APPENDIX A
1z2 P1Z z2 z
1
22
e
1 u2
2 d
653
u
Φ (z)
z
T a b le I I
z
3 .9
3 .8
3 .7
3 .6
3 .5
3 .4
3 .3
3 .2
3 .1
3 .0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
C u m u la tiv e S ta n d a rd No rm a l Distrib u tio n
0.09
0.00003 3
0.00005 0
0.00007 5
0.000112
0.00016 5
0.00024 2
0.0003 5 0
0.0005 01
0.0007 11
0.001001
0.0013 95
0.001926
0.0026 3 5
0.003 5 7 3
0.004 7 99
0.006 3 8 7
0.008 4 24
0.011011
0.014 26 2
0.018 3 09
0.023 295
0.0293 7 9
0.03 6 7 27
0.04 5 5 14
0.05 5 917
0.06 8 112
0.08 226 4
0.098 5 25
0.117 023
0.13 7 8 5 7
0.16 108 7
0.18 6 7 3 3
0.214 7 6 4
0.24 5 097
0.27 7 5 95
0.3 1206 7
0.3 4 8 26 8
0.3 8 5 908
0.4 24 6 5 5
0.4 6 4 14 4
0.08
0.00003 4
0.00005 2
0.00007 8
0.000117
0.00017 2
0.00025 1
0.0003 6 2
0.0005 19
0.0007 3 6
0.00103 5
0.0014 4 1
0.00198 8
0.0027 18
0.003 6 8 1
0.004 94 0
0.006 5 6 9
0.008 6 5 6
0.0113 04
0.014 6 29
0.018 7 6 3
0.023 8 5 2
0.03 005 4
0.03 7 5 3 8
0.04 6 4 7 9
0.05 7 05 3
0.06 94 3 7
0.08 3 7 93
0.10027 3
0.119000
0.14 007 1
0.16 3 5 4 3
0.18 94 3 0
0.217 6 95
0.24 8 25 2
0.28 095 7
0.3 15 6 14
0.3 5 197 3
0.3 8 97 3 9
0.4 28 5 7 6
0.4 6 8 119
0.07
0.06
0.05
0.04
0.00003 6
0.00005 4
0.00008 2
0.000121
0.00017 9
0.00026 0
0.0003 7 6
0.0005 3 8
0.0007 6 2
0.00107 0
0.0014 8 9
0.00205 2
0.0028 03
0.003 7 93
0.005 08 5
0.006 7 5 6
0.008 8 94
0.0116 04
0.015 003
0.019226
0.024 4 19
0.03 07 4 2
0.03 8 3 6 4
0.04 7 4 6 0
0.05 8 208
0.07 07 8 1
0.08 5 3 4 3
0.10204 2
0.121001
0.14 23 10
0.16 6 023
0.19215 0
0.2206 5 0
0.25 14 29
0.28 4 3 3 9
0.3 1917 8
0.3 5 5 6 91
0.3 93 5 8 0
0.4 3 25 05
0.4 7 2097
0.00003 7
0.00005 7
0.00008 5
0.000126
0.00018 5
0.00027 0
0.0003 90
0.0005 5 7
0.0007 8 9
0.001107
0.0015 3 8
0.002118
0.0028 90
0.003 907
0.005 23 4
0.006 94 7
0.00913 7
0.011911
0.015 3 8 6
0.0196 99
0.024 998
0.03 14 4 3
0.03 9204
0.04 8 4 5 7
0.05 93 8 0
0.07 214 5
0.08 6 915
0.103 8 3 5
0.123 024
0.14 4 5 7 2
0.16 8 5 28
0.194 8 94
0.223 6 27
0.25 4 6 27
0.28 7 7 4 0
0.3 227 5 8
0.3 5 94 24
0.3 97 4 3 2
0.4 3 6 4 4 1
0.4 7 6 07 8
0.00003 9
0.00005 9
0.00008 8
0.00013 1
0.000193
0.00028 0
0.0004 04
0.0005 7 7
0.0008 16
0.00114 4
0.0015 8 9
0.00218 6
0.00298 0
0.004 025
0.005 3 8 6
0.007 14 3
0.0093 8 7
0.012224
0.015 7 7 8
0.02018 2
0.025 5 8 8
0.03 215 7
0.04 005 9
0.04 94 7 1
0.06 05 7 1
0.07 3 5 29
0.08 8 5 08
0.105 6 5 0
0.125 07 2
0.14 6 8 5 9
0.17 105 6
0.197 6 6 2
0.226 6 27
0.25 7 8 4 6
0.29116 0
0.3 26 3 5 5
0.3 6 3 16 9
0.4 01294
0.4 4 03 8 2
0.4 8 006 1
0.00004 1
0.00006 2
0.000092
0.00013 6
0.000200
0.000291
0.0004 19
0.0005 98
0.0008 4 5
0.00118 3
0.0016 4 1
0.00225 6
0.003 07 2
0.004 14 5
0.005 5 4 3
0.007 3 4 4
0.0096 4 2
0.0125 4 5
0.016 17 7
0.0206 7 5
0.026 190
0.03 28 8 4
0.04 0929
0.05 05 03
0.06 17 8 0
0.07 4 93 4
0.090123
0.107 4 8 8
0.127 14 3
0.14 917 0
0.17 3 6 09
0.2004 5 4
0.2296 5 0
0.26 108 6
0.294 5 99
0.3 2996 9
