Binomial Tables

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Tables of the Binomial Cumulative Distribution The table below gives the probability of obtaining at most x successes in n independent trials, each of which has a probability p of success. That is, if X denotes the number of successes, the table shows

x

P ( X ≤ x) = ∑ Crn p r (1 − p ) n−r r =0

p= n= 2

n= 3

n= 4

n= 5

n= 6

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

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.9801 0.9604 0.9409 0.9216 0.9025 0.8836 0.8649 0.8464 0.8281 0.8100 0.7225 0.6400 0.5625 0.4900 0.4225 0.3600 0.3025 0.2500 0.9999 0.9996 0.9991 0.9984 0.9975 0.9964 0.9951 0.9936 0.9919 0.9900 0.9775 0.9600 0.9375 0.9100 0.8775 0.8400 0.7975 0.7500 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9703 0.9997 1.0000 1.0000

0.9412 0.9988 1.0000 1.0000

0.9127 0.9974 1.0000 1.0000

0.8847 0.9953 0.9999 1.0000

0.8574 0.9928 0.9999 1.0000

0.8306 0.9896 0.9998 1.0000

0.8044 0.9860 0.9997 1.0000

0.7787 0.9818 0.9995 1.0000

0.7536 0.9772 0.9993 1.0000

0.7290 0.9720 0.9990 1.0000

0.6141 0.9393 0.9966 1.0000

0.5120 0.8960 0.9920 1.0000

0.4219 0.8438 0.9844 1.0000

0.3430 0.7840 0.9730 1.0000

0.2746 0.7183 0.9571 1.0000

0.2160 0.6480 0.9360 1.0000

0.1664 0.5748 0.9089 1.0000

0.1250 0.5000 0.8750 1.0000

0.9606 0.9994 1.0000 1.0000 1.0000

0.9224 0.9977 1.0000 1.0000 1.0000

0.8853 0.9948 0.9999 1.0000 1.0000

0.8493 0.9909 0.9998 1.0000 1.0000

0.8145 0.9860 0.9995 1.0000 1.0000

0.7807 0.9801 0.9992 1.0000 1.0000

0.7481 0.9733 0.9987 1.0000 1.0000

0.7164 0.9656 0.9981 1.0000 1.0000

0.6857 0.9570 0.9973 0.9999 1.0000

0.6561 0.9477 0.9963 0.9999 1.0000

0.5220 0.8905 0.9880 0.9995 1.0000

0.4096 0.8192 0.9728 0.9984 1.0000

0.3164 0.7383 0.9492 0.9961 1.0000

0.2401 0.6517 0.9163 0.9919 1.0000

0.1785 0.5630 0.8735 0.9850 1.0000

0.1296 0.4752 0.8208 0.9744 1.0000

0.0915 0.3910 0.7585 0.9590 1.0000

0.0625 0.3125 0.6875 0.9375 1.0000

0.9510 0.9990 1.0000 1.0000 1.0000 1.0000

0.9039 0.9962 0.9999 1.0000 1.0000 1.0000

0.8587 0.9915 0.9997 1.0000 1.0000 1.0000

0.8154 0.9852 0.9994 1.0000 1.0000 1.0000

0.7738 0.9774 0.9988 1.0000 1.0000 1.0000

0.7339 0.9681 0.9980 0.9999 1.0000 1.0000

0.6957 0.9575 0.9969 0.9999 1.0000 1.0000

0.6591 0.9456 0.9955 0.9998 1.0000 1.0000

0.6240 0.9326 0.9937 0.9997 1.0000 1.0000

0.5905 0.9185 0.9914 0.9995 1.0000 1.0000

0.4437 0.8352 0.9734 0.9978 0.9999 1.0000

0.3277 0.7373 0.9421 0.9933 0.9997 1.0000

0.2373 0.6328 0.8965 0.9844 0.9990 1.0000

0.1681 0.5282 0.8369 0.9692 0.9976 1.0000

0.1160 0.4284 0.7648 0.9460 0.9947 1.0000

0.0778 0.3370 0.6826 0.9130 0.9898 1.0000

0.0503 0.2562 0.5931 0.8688 0.9815 1.0000

0.0313 0.1875 0.5000 0.8125 0.9688 1.0000

0.9415 0.9985 1.0000 1.0000 1.0000 1.0000 1.0000

0.8858 0.9943 0.9998 1.0000 1.0000 1.0000 1.0000

0.8330 0.9875 0.9995 1.0000 1.0000 1.0000 1.0000

0.7828 0.9784 0.9988 1.0000 1.0000 1.0000 1.0000

0.7351 0.9672 0.9978 0.9999 1.0000 1.0000 1.0000

0.6899 0.9541 0.9962 0.9998 1.0000 1.0000 1.0000

