STANDARD NORMAL DISTRIBUTION TABLE

Entries represent Pr(Z ≤ z). The value of z to the first decimal is given in the left column. The second
decimal is given in the top row.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998
3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Values of z for selected values of Pr(Z ≤ z)

z 0.842 1.036 1.282 1.645 1.960 2.326 2.576
Pr(Z ≤ z) 0.800 0.850 0.900 0.950 0.975 0.990 0.995
 t DISTRIBUTION TABLE
Entries provide the solution to Pr(t > tp) = p where t has a t distribution with the indicated degrees
of freedom.
df t0.100 t0.050 t0.025 t0.010 t0.005
1 3.0777 6.3138 12.7062 31.8205 63.6567
2 1.8856 2.9200 4.3027 6.9646 9.9248
3 1.6377 2.3534 3.1824 4.5407 5.8409
4 1.5332 2.1318 2.7764 3.7469 4.6041
5 1.4759 2.0150 2.5706 3.3649 4.0321
6 1.4398 1.9432 2.4469 3.1427 3.7074
7 1.4149 1.8946 2.3646 2.9980 3.4995
8 1.3968 1.8595 2.3060 2.8965 3.3554
9 1.3830 1.8331 2.2622 2.8214 3.2498
10 1.3722 1.8125 2.2281 2.7638 3.1693
11 1.3634 1.7959 2.2010 2.7181 3.1058
12 1.3562 1.7823 2.1788 2.6810 3.0545
13 1.3502 1.7709 2.1604 2.6503 3.0123
14 1.3450 1.7613 2.1448 2.6245 2.9768
15 1.3406 1.7531 2.1314 2.6025 2.9467
16 1.3368 1.7459 2.1199 2.5835 2.9208
17 1.3334 1.7396 2.1098 2.5669 2.8982
18 1.3304 1.7341 2.1009 2.5524 2.8784
19 1.3277 1.7291 2.0930 2.5395 2.8609
20 1.3253 1.7247 2.0860 2.5280 2.8453
21 1.3232 1.7207 2.0796 2.5176 2.8314
22 1.3212 1.7171 2.0739 2.5083 2.8188
23 1.3195 1.7139 2.0687 2.4999 2.8073
24 1.3178 1.7109 2.0639 2.4922 2.7969
25 1.3163 1.7081 2.0595 2.4851 2.7874
26 1.3150 1.7056 2.0555 2.4786 2.7787
27 1.3137 1.7033 2.0518 2.4727 2.7707
28 1.3125 1.7011 2.0484 2.4671 2.7633
29 1.3114 1.6991 2.0452 2.4620 2.7564
infinity 1.2816 1.6449 1.9600 2.3263 2.5758
 CHI-SQUARE DISTRIBUTION TABLE

Entries provide the solution to Pr(  2   2p )  p where  2 has a chi-square distribution with the indicated
degrees of freedom.

df  0.100
2
 0.050
2
 0.025
2
 0.010
2
 0.005
2

1 2.706 3.841 5.024 6.635 7.879

2 4.605 5.991 7.378 9.210 10.597
3 6.251 7.815 9.348 11.345 12.838
4 7.779 9.488 11.143 13.277 14.860
5 9.236 11.070 12.833 15.086 16.750
6 10.645 12.592 14.449 16.812 18.548
7 12.017 14.067 16.013 18.475 20.278
8 13.362 15.507 17.535 20.090 21.955
9 14.684 16.919 19.023 21.666 23.589
10 15.987 18.307 20.483 23.209 25.188
11 17.275 19.675 21.920 24.725 26.757
12 18.549 21.026 23.337 26.217 28.300
13 19.812 22.362 24.736 27.688 29.819
14 21.064 23.685 26.119 29.141 31.319
15 22.307 24.996 27.488 30.578 32.801
16 23.542 26.296 28.845 32.000 34.267
17 24.769 27.587 30.191 33.409 35.718
18 25.989 28.869 31.526 34.805 37.156
19 27.204 30.144 32.852 36.191 38.582
20 28.412 31.410 34.170 37.566 39.997
21 29.615 32.671 35.479 38.932 41.401
22 30.813 33.924 36.781 40.289 42.796
23 32.007 35.172 38.076 41.638 44.181
24 33.196 36.415 39.364 42.980 45.559
25 34.382 37.652 40.646 44.314 46.928
26 35.563 38.885 41.923 45.642 48.290
27 36.741 40.113 43.195 46.963 49.645
28 37.916 41.337 44.461 48.278 50.993
29 39.087 42.557 45.722 49.588 52.336
30 40.256 43.773 46.979 50.892 53.672
40 51.805 55.758 59.342 63.691 66.766
50 63.167 67.505 71.420 76.154 79.490
60 74.397 79.082 83.298 88.379 91.952
70 85.527 90.531 95.023 100.425 104.215
80 96.578 101.879 106.629 112.329 116.321
90 107.565 113.145 118.136 124.116 128.299
100 118.498 124.342 129.561 135.807 140.169