0.3 6 6 928
0.4 05 16 5
0.4 4 4 3 3 0
0.4 8 4 04 7
0.03
0.00004 2
0.00006 4
0.000096
0.00014 2
0.000208
0.0003 02
0.0004 3 4
0.0006 19
0.0008 7 4
0.001223
0.0016 95
0.0023 27
0.003 16 7
0.004 26 9
0.005 7 03
0.007 5 4 9
0.009903
0.0128 7 4
0.016 5 8 6
0.02117 8
0.026 8 03
0.03 3 6 25
0.04 18 15
0.05 15 5 1
0.06 3 008
0.07 6 3 5 9
0.0917 5 9
0.1093 4 9
0.12923 8
0.15 15 05
0.17 6 18 5
0.203 26 9
0.23 26 95
0.26 4 3 4 7
0.298 05 6
0.3 3 3 5 98
0.3 7 07 00
0.4 0904 6
0.4 4 8 28 3
0.4 8 8 03 3
0.02
0.00004 4
0.00006 7
0.000100
0.00014 7
0.000216
0.0003 13
0.0004 5 0
0.0006 4 1
0.000904
0.00126 4
0.0017 5 0
0.0024 01
0.003 26 4
0.004 3 96
0.005 8 6 8
0.007 7 6 0
0.01017 0
0.013 209
0.017 003
0.0216 92
0.027 4 29
0.03 4 3 7 9
0.04 27 16
0.05 26 16
0.06 4 25 6
0.07 7 8 04
0.093 4 18
0.11123 3
0.13 13 5 7
0.15 3 8 6 4
0.17 8 7 8 6
0.206 108
0.23 5 7 6 2
0.26 7 6 29
0.3 015 3 2
0.3 3 7 24 3
0.3 7 4 4 8 4
0.4 1293 6
0.4 5 224 2
0.4 92022
0.01
0.00004 6
0.00006 9
0.000104
0.00015 3
0.000224
0.0003 25
0.0004 6 7
0.0006 6 4
0.00093 5
0.0013 06
0.0018 07
0.0024 7 7
0.003 3 6 4
0.004 5 27
0.006 03 7
0.007 97 6
0.0104 4 4
0.013 5 5 3
0.017 4 29
0.022216
0.028 06 7
0.03 5 14 8
0.04 3 6 3 3
0.05 3 6 99
0.06 5 5 22
0.07 927 0
0.095 098
0.113 14 0
0.13 3 5 00
0.15 6 24 8
0.18 14 11
0.208 97 0
0.23 8 8 5 2
0.27 093 1
0.3 05 026
0.3 4 0903
0.3 7 8 28 1
0.4 16 8 3 4
0.4 5 6 205
0.4 96 011
0.00
0.00004 8
0.00007 2
0.000108
0.00015 9
0.00023 3
0.0003 3 7
0.0004 8 3
0.0006 8 7
0.00096 8
0.0013 5 0
0.0018 6 6
0.0025 5 5
0.003 4 6 7
0.004 6 6 1
0.006 210
0.008 198
0.0107 24
0.013 903
0.017 8 6 4
0.0227 5 0
0.028 7 17
0.03 5 93 0
0.04 4 5 6 5
0.05 4 7 99
0.06 6 8 07
0.08 07 5 7
0.096 8 01
0.115 07 0
0.13 5 6 6 6
0.15 8 6 5 5
0.18 4 06 0
0.2118 5 5
0.24 196 4
0.27 4 25 3
0.3 08 5 3 8
0.3 4 4 5 7 8
0.3 8 208 9
0.4 207 4 0
0.4 6 017 2
0.5 00000
654
APPENDIX A STATISTICAL TABLES AND CHARTS
1z2 P1Z z2 z
1
22
e
1 u2
2
du
Φ (z)
z
0
Table II
Cumulative Standard Normal Distribution ( continued)
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
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
0.500000
0.539828
0.579260
0.617911
0.655422
0.691462
0.725747
0.758036
0.788145
0.815940
0.841345
0.864334
0.884930
0.903199
0.919243
0.933193
0.945201
0.955435
0.964070
0.971283
0.977250
0.982136
0.986097
0.989276
0.991802
0.993790
0.995339
0.996533
0.997445
0.998134
0.998650
0.999032
0.999313
0.999517
0.999663
0.999767
0.999841
0.999892
0.999928
0.999952
0.503989
0.543795
0.583166
0.621719
0.659097
0.694974
0.729069
0.761148
0.791030
0.818589
0.843752
0.866500
0.886860
0.904902
0.920730
0.934478
0.946301
0.956367
0.964852
0.971933
0.977784
0.982571
0.986447
0.989556
0.992024
0.993963
0.995473
0.996636
0.997523
0.998193
0.998694
0.999065
0.999336
0.999533
0.999675
0.999776
0.999847
0.999896
0.999931
0.999954
0.507978
0.547758
0.587064