0.6470 0.9392 0.9942 0.9997 1.0000 1.0000 1.0000

0.6064 0.9227 0.9915 0.9995 1.0000 1.0000 1.0000

0.5679 0.9048 0.9882 0.9992 1.0000 1.0000 1.0000

0.5314 0.8857 0.9842 0.9987 0.9999 1.0000 1.0000

0.3771 0.7765 0.9527 0.9941 0.9996 1.0000 1.0000

0.2621 0.6554 0.9011 0.9830 0.9984 0.9999 1.0000

0.1780 0.5339 0.8306 0.9624 0.9954 0.9998 1.0000

0.1176 0.4202 0.7443 0.9295 0.9891 0.9993 1.0000

0.0754 0.3191 0.6471 0.8826 0.9777 0.9982 1.0000

0.0467 0.2333 0.5443 0.8208 0.9590 0.9959 1.0000

0.0277 0.1636 0.4415 0.7447 0.9308 0.9917 1.0000

0.0156 0.1094 0.3438 0.6563 0.8906 0.9844 1.0000

p= n= 7

x= 0 1 2 3 4 5 6 7 n= 8 x= 0 1 2 3 4 5 6 7 8 n= 9 x= 0 1 2 3 4 5 6 7 8 9 n= 10 x= 0 1 2 3 4 5 6 7 8 9 10

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.9321 0.9980 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9227 0.9973 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9135 0.9966 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.8681 0.9921 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 0.8508 0.9897 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.8337 0.9869 0.9994 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.8080 0.9829 0.9991 1.0000 1.0000 1.0000 1.0000 1.0000 0.7837 0.9777 0.9987 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.7602 0.9718 0.9980 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.7514 0.9706 0.9980 0.9999 1.0000 1.0000 1.0000 1.0000 0.7214 0.9619 0.9969 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 0.6925 0.9522 0.9955 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.6983 0.9556 0.9962 0.9998 1.0000 1.0000 1.0000 1.0000 0.6634 0.9428 0.9942 0.9996 1.0000 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 1.0000

0.6485 0.9382 0.9937 0.9996 1.0000 1.0000 1.0000 1.0000 0.6096 0.9208 0.9904 0.9993 1.0000 1.0000 1.0000 1.0000 1.0000 0.5730 0.9022 0.9862 0.9987 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000

0.6017 0.9187 0.9903 0.9993 1.0000 1.0000 1.0000 1.0000 0.5596 0.8965 0.9853 0.9987 0.9999 1.0000 1.0000 1.0000 1.0000 0.5204 0.8729 0.9791 0.9977 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000

0.5578 0.8974 0.9860 0.9988 0.9999 1.0000 1.0000 1.0000 0.5132 0.8702 0.9789 0.9978 0.9999 1.0000 1.0000 1.0000 1.0000 0.4722 0.8417 0.9702 0.9963 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000

0.5168 0.8745 0.9807 0.9982 0.9999 1.0000 1.0000 1.0000 0.4703 0.8423 0.9711 0.9966 0.9997 1.0000 1.0000 1.0000 1.0000 0.4279 0.8088 0.9595 0.9943 0.9995 1.0000 1.0000 1.0000 1.0000 1.0000

0.4783 0.8503 0.9743 0.9973 0.9998 1.0000 1.0000 1.0000 0.4305 0.8131 0.9619 0.9950 0.9996 1.0000 1.0000 1.0000 1.0000 0.3874 0.7748 0.9470 0.9917 0.9991 0.9999 1.0000 1.0000 1.0000 1.0000

0.3206 0.7166 0.9262 0.9879 0.9988 0.9999 1.0000 1.0000 0.2725 0.6572 0.8948 0.9786 0.9971 0.9998 1.0000 1.0000 1.0000 0.2316 0.5995 0.8591 0.9661 0.9944 0.9994 1.0000 1.0000 1.0000 1.0000

0.2097 0.5767 0.8520 0.9667 0.9953 0.9996 1.0000 1.0000 0.1678 0.5033 0.7969 0.9437 0.9896 0.9988 0.9999 1.0000 1.0000 0.1342 0.4362 0.7382 0.9144 0.9804 0.9969 0.9997 1.0000 1.0000 1.0000

