(z)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
0.00
0.01
0.50000
0.53983
0.57926
0.61791
0.65542
0.69146
0.72575
0.75804
0.78814
0.81594
0.84134
0.86433
0.88493
0.90320
0.91924
0.93319
0.94520
0.95543
0.96407
0.97128
0.97725
0.98214
0.98610
0.98928
0.99180
0.99379
0.99534
0.99653
0.99744
0.99813
0.99865
0.99903
0.99931
0.99952
0.99966
0.99977
0.99984
0.99989
0.99993
0.99995
0.50399
0.54380
0.58317
0.62172
0.65910
0.69497
0.72907
0.76115
0.79103
0.81859
0.84375
0.86650
0.88686
0.90490
0.92073
0.93448
0.94630
0.95637
0.96485
0.97193
0.97778
0.98257
0.98645
0.98956
0.99202
0.99396
0.99547
0.99664
0.99752
0.99819
0.99869
0.99906
0.99934
0.99953
0.99968
0.99978
0.99985
0.99990
0.99993
0.99995
NORMAL DISTRIBUTION PROBABILITIES
0.02
0.03
0.04
0.05
0.06
0.50798
0.54776
0.58706
0.62552
0.66276
0.69847
0.73237
0.76424
0.79389
0.82121
0.84614
0.86864
0.88877
0.90658
0.92220
0.93574
0.94738
0.95728
0.96562
0.97257
0.97831
0.98300
0.98679
0.98983
0.99224
0.99413
0.99560
0.99674
0.99760
0.99825
0.99874
0.99910
0.99936
0.99955
0.99969
0.99978
0.99985
0.99990
0.99993
0.99996
0.51197
0.55172
0.59095
0.62930
0.66640
0.70194
0.73565
0.76730
0.79673
0.82381
0.84849
0.87076
0.89065
0.90824
0.92364
0.93699
0.94845
0.95818
0.96638
0.97320
0.97882
0.98341
0.98713
0.99010
0.99245
0.99430
0.99573
0.99683
0.99767
0.99831
0.99878
0.99913
0.99938
0.99957
0.99970
0.99979
0.99986
0.99990
0.99994
0.99996
0.51595
0.55567
0.59483
0.63307
0.67003
0.70540
0.73891
0.77035
0.79955
0.82639
0.85083
0.87286
0.89251
0.90988
0.92507
0.93822
0.94950
0.95907
0.96712
0.97381
0.97932
0.98382
0.98745
0.99036
0.99266
0.99446
0.99585
0.99693
0.99774
0.99836
0.99882
0.99916
0.99940
0.99958
0.99971
0.99980
0.99986
0.99991
0.99994
0.99996
0.51994
0.55962
0.59871
0.63683
0.67364
0.70884
0.74215
0.77337
0.80234
0.82894
0.85314
0.87493
0.89435
0.91149
0.92647
0.93943
0.95053
0.95994
0.96784
0.97441
0.97982
0.98422
0.98778
0.99061
0.99286
0.99461
0.99598
0.99702
0.99781
0.99841
0.99886
0.99918
0.99942
0.99960
0.99972
0.99981
0.99987
0.99991
0.99994
0.99996
0.52392
0.56356
0.60257
0.64058
0.67724
0.71226
0.74537
0.77637
0.80511
0.83147
0.85543
0.87698
0.89617
0.91309
0.92785
0.94062
0.95154
0.96080
0.96856
0.97500
0.98030
0.98461
0.98809
0.99086
0.99305
0.99477
0.99609
0.99711
0.99788
0.99846
0.99889
0.99921
0.99944
0.99961
0.99973
0.99981
0.99987
0.99992
0.99994
0.99996
0.07
0.08
0.09
0.52790
0.56749
0.60642
0.64431
0.68082
0.71566
0.74857
0.77935
0.80785
0.83398
0.85769
0.87900
0.89796
0.91466
0.92922
0.94179
0.95254
0.96164
0.96926
0.97558
0.98077
0.98500
0.98840
0.99111
0.99324
0.99492
0.99621
0.99720
0.99795
0.99851
0.99893
0.99924
0.99946
0.99962
0.99974
0.99982
0.99988
0.99992
0.99995
0.99996
0.53188
0.57142
0.61026
0.64803
0.68439
0.71904
0.75175
0.78230
0.81057
0.83646
0.85993
0.88100
0.89973
0.91621
0.93056
0.94295
0.95352
0.96246
0.96995
0.97615
0.98124
0.98537
0.98870
0.99134
0.99343
0.99506
0.99632
0.99728
0.99801
0.99856
0.99896
0.99926
0.99948
0.99964
0.99975
0.99983
0.99988
0.99992
0.99995
0.99997
0.53586
0.57535
0.61409
0.65173
0.68793
0.72240
0.75490
0.78524
0.81327
0.83891
0.86214
0.88298
0.90147
0.91774
0.93189
0.94408
0.95449
0.96327
0.97062
0.97670
0.98169
0.98574
0.98899
0.99158
0.99361
0.99520
0.99643
0.99736
0.99807
0.99861
0.99900
0.99929
0.99950
0.99965
0.99976
0.99983
0.99989
0.99992
0.99995
0.99997
d.f.
