
1.11 1.58
1.16 1.59
1.21 1.59
1.25 1.60
1.28 1.61
1.31 1.61
1.34 1.62
1.36 1.62
1.39 1.63
1.41 1.64
1.42 1.64
1.44 1.65

k : number of explanatory variables, excluding the constant term.

´
CATOLICA-LISBON

Statistical Tables

Kolmogorov-Smirnov acceptance limits

44

Kolmogorov-Smirnov acceptance limits

n
1
2
3
4
5

20%
0.900
0.684
0.565
0.494
0.446

15%
0.925
0.726
0.597
0.525
0.474

α
10%
0.950
0.776
0.642
0.564
0.510

5%
0.975
0.842
0.708
0.624
0.565

1%
0.995
0.929
0.828
0.733
0.669

6
7
8
9
10

0.410
0.381
0.358
0.339
0.322

0.436
0.405
0.381
0.360
0.342

0.470
0.438
0.411
0.388
0.368

0.521
0.486
0.457
0.432
0.410

0.618
0.577
0.543
0.514
0.490

11
12
13
14
15

0.307
0.295
0.284
0.274
0.266

0.326
0.313
0.302
0.292
0.283

0.352
0.338
0.325
0.314
0.304

0.391
0.375
0.361
0.349
0.338

0.468
0.450
0.433
0.418
0.404

16
17
18
19
20

0.258
0.250
0.244
0.237
0.231

0.274
0.266
0.259
0.252
0.246

0.295
0.286
0.278
0.272
0.264

0.328
0.318
0.309
0.301
0.294

0.392
0.381
0.371
0.363
0.356

25
30
35

0.210
0.190
0.180
1.07
n

0.220
0.200
0.190
1.14
n

0.240
0.220
0.210
1.22
n

0.270
0.240
0.230
1.36
n

0.320
0.290
0.270
1.63
n

> 35

´
CATOLICA-LISBON

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