0.1335 0.4449 0.7564 0.9294 0.9871 0.9987 0.9999 1.0000 0.1001 0.3671 0.6785 0.8862 0.9727 0.9958 0.9996 1.0000 1.0000 0.0751 0.3003 0.6007 0.8343 0.9511 0.9900 0.9987 0.9999 1.0000 1.0000

0.0824 0.3294 0.6471 0.8740 0.9712 0.9962 0.9998 1.0000 0.0576 0.2553 0.5518 0.8059 0.9420 0.9887 0.9987 0.9999 1.0000 0.0404 0.1960 0.4628 0.7297 0.9012 0.9747 0.9957 0.9996 1.0000 1.0000

0.0490 0.2338 0.5323 0.8002 0.9444 0.9910 0.9994 1.0000 0.0319 0.1691 0.4278 0.7064 0.8939 0.9747 0.9964 0.9998 1.0000 0.0207 0.1211 0.3373 0.6089 0.8283 0.9464 0.9888 0.9986 0.9999 1.0000

0.0280 0.1586 0.4199 0.7102 0.9037 0.9812 0.9984 1.0000 0.0168 0.1064 0.3154 0.5941 0.8263 0.9502 0.9915 0.9993 1.0000 0.0101 0.0705 0.2318 0.4826 0.7334 0.9006 0.9750 0.9962 0.9997 1.0000

0.0152 0.1024 0.3164 0.6083 0.8471 0.9643 0.9963 1.0000 0.0084 0.0632 0.2201 0.4770 0.7396 0.9115 0.9819 0.9983 1.0000 0.0046 0.0385 0.1495 0.3614 0.6214 0.8342 0.9502 0.9909 0.9992 1.0000

0.0078 0.0625 0.2266 0.5000 0.7734 0.9375 0.9922 1.0000 0.0039 0.0352 0.1445 0.3633 0.6367 0.8555 0.9648 0.9961 1.0000 0.0020 0.0195 0.0898 0.2539 0.5000 0.7461 0.9102 0.9805 0.9980 1.0000

0.9044 0.9957 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.8171 0.9838 0.9991 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.7374 0.9655 0.9972 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.6648 0.9418 0.9938 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.5987 0.9139 0.9885 0.9990 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.5386 0.8824 0.9812 0.9980 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.4840 0.8483 0.9717 0.9964 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.4344 0.8121 0.9599 0.9942 0.9994 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3894 0.7746 0.9460 0.9912 0.9990 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000

0.3487 0.7361 0.9298 0.9872 0.9984 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000

0.1969 0.5443 0.8202 0.9500 0.9901 0.9986 0.9999 1.0000 1.0000 1.0000 1.0000

0.1074 0.3758 0.6778 0.8791 0.9672 0.9936 0.9991 0.9999 1.0000 1.0000 1.0000

0.0563 0.2440 0.5256 0.7759 0.9219 0.9803 0.9965 0.9996 1.0000 1.0000 1.0000

0.0282 0.1493 0.3828 0.6496 0.8497 0.9527 0.9894 0.9984 0.9999 1.0000 1.0000

0.0135 0.0860 0.2616 0.5138 0.7515 0.9051 0.9740 0.9952 0.9995 1.0000 1.0000

0.0060 0.0464 0.1673 0.3823 0.6331 0.8338 0.9452 0.9877 0.9983 0.9999 1.0000

0.0025 0.0233 0.0996 0.2660 0.5044 0.7384 0.8980 0.9726 0.9955 0.9997 1.0000

0.0010 0.0107 0.0547 0.1719 0.3770 0.6230 0.8281 0.9453 0.9893 0.9990 1.0000

p= n= 11 x= 0 1 2 3 4 5 6 7 8 9 10 11 n= 12 x= 0 1 2 3 4 5 6 7 8 9 10 11 12 n= 13 x= 0 1 2 3 4 5 6 7 8 9 10 11 12 13

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.8953 0.9948 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.8007 0.9805 0.9988 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.7153 0.9587 0.9963 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.6382 0.9308 0.9917 0.9993 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.5688 0.8981 0.9848 0.9984 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.5063 0.8618 0.9752 0.9970 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.4501 0.8228 0.9630 0.9947 0.9995 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3996 0.7819 0.9481 0.9915 0.9990 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3544 0.7399 0.9305 0.9871 0.9983 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3138 0.6974 0.9104 0.9815 0.9972 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.1673 0.4922 0.7788 0.9306 0.9841 0.9973 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000