1
2
3
4
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
50
60
120
∞
0.05
Critical Values of t-distribution
0.025
0.01
0.005
0.001
0.0005
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.684
1.676
1.671
1.658
1.645
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.021
2.009
2.000
1.980
1.960
636.619
31.599
12.924
8.610
6.869
5.959
5.408
5.041
4.781
4.587
4.437
4.318
4.221
4.140
4.073
4.015
3.965
3.922
3.883
3.850
3.819
3.792
3.768
3.745
3.725
3.707
3.690
3.674
3.659
3.646
3.551
3.496
3.460
3.373
3.291
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.423
2.403
2.390
2.358
2.326
63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.704
2.678
2.660
2.617
2.576
318.309
22.327
10.215
7.173
5.893
5.208
4.785
4.501
4.297
4.144
4.025
3.930
3.852
3.787
3.733
3.686
3.646
3.610
3.579
3.552
3.527
3.505
3.485
3.467
3.450
3.435
3.421
3.408
3.396
3.385
3.307
3.261
3.232
3.160
3.090
d.o.f.
1
2
3
4
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
50
60
70
80
90
100
Critical values of χ2 distribution
0.001
0
0.002
0.0243
0.0908
0.2102
0.3811
0.5985
0.8571
1.1519
1.4787
1.8339
2.2142
2.6172
3.0407
3.4827
3.9416
4.4161
4.9048
5.4068
5.921
6.4467
6.983
7.5292
8.0849
8.6493
9.2221
9.8028
10.391
10.986
11.588
17.916
24.674
31.738
39.036
46.52
54.155
61.918
0.005
0
0.01
0.0717
0.207
0.4117
0.6757
0.9893
1.3444
1.7349
2.1559
2.6032
3.0738
3.565
4.0747
4.6009
5.1422
5.6972
6.2648
6.844
7.4338
8.0337
8.6427
9.2604
9.8862
10.52
11.16
11.808
12.461
13.121
13.787
20.707
27.991
35.535
43.275
51.172
59.196
67.328
0.01
0.02
2.00E-04 6.00E-04
0.0201
0.1148
0.2971
0.5543
0.8721
1.239
1.6465
2.0879
2.5582
3.0535
3.5706
4.1069
4.6604
5.2293
5.8122
6.4078
7.0149
7.6327
8.2604
8.8972
9.5425
10.196
10.856
11.524
12.198
12.879
13.565
14.257
14.954
22.164
29.707
37.485
45.442
53.54
61.754
70.065
0.0404
0.1848
0.4294
0.7519
1.1344
1.5643
2.0325
2.5324
3.0591
3.6087
4.1783
4.7654
5.3682
5.9849
6.6142
7.255
7.9062
8.567
9.2367
9.9146
10.6
11.293
11.992
12.697
13.409
14.125
14.848
15.575
16.306
23.838
31.664
39.699
47.893
56.213
64.635
73.142
0.025
0.001
0.0506
0.2158
0.4844
0.8312
1.2373
1.6899
2.1797
2.7004
3.247
3.8157
4.4038
5.0088
5.6287
6.2621
6.9077
7.5642
8.2307
8.9065
9.5908
10.283
10.982
11.689
12.401
13.12
13.844
14.573
15.308
16.047
16.791
24.433
32.357
40.482
48.758
57.153
65.647
74.222
0.05
0.0039
0.1026
0.3518
0.7107
1.1455
1.6354
2.1673
2.7326
3.3251
3.9403
4.5748
5.226
5.8919
6.5706
7.2609
7.9616
8.6718
9.3905
10.117
10.851
11.591
12.338
13.091
13.848
14.611
15.379
16.151
16.928
17.708
18.493
26.509
34.764
43.188
51.739
60.392
69.126
77.93
0.10
0.0158
