Poisson Cumulative Distribution Tables
The table below gives the probability of that a Poisson random variable X with mean = λ is less than or equal to x.
x\λ | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 |
0 | 0.9048 | 0.8187 | 0.7408 | 0.6703 | 0.6065 | 0.5488 | 0.4966 | 0.4493 | 0.4066 | 0.3679 | 0.3012 | 0.2466 | 0.2019 | 0.1653 |
1 | 0.9953 | 0.9825 | 0.9631 | 0.9384 | 0.9098 | 0.8781 | 0.8442 | 0.8088 | 0.7725 | 0.7358 | 0.6626 | 0.5918 | 0.5249 | 0.4628 |
2 | 0.9998 | 0.9989 | 0.9964 | 0.9921 | 0.9856 | 0.9769 | 0.9659 | 0.9526 | 0.9371 | 0.9197 | 0.8795 | 0.8335 | 0.7834 | 0.7306 |
3 | 1.0000 | 0.9999 | 0.9997 | 0.9992 | 0.9982 | 0.9966 | 0.9942 | 0.9909 | 0.9865 | 0.9810 | 0.9662 | 0.9463 | 0.9212 | 0.8913 |
4 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9998 | 0.9996 | 0.9992 | 0.9986 | 0.9977 | 0.9963 | 0.9923 | 0.9857 | 0.9763 | 0.9636 |
5 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9998 | 0.9997 | 0.9994 | 0.9985 | 0.9968 | 0.9940 | 0.9896 |
6 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9997 | 0.9994 | 0.9987 | 0.9974 |
7 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9997 | 0.9994 |
8 | 1.0000 | 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 |
9 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
x\λ = | 2.0 | 2.2 | 2.4 | 2.6 | 2.8 | 3.0 | 3.2 | 3.4 | 3.6 | 3.8 | 4.0 | 4.5 | 5.0 | 5.5 |
0 | 0.1353 | 0.1108 | 0.0907 | 0.0743 | 0.0608 | 0.0498 | 0.0408 | 0.0334 | 0.0273 | 0.0224 | 0.0183 | 0.0111 | 0.0067 | 0.0041 |
1 | 0.4060 | 0.3546 | 0.3084 | 0.2674 | 0.2311 | 0.1991 | 0.1712 | 0.1468 | 0.1257 | 0.1074 | 0.0916 | 0.0611 | 0.0404 | 0.0266 |
2 | 0.6767 | 0.6227 | 0.5697 | 0.5184 | 0.4695 | 0.4232 | 0.3799 | 0.3397 | 0.3027 | 0.2689 | 0.2381 | 0.1736 | 0.1247 | 0.0884 |
3 | 0.8571 | 0.8194 | 0.7787 | 0.7360 | 0.6919 | 0.6472 | 0.6025 | 0.5584 | 0.5152 | 0.4735 | 0.4335 | 0.3423 | 0.2650 | 0.2017 |
4 | 0.9473 | 0.9275 | 0.9041 | 0.8774 | 0.8477 | 0.8153 | 0.7806 | 0.7442 | 0.7064 | 0.6678 | 0.6288 | 0.5321 | 0.4405 | 0.3575 |
5 | 0.9834 | 0.9751 | 0.9643 | 0.9510 | 0.9349 | 0.9161 | 0.8946 | 0.8705 | 0.8441 | 0.8156 | 0.7851 | 0.7029 | 0.6160 | 0.5289 |
6 | 0.9955 | 0.9925 | 0.9884 | 0.9828 | 0.9756 | 0.9665 | 0.9554 | 0.9421 | 0.9267 | 0.9091 | 0.8893 | 0.8311 | 0.7622 | 0.6860 |
7 | 0.9989 | 0.9980 | 0.9967 | 0.9947 | 0.9919 | 0.9881 | 0.9832 | 0.9769 | 0.9692 | 0.9599 | 0.9489 | 0.9134 | 0.8666 | 0.8095 |
8 | 0.9998 | 0.9995 | 0.9991 | 0.9985 | 0.9976 | 0.9962 | 0.9943 | 0.9917 | 0.9883 | 0.9840 | 0.9786 | 0.9597 | 0.9319 | 0.8944 |