0.0859 0.3221 0.6174 0.8389 0.9496 0.9883 0.9980 0.9998 1.0000 1.0000 1.0000 1.0000

0.0422 0.1971 0.4552 0.7133 0.8854 0.9657 0.9924 0.9988 0.9999 1.0000 1.0000 1.0000

0.0198 0.1130 0.3127 0.5696 0.7897 0.9218 0.9784 0.9957 0.9994 1.0000 1.0000 1.0000

0.0088 0.0606 0.2001 0.4256 0.6683 0.8513 0.9499 0.9878 0.9980 0.9998 1.0000 1.0000

0.0036 0.0302 0.1189 0.2963 0.5328 0.7535 0.9006 0.9707 0.9941 0.9993 1.0000 1.0000

0.0014 0.0139 0.0652 0.1911 0.3971 0.6331 0.8262 0.9390 0.9852 0.9978 0.9998 1.0000

0.0005 0.0059 0.0327 0.1133 0.2744 0.5000 0.7256 0.8867 0.9673 0.9941 0.9995 1.0000

0.8864 0.9938 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.8775 0.9928 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.7847 0.9769 0.9985 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7690 0.9730 0.9980 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.6938 0.9514 0.9952 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.6730 0.9436 0.9938 0.9995 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.6127 0.9191 0.9893 0.9990 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.5882 0.9068 0.9865 0.9986 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.5404 0.8816 0.9804 0.9978 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.5133 0.8646 0.9755 0.9969 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.4759 0.8405 0.9684 0.9957 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.4474 0.8186 0.9608 0.9940 0.9993 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.4186 0.7967 0.9532 0.9925 0.9991 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.3893 0.7702 0.9422 0.9897 0.9987 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3677 0.7513 0.9348 0.9880 0.9984 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.3383 0.7206 0.9201 0.9837 0.9976 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3225 0.7052 0.9134 0.9820 0.9973 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2935 0.6707 0.8946 0.9758 0.9959 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.2824 0.6590 0.8891 0.9744 0.9957 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2542 0.6213 0.8661 0.9658 0.9935 0.9991 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.1422 0.4435 0.7358 0.9078 0.9761 0.9954 0.9993 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.1209 0.3983 0.6920 0.8820 0.9658 0.9925 0.9987 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0687 0.2749 0.5583 0.7946 0.9274 0.9806 0.9961 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 0.0550 0.2336 0.5017 0.7473 0.9009 0.9700 0.9930 0.9988 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000

0.0317 0.1584 0.3907 0.6488 0.8424 0.9456 0.9857 0.9972 0.9996 1.0000 1.0000 1.0000 1.0000 0.0238 0.1267 0.3326 0.5843 0.7940 0.9198 0.9757 0.9944 0.9990 0.9999 1.0000 1.0000 1.0000 1.0000

0.0138 0.0850 0.2528 0.4925 0.7237 0.8822 0.9614 0.9905 0.9983 0.9998 1.0000 1.0000 1.0000 0.0097 0.0637 0.2025 0.4206 0.6543 0.8346 0.9376 0.9818 0.9960 0.9993 0.9999 1.0000 1.0000 1.0000

0.0057 0.0424 0.1513 0.3467 0.5833 0.7873 0.9154 0.9745 0.9944 0.9992 0.9999 1.0000 1.0000 0.0037 0.0296 0.1132 0.2783 0.5005 0.7159 0.8705 0.9538 0.9874 0.9975 0.9997 1.0000 1.0000 1.0000

0.0022 0.0196 0.0834 0.2253 0.4382 0.6652 0.8418 0.9427 0.9847 0.9972 0.9997 1.0000 1.0000 0.0013 0.0126 0.0579 0.1686 0.3530 0.5744 0.7712 0.9023 0.9679 0.9922 0.9987 0.9999 1.0000 1.0000

0.0008 0.0083 0.0421 0.1345 0.3044 0.5269 0.7393 0.8883 0.9644 0.9921 0.9989 0.9999 1.0000 0.0004 0.0049 0.0269 0.0929 0.2279 0.4268 0.6437 0.8212 0.9302 0.9797 0.9959 0.9995 1.0000 1.0000

0.0002 0.0032 0.0193 0.0730 0.1938 0.3872 0.6128 0.8062 0.9270 0.9807 0.9968 0.9998 1.0000 0.0001 0.0017 0.0112 0.0461 0.1334 0.2905 0.5000 0.7095 0.8666 0.9539 0.9888 0.9983 0.9999 1.0000

p= n= 14 x= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 n= 15 x= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 n= 20 x= 0 1 2 3 4 5 6 7

