Cumulative probabilities for the standard normal distribution
Table A.1: Cumulative proportions \(p\) for the standard normal distribution.
|
z
|
p
|
z
|
p
|
z
|
p
|
z
|
p
|
z
|
p
|
z
|
p
|
|
-4.00
|
0.0000
|
-1.43
|
0.0764
|
-0.71
|
0.239
|
0.01
|
0.504
|
0.73
|
0.7673
|
1.45
|
0.9265
|
|
-3.80
|
0.0001
|
-1.42
|
0.0778
|
-0.70
|
0.242
|
0.02
|
0.508
|
0.74
|
0.7704
|
1.46
|
0.9279
|
|
-3.60
|
0.0002
|
-1.41
|
0.0793
|
-0.69
|
0.245
|
0.03
|
0.512
|
0.75
|
0.7734
|
1.47
|
0.9292
|
|
-3.40
|
0.0003
|
-1.40
|
0.0808
|
-0.68
|
0.248
|
0.04
|
0.516
|
0.76
|
0.7764
|
1.48
|
0.9306
|
|
-3.20
|
0.0007
|
-1.39
|
0.0823
|
-0.67
|
0.251
|
0.05
|
0.520
|
0.77
|
0.7794
|
1.49
|
0.9319
|
|
-3.00
|
0.0013
|
-1.38
|
0.0838
|
-0.66
|
0.255
|
0.06
|
0.524
|
0.78
|
0.7823
|
1.50
|
0.9332
|
|
-2.90
|
0.0019
|
-1.37
|
0.0853
|
-0.65
|
0.258
|
0.07
|
0.528
|
0.79
|
0.7852
|
1.51
|
0.9345
|
|
-2.80
|
0.0026
|
-1.36
|
0.0869
|
-0.64
|
0.261
|
0.08
|
0.532
|
0.80
|
0.7881
|
1.52
|
0.9357
|
|
-2.70
|
0.0035
|
-1.35
|
0.0885
|
-0.63
|
0.264
|
0.09
|
0.536
|
0.81
|
0.7910
|
1.53
|
0.9370
|
|
-2.60
|
0.0047
|
-1.34
|
0.0901
|
-0.62
|
0.268
|
0.10
|
0.540
|
0.82
|
0.7939
|
1.54
|
0.9382
|
|
-2.50
|
0.0062
|
-1.33
|
0.0918
|
-0.61
|
0.271
|
0.11
|
0.544
|
0.83
|
0.7967
|
1.55
|
0.9394
|
|
-2.40
|
0.0082
|
-1.32
|
0.0934
|
-0.60
|
0.274
|
0.12
|
0.548
|
0.84
|
0.7995
|
1.56
|
0.9406
|
|
-2.30
|
0.0107
|
-1.31
|
0.0951
|
-0.59
|
0.278
|
0.13
|
0.552
|
0.85
|
0.8023
|
1.57
|
0.9418
|
|
-2.20
|
0.0139
|
-1.30
|
0.0968
|
-0.58
|
0.281
|
0.14
|
0.556
|
0.86
|
0.8051
|
1.58
|
0.9429
|
|
-2.10
|
0.0179
|
-1.29
|
0.0985
|
-0.57
|
0.284
|
0.15
|
0.560
|
0.87
|
0.8078
|
1.59
|
0.9441
|
|
-2.00
|
0.0228
|
-1.28
|
0.1003
|
-0.56
|
0.288
|
0.16
|
0.564
|
0.88
|
0.8106
|
1.60
|
0.9452
|
|
-1.99
|
0.0233
|
-1.27
|
0.1020
|
-0.55
|
0.291
|
0.17
|
0.567
|
0.89
|
0.8133
|
1.61
|
0.9463
|
|
-1.98
|
0.0239
|
-1.26
|
0.1038
|
-0.54
|
0.295
|
0.18
|
0.571
|
0.90
|
0.8159
|
1.62
|
0.9474
|
|
-1.97
|
0.0244
|
-1.25
|
0.1056
|
-0.53
|
0.298
|
0.19
|
0.575
|
0.91
|
0.8186
|
1.63
|
0.9484
|
|
-1.96
|
0.0250
|
-1.24
|
0.1075
|
-0.52
|
0.302
|
0.20
|
0.579
|
0.92
|
0.8212
|
1.64
|
0.9495
|
|
-1.95
|
0.0256
|
-1.23
|
0.1093
|
-0.51
|
0.305
|
0.21
|
0.583
|
0.93
|
0.8238
|
1.65
|
0.9505
|
|
-1.94
|
0.0262
|
-1.22
|
0.1112
|
-0.50
|
0.309
|
0.22
|
0.587
|
0.94
|
0.8264
|
1.66
|
0.9515
|
|
-1.93
|
0.0268
|
-1.21
|
0.1131
|
-0.49
|
0.312
|
0.23
|
0.591
|
0.95