0.625516
0.662757
0.698468
0.732371
0.764238
0.793892
0.821214
0.846136
0.868643
0.888767
0.906582
0.922196
0.935744
0.947384
0.957284
0.965621
0.972571
0.978308
0.982997
0.986791
0.989830
0.992240
0.994132
0.995604
0.996736
0.997599
0.998250
0.998736
0.999096
0.999359
0.999550
0.999687
0.999784
0.999853
0.999900
0.999933
0.999956
0.511967
0.551717
0.590954
0.629300
0.666402
0.701944
0.735653
0.767305
0.796731
0.823815
0.848495
0.870762
0.890651
0.908241
0.923641
0.936992
0.948449
0.958185
0.966375
0.973197
0.978822
0.983414
0.987126
0.990097
0.992451
0.994297
0.995731
0.996833
0.997673
0.998305
0.998777
0.999126
0.999381
0.999566
0.999698
0.999792
0.999858
0.999904
0.999936
0.999958
0.515953
0.555760
0.594835
0.633072
0.670031
0.705401
0.738914
0.770350
0.799546
0.826391
0.850830
0.872857
0.892512
0.909877
0.925066
0.938220
0.949497
0.959071
0.967116
0.973810
0.979325
0.983823
0.987455
0.990358
0.992656
0.994457
0.995855
0.996928
0.997744
0.998359
0.998817
0.999155
0.999402
0.999581
0.999709
0.999800
0.999864
0.999908
0.999938
0.999959
0.519939
0.559618
0.598706
0.636831
0.673645
0.708840
0.742154
0.773373
0.802338
0.828944
0.853141
0.874928
0.894350
0.911492
0.926471
0.939429
0.950529
0.959941
0.967843
0.974412
0.979818
0.984222
0.987776
0.990613
0.992857
0.994614
0.995975
0.997020
0.997814
0.998411
0.998856
0.999184
0.999423
0.999596
0.999720
0.999807
0.999869
0.999912
0.999941
0.999961
0.532922
0.563559
0.602568
0.640576
0.677242
0.712260
0.745373
0.776373
0.805106
0.831472
0.855428
0.876976
0.896165
0.913085
0.927855
0.940620
0.951543
0.960796
0.968557
0.975002
0.980301
0.984614
0.988089
0.990863
0.993053
0.994766
0.996093
0.997110
0.997882
0.998462
0.998893
0.999211
0.999443
0.999610
0.999730
0.999815
0.999874
0.999915
0.999943
0.999963
0.527903
0.567495
0.606420
0.644309
0.680822
0.715661
0.748571
0.779350
0.807850
0.833977
0.857690
0.878999
0.897958
0.914657
0.929219
0.941792
0.952540
0.961636
0.969258
0.975581
0.980774
0.984997
0.988396
0.991106
0.993244
0.994915
0.996207
0.997197
0.997948
0.998511
0.998930
0.999238
0.999462
0.999624
0.999740
0.999821
0.999879
0.999918
0.999946
0.999964
0.531881
0.571424
0.610261
0.648027
0.684386
0.719043
0.751748
0.782305
0.810570
0.836457
0.859929
0.881000
0.899727
0.916207
0.930563
0.942947
0.953521
0.962462
0.969946
0.976148
0.981237
0.985371
0.988696
0.991344
0.993431
0.995060
0.996319
0.997282
0.998012
0.998559
0.998965
0.999264
0.999481
0.999638
0.999749
0.999828
0.999883
0.999922
0.999948
0.999966
0.535856
0.575345
0.614092
0.651732
0.687933
0.722405
0.754903
0.785236
0.813267
0.838913
0.862143
0.882977
0.901475
0.917736
0.931888
0.944083
0.954486
0.963273
0.970621
0.976705
0.981691
0.985738
0.988989
0.991576
0.993613
0.995201
0.996427
0.997365
0.998074
0.998605
0.998999
0.999289
0.999499
0.999650
0.999758
0.999835
0.999888
0.999925
0.999950
0.999967