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.8687 0.9916 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.7536 0.9690 0.9975 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.6528 0.9355 0.9923 0.9994 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.5647 0.8941 0.9833 0.9981 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 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 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.4205 0.7963 0.9522 0.9920 0.9990 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3620 0.7436 0.9302 0.9864 0.9980 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3112 0.6900 0.9042 0.9786 0.9965 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.2670 0.6368 0.8745 0.9685 0.9941 0.9992 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.2288 0.5846 0.8416 0.9559 0.9908 0.9985 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.1028 0.3567 0.6479 0.8535 0.9533 0.9885 0.9978 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0440 0.1979 0.4481 0.6982 0.8702 0.9561 0.9884 0.9976 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0178 0.1010 0.2811 0.5213 0.7415 0.8883 0.9617 0.9897 0.9978 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000

0.0068 0.0475 0.1608 0.3552 0.5842 0.7805 0.9067 0.9685 0.9917 0.9983 0.9998 1.0000 1.0000 1.0000 1.0000

0.0024 0.0205 0.0839 0.2205 0.4227 0.6405 0.8164 0.9247 0.9757 0.9940 0.9989 0.9999 1.0000 1.0000 1.0000

0.0008 0.0081 0.0398 0.1243 0.2793 0.4859 0.6925 0.8499 0.9417 0.9825 0.9961 0.9994 0.9999 1.0000 1.0000

0.0002 0.0029 0.0170 0.0632 0.1672 0.3373 0.5461 0.7414 0.8811 0.9574 0.9886 0.9978 0.9997 1.0000 1.0000

0.0001 0.0009 0.0065 0.0287 0.0898 0.2120 0.3953 0.6047 0.7880 0.9102 0.9713 0.9935 0.9991 0.9999 1.0000

0.8601 0.9904 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.8179 0.9831 0.9990 1.0000 1.0000 1.0000 1.0000 1.0000

0.7386 0.9647 0.9970 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.6676 0.9401 0.9929 0.9994 1.0000 1.0000 1.0000 1.0000

0.6333 0.9270 0.9906 0.9992 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.5438 0.8802 0.9790 0.9973 0.9997 1.0000 1.0000 1.0000

0.5421 0.8809 0.9797 0.9976 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.4420 0.8103 0.9561 0.9926 0.9990 0.9999 1.0000 1.0000

0.4633 0.8290 0.9638 0.9945 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.3585 0.7358 0.9245 0.9841 0.9974 0.9997 1.0000 1.0000

0.3953 0.7738 0.9429 0.9896 0.9986 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2901 0.6605 0.8850 0.9710 0.9944 0.9991 0.9999 1.0000

0.3367 0.7168 0.9171 0.9825 0.9972 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2342 0.5869 0.8390 0.9529 0.9893 0.9981 0.9997 1.0000

0.2863 0.6597 0.8870 0.9727 0.9950 0.9993 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1887 0.5169 0.7879 0.9294 0.9817 0.9962 0.9994 0.9999

0.2430 0.6035 0.8531 0.9601 0.9918 0.9987 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1516 0.4516 0.7334 0.9007 0.9710 0.9932 0.9987 0.9998

0.2059 0.5490 0.8159 0.9444 0.9873 0.9978 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1216 0.3917 0.6769 0.8670 0.9568 0.9887 0.9976 0.9996

0.0874 0.3186 0.6042 0.8227 0.9383 0.9832 0.9964 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0388 0.1756 0.4049 0.6477 0.8298 0.9327 0.9781 0.9941

0.0352 0.1671 0.3980 0.6482 0.8358 0.9389 0.9819 0.9958 0.9992 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0115 0.0692 0.2061 0.4114 0.6296 0.8042 0.9133 0.9679

0.0134 0.0802 0.2361 0.4613 0.6865 0.8516 0.9434 0.9827 0.9958 0.9992 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.0032 0.0243 0.0913 0.2252 0.4148 0.6172 0.7858 0.8982

0.0047 0.0353 0.1268 0.2969 0.5155 0.7216 0.8689 0.9500 0.9848 0.9963 0.9993 0.9999 1.0000 1.0000 1.0000 1.0000 0.0008 0.0076 0.0355 0.1071 0.2375 0.4164 0.6080 0.7723

0.0016 0.0142 0.0617 0.1727 0.3519 0.5643 0.7548 0.8868 0.9578 0.9876 0.9972 0.9995 0.9999 1.0000 1.0000 1.0000 0.0002 0.0021 0.0121 0.0444 0.1182 0.2454 0.4166 0.6010