|
0.8289
|
1.67
|
0.9525
|
|
-1.92
|
0.0274
|
-1.20
|
0.1151
|
-0.48
|
0.316
|
0.24
|
0.595
|
0.96
|
0.8315
|
1.68
|
0.9535
|
|
-1.91
|
0.0281
|
-1.19
|
0.1170
|
-0.47
|
0.319
|
0.25
|
0.599
|
0.97
|
0.8340
|
1.69
|
0.9545
|
|
-1.90
|
0.0287
|
-1.18
|
0.1190
|
-0.46
|
0.323
|
0.26
|
0.603
|
0.98
|
0.8365
|
1.70
|
0.9554
|
|
-1.89
|
0.0294
|
-1.17
|
0.1210
|
-0.45
|
0.326
|
0.27
|
0.606
|
0.99
|
0.8389
|
1.71
|
0.9564
|
|
-1.88
|
0.0301
|
-1.16
|
0.1230
|
-0.44
|
0.330
|
0.28
|
0.610
|
1.00
|
0.8413
|
1.72
|
0.9573
|
|
-1.87
|
0.0307
|
-1.15
|
0.1251
|
-0.43
|
0.334
|
0.29
|
0.614
|
1.01
|
0.8438
|
1.73
|
0.9582
|
|
-1.86
|
0.0314
|
-1.14
|
0.1271
|
-0.42
|
0.337
|
0.30
|
0.618
|
1.02
|
0.8461
|
1.74
|
0.9591
|
|
-1.85
|
0.0322
|
-1.13
|
0.1292
|
-0.41
|
0.341
|
0.31
|
0.622
|
1.03
|
0.8485
|
1.75
|
0.9599
|
|
-1.84
|
0.0329
|
-1.12
|
0.1314
|
-0.40
|
0.345
|
0.32
|
0.626
|
1.04
|
0.8508
|
1.76
|
0.9608
|
|
-1.83
|
0.0336
|
-1.11
|
0.1335
|
-0.39
|
0.348
|
0.33
|
0.629
|
1.05
|
0.8531
|
1.77
|
0.9616
|
|
-1.82
|
0.0344
|
-1.10
|
0.1357
|
-0.38
|
0.352
|
0.34
|
0.633
|
1.06
|
0.8554
|
1.78
|
0.9625
|
|
-1.81
|
0.0351
|
-1.09
|
0.1379
|
-0.37
|
0.356
|
0.35
|
0.637
|
1.07
|
0.8577
|
1.79
|
0.9633
|
|
-1.80
|
0.0359
|
-1.08
|
0.1401
|
-0.36
|
0.359
|
0.36
|
0.641
|
1.08
|
0.8599
|
1.80
|
0.9641
|
|
-1.79
|
0.0367
|
-1.07
|
0.1423
|
-0.35
|
0.363
|
0.37
|
0.644
|
1.09
|
0.8621
|
1.81
|
0.9649
|
|
-1.78
|
0.0375
|
-1.06
|
0.1446
|
-0.34
|
0.367
|
0.38
|
0.648
|
1.10
|
0.8643
|
1.82
|
0.9656
|
|
-1.77
|
0.0384
|
-1.05
|
0.1469
|
-0.33
|
0.371
|
0.39
|
0.652
|
1.11
|
0.8665
|
1.83
|
0.9664
|
|
-1.76
|
0.0392
|
-1.04
|
0.1492
|
-0.32
|
0.374
|
0.40
|
0.655
|
1.12
|
0.8686
|
1.84
|
0.9671
|
|
-1.75
|
0.0401
|
-1.03
|
0.1515
|
-0.31
|
0.378
|
0.41
|
0.659
|
1.13
|
0.8708
|
1.85
|
0.9678
|
|
-1.74
|
0.0409
|
-1.02
|
0.1539
|
-0.30
|
0.382
|
0.42
|
0.663
|
1.14
|
0.8729
|
1.86
|
0.9686
|
|
-1.73
|
0.0418
|
-1.01
|
0.1562
|
-0.29
|
0.386
|
0.43
|
0.666
|
1.15
|
0.8749
|
1.87
|
0.9693
|
|
-1.72
|
0.0427
|
-1.00
|
0.1587
|
-0.28
|
0.390
|
0.44
|
0.670
|
1.16
|
0.8770
|
1.88
|
0.9699
|
|
-1.71
|
0.0436
|
-0.99
|
0.1611
|
-0.27
|
0.394
|
0.45
|
0.674
|
1.17
|
0.8790
|
1.89
|
0.9706
|
|
-1.70
|
0.0446
|
-0.98
|
0.1635
|
-0.26
|
0.397
|
0.46
|
0.677
|
1.18
|
0.8810
|
1.90
|
0.9713
|
|
-1.69
|
0.0455
|
-0.97
|
0.1660
|
-0.25
|
0.401
|
0.47
|
0.681
|
1.19
|
0.8830
|
1.91
|
0.9719
|
|
-1.68
|
0.0465
|
-0.96
|
0.1685