0.2107
0.5844
1.0636
1.6103
2.2041
2.8331
3.4895
4.1682
4.8652
5.5778
6.3038
7.0415
7.7895
8.5468
9.3122
10.085
10.865
11.651
12.443
13.24
14.042
14.848
15.659
16.473
17.292
18.114
18.939
19.768
20.599
29.051
37.689
46.459
55.329
64.278
73.291
82.358
0.20
0.0642
0.4463
1.0052
1.6488
2.3425
3.0701
3.8223
4.5936
5.3801
6.1791
6.9887
7.8073
8.6339
9.4673
10.307
11.152
12.002
12.857
13.716
14.578
15.445
16.314
17.187
18.062
18.94
19.82
20.703
21.588
22.475
23.364
32.345
41.449
50.641
59.898
69.207
78.558
87.945
0.80
1.6424
3.2189
4.6416
5.9886
7.2893
8.5581
9.8032
11.03
12.242
13.442
14.631
15.812
16.985
18.151
19.311
20.465
21.615
22.76
23.9
25.038
26.171
27.302
28.429
29.553
30.675
31.795
32.912
34.027
35.139
36.25
47.269
58.164
68.972
79.715
90.405
101.05
111.67
0.90
2.7055
4.6052
6.2514
7.7794
9.2364
10.645
12.017
13.362
14.684
15.987
17.275
18.549
19.812
21.064
22.307
23.542
24.769
25.989
27.204
28.412
29.615
30.813
32.007
33.196
34.382
35.563
36.741
37.916
39.088
40.256
51.805
63.167
74.397
85.527
96.578
107.57
118.5
0.95
3.8415
5.9915
7.8147
9.4877
11.071
12.592
14.067
15.507
16.919
18.307
19.675
21.026
22.362
23.685
24.996
26.296
27.587
28.869
30.144
31.41
32.671
33.924
35.173
36.415
37.653
38.885
40.113
41.337
42.557
43.773
55.759
67.505
79.082
90.531
101.88
113.15
124.34
0.975
5.0239
7.3778
9.3484
11.143
12.833
14.449
16.013
17.535
19.023
20.483
21.92
23.337
24.736
26.119
27.488
28.845
30.191
31.526
32.852
34.17
35.479
36.781
38.076
39.364
40.647
41.923
43.195
44.461
45.722
46.979
59.342
71.42
83.298
95.023
106.63
118.14
129.56
0.98
5.4119
7.824
9.8374
11.668
13.388
15.033
16.622
18.168
19.679
21.161
22.618
24.054
25.472
26.873
28.26
29.633
30.995
32.346
33.687
35.02
36.343
37.66
38.968
40.27
41.566
42.856
44.14
45.419
46.693
47.962
60.436
72.613
84.58
96.388
108.07
119.65
131.14
0.99
6.6349
9.2103
11.345
13.277
15.086
16.812
18.475
20.09
21.666
23.209
24.725
26.217
27.688
29.141
30.578
32
33.409
34.805
36.191
37.566
38.932
40.289
41.638
42.98
44.314
45.642
46.963
48.278
49.588
50.892
63.691
76.154
88.379
100.43
112.33
124.12
135.81
0.995
7.8794
10.597
12.838
14.86
16.75
18.548
20.278
21.955
23.589
25.188
26.757
28.3
29.82
31.319
32.801
34.267
35.719
37.157
38.582
39.997
41.401
42.796
44.181
45.559
46.928
48.29
49.645
50.993
52.336
53.672
66.766
79.49
91.952
104.21
116.32
128.3
140.17
0.999
10.828
13.816
16.266
18.467
20.515
22.458
24.322
26.125
27.877
29.588
31.264
32.91
34.528
36.123
37.697
39.252
40.79
42.312
43.82
45.315
46.797
48.268
49.728
51.179
52.62
54.052
55.476
56.892
58.301
59.703
73.402
86.661
99.607
112.32
124.84
137.21
149.45