0.0005 0.0052 0.0271 0.0905 0.2173 0.4032 0.6098 0.7869 0.9050 0.9662 0.9907 0.9981 0.9997 1.0000 1.0000 1.0000 0.0000 0.0005 0.0036 0.0160 0.0510 0.1256 0.2500 0.4159

0.0001 0.0017 0.0107 0.0424 0.1204 0.2608 0.4522 0.6535 0.8182 0.9231 0.9745 0.9937 0.9989 0.9999 1.0000 1.0000 0.0000 0.0001 0.0009 0.0049 0.0189 0.0553 0.1299 0.2520

0.0000 0.0005 0.0037 0.0176 0.0592 0.1509 0.3036 0.5000 0.6964 0.8491 0.9408 0.9824 0.9963 0.9995 1.0000 1.0000 0.0000 0.0000 0.0002 0.0013 0.0059 0.0207 0.0577 0.1316

p= n= 20 x= 8 9 10 11 12 13 14 15 16 17 18 n= 25 x= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 n= 30 x= 0 1 2 3 4

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7778 0.9742 0.9980 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7397 0.9639 0.9967 0.9998 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.6035 0.9114 0.9868 0.9986 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.5455 0.8795 0.9783 0.9971 0.9997

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.4670 0.8280 0.9620 0.9938 0.9992 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.4010 0.7731 0.9399 0.9881 0.9982

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.3604 0.7358 0.9235 0.9835 0.9972 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2939 0.6612 0.8831 0.9694 0.9937

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2774 0.6424 0.8729 0.9659 0.9928 0.9988 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2146 0.5535 0.8122 0.9392 0.9844

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2129 0.5527 0.8129 0.9402 0.9850 0.9969 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1563 0.4555 0.7324 0.8974 0.9685

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1630 0.4696 0.7466 0.9064 0.9726 0.9935 0.9987 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1134 0.3694 0.6487 0.8450 0.9447

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1244 0.3947 0.6768 0.8649 0.9549 0.9877 0.9972 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0820 0.2958 0.5654 0.7842 0.9126

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0946 0.3286 0.6063 0.8169 0.9314 0.9790 0.9946 0.9989 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0591 0.2343 0.4855 0.7175 0.8723

0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0718 0.2712 0.5371 0.7636 0.9020 0.9666 0.9905 0.9977 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0424 0.1837 0.4114 0.6474 0.8245

0.9987 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0172 0.0931 0.2537 0.4711 0.6821 0.8385 0.9305 0.9745 0.9920 0.9979 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0076 0.0480 0.1514 0.3217 0.5245

0.9900 0.9974 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0038 0.0274 0.0982 0.2340 0.4207 0.6167 0.7800 0.8909 0.9532 0.9827 0.9944 0.9985 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0012 0.0105 0.0442 0.1227 0.2552

0.9591 0.9861 0.9961 0.9991 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0008 0.0070 0.0321 0.0962 0.2137 0.3783 0.5611 0.7265 0.8506 0.9287 0.9703 0.9893 0.9966 0.9991 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0002 0.0020 0.0106 0.0374 0.0979

0.8867 0.9520 0.9829 0.9949 0.9987 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 0.0001 0.0016 0.0090 0.0332 0.0905 0.1935 0.3407 0.5118 0.6769 0.8106 0.9022 0.9558 0.9825 0.9940 0.9982 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0003 0.0021 0.0093 0.0302

0.7624 0.8782 0.9468 0.9804 0.9940 0.9985 0.9997 1.0000 1.0000 1.0000 1.0000 0.0000 0.0003 0.0021 0.0097 0.0320 0.0826 0.1734 0.3061 0.4668 0.6303 0.7712 0.8746 0.9396 0.9745 0.9907 0.9971 0.9992 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0003 0.0019 0.0075

0.5956 0.7553 0.8725 0.9435 0.9790 0.9935 0.9984 0.9997 1.0000 1.0000 1.0000 0.0000 0.0001 0.0004 0.0024 0.0095 0.0294 0.0736 0.1536 0.2735 0.4246 0.5858 0.7323 0.8462 0.9222 0.9656 0.9868 0.9957 0.9988 0.9997 0.9999 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0003 0.0015