|
-0.24
|
0.405
|
0.48
|
0.684
|
1.20
|
0.8849
|
1.92
|
0.9726
|
|
-1.67
|
0.0475
|
-0.95
|
0.1711
|
-0.23
|
0.409
|
0.49
|
0.688
|
1.21
|
0.8869
|
1.93
|
0.9732
|
|
-1.66
|
0.0485
|
-0.94
|
0.1736
|
-0.22
|
0.413
|
0.50
|
0.691
|
1.22
|
0.8888
|
1.94
|
0.9738
|
|
-1.65
|
0.0495
|
-0.93
|
0.1762
|
-0.21
|
0.417
|
0.51
|
0.695
|
1.23
|
0.8907
|
1.95
|
0.9744
|
|
-1.64
|
0.0505
|
-0.92
|
0.1788
|
-0.20
|
0.421
|
0.52
|
0.698
|
1.24
|
0.8925
|
1.96
|
0.9750
|
|
-1.63
|
0.0516
|
-0.91
|
0.1814
|
-0.19
|
0.425
|
0.53
|
0.702
|
1.25
|
0.8944
|
1.97
|
0.9756
|
|
-1.62
|
0.0526
|
-0.90
|
0.1841
|
-0.18
|
0.429
|
0.54
|
0.705
|
1.26
|
0.8962
|
1.98
|
0.9761
|
|
-1.61
|
0.0537
|
-0.89
|
0.1867
|
-0.17
|
0.433
|
0.55
|
0.709
|
1.27
|
0.8980
|
1.99
|
0.9767
|
|
-1.60
|
0.0548
|
-0.88
|
0.1894
|
-0.16
|
0.436
|
0.56
|
0.712
|
1.28
|
0.8997
|
2.00
|
0.9772
|
|
-1.59
|
0.0559
|
-0.87
|
0.1922
|
-0.15
|
0.440
|
0.57
|
0.716
|
1.29
|
0.9015
|
2.10
|
0.9821
|
|
-1.58
|
0.0571
|
-0.86
|
0.1949
|
-0.14
|
0.444
|
0.58
|
0.719
|
1.30
|
0.9032
|
2.20
|
0.9861
|
|
-1.57
|
0.0582
|
-0.85
|
0.1977
|
-0.13
|
0.448
|
0.59
|
0.722
|
1.31
|
0.9049
|
2.30
|
0.9893
|
|
-1.56
|
0.0594
|
-0.84
|
0.2005
|
-0.12
|
0.452
|
0.60
|
0.726
|
1.32
|
0.9066
|
2.40
|
0.9918
|
|
-1.55
|
0.0606
|
-0.83
|
0.2033
|
-0.11
|
0.456
|
0.61
|
0.729
|
1.33
|
0.9082
|
2.50
|
0.9938
|
|
-1.54
|
0.0618
|
-0.82
|
0.2061
|
-0.10
|
0.460
|
0.62
|
0.732
|
1.34
|
0.9099
|
2.60
|
0.9953
|
|
-1.53
|
0.0630
|
-0.81
|
0.2090
|
-0.09
|
0.464
|
0.63
|
0.736
|
1.35
|
0.9115
|
2.70
|
0.9965
|
|
-1.52
|
0.0643
|
-0.80
|
0.2119
|
-0.08
|
0.468
|
0.64
|
0.739
|
1.36
|
0.9131
|
2.80
|
0.9974
|
|
-1.51
|
0.0655
|
-0.79
|
0.2148
|
-0.07
|
0.472
|
0.65
|
0.742
|
1.37
|
0.9147
|
2.90
|
0.9981
|
|
-1.50
|
0.0668
|
-0.78
|
0.2177
|
-0.06
|
0.476
|
0.66
|
0.745
|
1.38
|
0.9162
|
3.00
|
0.9987
|
|
-1.49
|
0.0681
|
-0.77
|
0.2206
|
-0.05
|
0.480
|
0.67
|
0.749
|
1.39
|
0.9177
|
3.20
|
0.9993
|
|
-1.48
|
0.0694
|
-0.76
|
0.2236
|
-0.04
|
0.484
|
0.68
|
0.752
|
1.40
|
0.9192
|
3.40
|
0.9997
|
|
-1.47
|
0.0708
|
-0.75
|
0.2266
|
-0.03
|
0.488
|
0.69
|
0.755
|
1.41
|
0.9207
|
3.60
|
0.9998
|
|
-1.46
|
0.0721
|
-0.74
|
0.2296
|
-0.02
|
0.492
|
0.70
|
0.758
|
1.42
|
0.9222
|
3.80
|
0.9999
|
|
-1.45
|
0.0735
|
-0.73
|
0.2327
|
-0.01
|
0.496
|
0.71
|
0.761
|
1.43
|
0.9236
|
4.00
|
1.0000
|
|
-1.44
|
0.0749
|
-0.72
|
0.2358
|
0.00
|
0.500
|
0.72
|
0.764
|
1.44
|
0.9251
|
4.01
|
1.0000
|