0.4143 0.5914 0.7507 0.8692 0.9420 0.9786 0.9936 0.9985 0.9997 1.0000 1.0000 0.0000 0.0000 0.0001 0.0005 0.0023 0.0086 0.0258 0.0639 0.1340 0.2424 0.3843 0.5426 0.6937 0.8173 0.9040 0.9560 0.9826 0.9942 0.9984 0.9996 0.9999 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0002

0.2517 0.4119 0.5881 0.7483 0.8684 0.9423 0.9793 0.9941 0.9987 0.9998 1.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0020 0.0073 0.0216 0.0539 0.1148 0.2122 0.3450 0.5000 0.6550 0.7878 0.8852 0.9461 0.9784 0.9927 0.9980 0.9995 0.9999 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000

p= n= 30 x= 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 n= 40 x= 0 1 2 3 4 5 6 7 8 9 n= 40 x= 10 11 12 13 14 15 16 17

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.6690 0.9393 0.9925 0.9993 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.4457 0.8095 0.9543 0.9918 0.9988 0.9999 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 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2957 0.6615 0.8822 0.9686 0.9933 0.9988 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9989 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1954 0.5210 0.7855 0.9252 0.9790 0.9951 0.9990 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9967 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1285 0.3991 0.6767 0.8619 0.9520 0.9861 0.9966 0.9993 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9921 0.9983 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0842 0.2990 0.5665 0.7827 0.9104 0.9691 0.9909 0.9977 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9838 0.9960 0.9992 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0549 0.2201 0.4625 0.6937 0.8546 0.9419 0.9801 0.9942 0.9985 0.9997 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9707 0.9918 0.9980 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0356 0.1594 0.3694 0.6007 0.7868 0.9033 0.9624 0.9873 0.9963 0.9990 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9519 0.9848 0.9959 0.9990 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0230 0.1140 0.2894 0.5092 0.7103 0.8535 0.9361 0.9758 0.9919 0.9976 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9268 0.9742 0.9922 0.9980 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0148 0.0805 0.2228 0.4231 0.6290 0.7937 0.9005 0.9581 0.9845 0.9949 0.9985 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000

0.7106 0.8474 0.9302 0.9722 0.9903 0.9971 0.9992 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0015 0.0121 0.0486 0.1302 0.2633 0.4325 0.6067 0.7559 0.8646 0.9328 0.9701 0.9880 0.9957 0.9986 0.9996 0.9999 1.0000 1.0000

0.4275 0.6070 0.7608 0.8713 0.9389 0.9744 0.9905 0.9969 0.9991 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0001 0.0015 0.0079 0.0285 0.0759 0.1613 0.2859 0.4371 0.5931 0.7318 0.8392 0.9125 0.9568 0.9806 0.9921 0.9971 0.9990 0.9997

0.2026 0.3481 0.5143 0.6736 0.8034 0.8943 0.9493 0.9784 0.9918 0.9973 0.9992 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0001 0.0010 0.0047 0.0160 0.0433 0.0962 0.1820 0.2998 0.4395 0.5839 0.7151 0.8209 0.8968 0.9456 0.9738 0.9884 0.9953

0.0766 0.1595 0.2814 0.4315 0.5888 0.7304 0.8407 0.9155 0.9599 0.9831 0.9936 0.9979 0.9994 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0001 0.0006 0.0026 0.0086 0.0238 0.0553 0.1110 0.1959 0.3087 0.4406 0.5772 0.7032 0.8074 0.8849 0.9367 0.9680

0.0233 0.0586 0.1238 0.2247 0.3575 0.5078 0.6548 0.7802 0.8737 0.9348 0.9699 0.9876 0.9955 0.9986 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0013 0.0044 0.0124 0.0303 0.0644 0.1215 0.2053 0.3143 0.4408 0.5721 0.6946 0.7978 0.8761

0.0057 0.0172 0.0435 0.0940 0.1763 0.2915 0.4311 0.5785 0.7145 0.8246 0.9029 0.9519 0.9788 0.9917 0.9971 0.9991 0.9998 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 0.0021 0.0061 0.0156 0.0352 0.0709 0.1285 0.2112 0.3174 0.4402 0.5681 0.6885

0.0011 0.0040 0.0121 0.0312 0.0694 0.1350 0.2327 0.3592 0.5025 0.6448 0.7691 0.8644 0.9286 0.9666 0.9862 0.9950 0.9984 0.9996 0.9999 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0009 0.0027 0.0074 0.0179 0.0386 0.0751 0.1326 0.2142 0.3185 0.4391

0.0002 0.0007 0.0026 0.0081 0.0214 0.0494 0.1002 0.1808 0.2923 0.4278 0.5722 0.7077 0.8192 0.8998 0.9506 0.9786 0.9919 0.9974 0.9993 0.9998 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0011 0.0032 0.0083 0.0192 0.0403 0.0769 0.1341 0.2148

p= n= 40 x= 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 n= 50 x= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 n= 50 x= 17 18 19 20 21 22 23

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.6050 0.9106 0.9862 0.9984 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.3642 0.7358 0.9216 0.9822 0.9968 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.2181 0.5553 0.8108 0.9372 0.9832 0.9963 0.9993 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1299 0.4005 0.6767 0.8609 0.9510 0.9856 0.9964 0.9992 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0769 0.2794 0.5405 0.7604 0.8964 0.9622 0.9882 0.9968 0.9992 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0453 0.1900 0.4162 0.6473 0.8206 0.9224 0.9711 0.9906 0.9973 0.9993 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0266 0.1265 0.3108 0.5327 0.7290 0.8650 0.9417 0.9780 0.9927 0.9978 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0155 0.0827 0.2260 0.4253 0.6290 0.7919 0.8981 0.9562 0.9833 0.9944 0.9983 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0090 0.0532 0.1605 0.3303 0.5277 0.7072 0.8404 0.9232 0.9672 0.9875 0.9957 0.9987 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0052 0.0338 0.1117 0.2503 0.4312 0.6161 0.7702 0.8779 0.9421 0.9755 0.9906 0.9968 0.9990 0.9997 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0003 0.0029 0.0142 0.0460 0.1121 0.2194 0.3613 0.5188 0.6681 0.7911 0.8801 0.9372 0.9699 0.9868 0.9947 0.9981 0.9993 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000

0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0002 0.0013 0.0057 0.0185 0.0480 0.1034 0.1904 0.3073 0.4437 0.5836 0.7107 0.8139 0.8894 0.9393 0.9692 0.9856 0.9937 0.9975 0.9991 0.9997 0.9999 1.0000 1.0000

0.9983 0.9994 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0001 0.0005 0.0021 0.0070 0.0194 0.0453 0.0916 0.1637 0.2622 0.3816 0.5110 0.6370 0.7481 0.8369 0.9017 0.9449 0.9713 0.9861 0.9937 0.9974 0.9990 0.9996

0.9852 0.9937 0.9976 0.9991 0.9997 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0007 0.0025 0.0073 0.0183 0.0402 0.0789 0.1390 0.2229 0.3279 0.4468 0.5692 0.6839 0.7822 0.8594 0.9152 0.9522 0.9749 0.9877 0.9944

0.9301 0.9637 0.9827 0.9925 0.9970 0.9989 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0008 0.0025 0.0067 0.0160 0.0342 0.0661 0.1163 0.1878 0.2801 0.3889 0.5060 0.6216 0.7264 0.8139 0.8813 0.9290 0.9604

0.7911 0.8702 0.9256 0.9608 0.9811 0.9917 0.9966 0.9988 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0008 0.0022 0.0057 0.0133 0.0280 0.0540 0.0955 0.1561 0.2369 0.3356 0.4465 0.5610 0.6701 0.7660 0.8438

0.5651 0.6844 0.7870 0.8669 0.9233 0.9595 0.9804 0.9914 0.9966 0.9988 0.9996 0.9999 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0006 0.0018 0.0045 0.0104 0.0220 0.0427 0.0765 0.1273 0.1974 0.2862 0.3900 0.5019 0.6134

0.3179 0.4373 0.5627 0.6821 0.7852 0.8659 0.9231 0.9597 0.9808 0.9917 0.9968 0.9989 0.9997 0.9999 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0005 0.0013 0.0033 0.0077 0.0164 0.0325 0.0595 0.1013 0.1611 0.2399 0.3359

p= n= 50 x= 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 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 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9976 0.9991 0.9997 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9793 0.9900 0.9955 0.9981 0.9993 0.9997 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9022 0.9427 0.9686 0.9840 0.9924 0.9966 0.9986 0.9995 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000

0.7160 0.8034 0.8721 0.9220 0.9556 0.9765 0.9884 0.9947 0.9978 0.9991 0.9997 0.9999 1.0000 1.0000 1.0000

0.4439 0.5561 0.6641 0.7601 0.8389 0.8987 0.9405 0.9675 0.9836 0.9923 0.9967 0.9987 0.9995 0.9998 1.0000

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Binomial Tables

Tables of the Binomial Cumulative Distribution The table below gives the probability of obtaining at most x successes in n independent trials, each of...

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