9 | 1.0000 | 0.9999 | 0.9998 | 0.9996 | 0.9993 | 0.9989 | 0.9982 | 0.9973 | 0.9960 | 0.9942 | 0.9919 | 0.9829 | 0.9682 | 0.9462 |
10 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9998 | 0.9997 | 0.9995 | 0.9992 | 0.9987 | 0.9981 | 0.9972 | 0.9933 | 0.9863 | 0.9747 |
11 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9998 | 0.9996 | 0.9994 | 0.9991 | 0.9976 | 0.9945 | 0.9890 |
12 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9998 | 0.9997 | 0.9992 | 0.9980 | 0.9955 |
13 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9997 | 0.9993 | 0.9983 |
14 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9998 | 0.9994 |
15 | 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 | 0.9998 |
16 | 1.0000 | 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 |
17 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
x\λ | 6.0 | 6.5 | 7.0 | 7.5 | 8.0 | 8.5 | 9.0 | 9.5 | 10.0 | 11.0 | 10.0 | 12.0 | 14.0 | 15.0 |
0 | 0.0025 | 0.0015 | 0.0009 | 0.0006 | 0.0003 | 0.0002 | 0.0001 | 0.0001 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
1 | 0.0174 | 0.0113 | 0.0073 | 0.0047 | 0.0030 | 0.0019 | 0.0012 | 0.0008 | 0.0005 | 0.0002 | 0.0005 | 0.0001 | 0.0000 | 0.0000 |
2 | 0.0620 | 0.0430 | 0.0296 | 0.0203 | 0.0138 | 0.0093 | 0.0062 | 0.0042 | 0.0028 | 0.0012 | 0.0028 | 0.0005 | 0.0001 | 0.0000 |
3 | 0.1512 | 0.1118 | 0.0818 | 0.0591 | 0.0424 | 0.0301 | 0.0212 | 0.0149 | 0.0103 | 0.0049 | 0.0103 | 0.0023 | 0.0005 | 0.0002 |
4 | 0.2851 | 0.2237 | 0.1730 | 0.1321 | 0.0996 | 0.0744 | 0.0550 | 0.0403 | 0.0293 | 0.0151 | 0.0293 | 0.0076 | 0.0018 | 0.0009 |
5 | 0.4457 | 0.3690 | 0.3007 | 0.2414 | 0.1912 | 0.1496 | 0.1157 | 0.0885 | 0.0671 | 0.0375 | 0.0671 | 0.0203 | 0.0055 | 0.0028 |
6 | 0.6063 | 0.5265 | 0.4497 | 0.3782 | 0.3134 | 0.2562 | 0.2068 | 0.1649 | 0.1301 | 0.0786 | 0.1301 | 0.0458 | 0.0142 | 0.0076 |
7 | 0.7440 | 0.6728 | 0.5987 | 0.5246 | 0.4530 | 0.3856 | 0.3239 | 0.2687 | 0.2202 | 0.1432 | 0.2202 | 0.0895 | 0.0316 | 0.0180 |
8 | 0.8472 | 0.7916 | 0.7291 | 0.6620 | 0.5925 | 0.5231 | 0.4557 | 0.3918 | 0.3328 | 0.2320 | 0.3328 | 0.1550 | 0.0621 | 0.0374 |
9 | 0.9161 | 0.8774 | 0.8305 | 0.7764 | 0.7166 | 0.6530 | 0.5874 | 0.5218 | 0.4579 | 0.3405 | 0.4579 | 0.2424 | 0.1094 | 0.0699 |
10 | 0.9574 | 0.9332 | 0.9015 | 0.8622 | 0.8159 | 0.7634 | 0.7060 | 0.6453 | 0.5830 | 0.4599 | 0.5830 | 0.3472 | 0.1757 | 0.1185 |
11 | 0.9799 | 0.9661 | 0.9467 | 0.9208 | 0.8881 | 0.8487 | 0.8030 | 0.7520 | 0.6968 | 0.5793 | 0.6968 | 0.4616 | 0.2600 | 0.1848 |
12 | 0.9912 | 0.9840 | 0.9730 | 0.9573 | 0.9362 | 0.9091 | 0.8758 | 0.8364 | 0.7916 | 0.6887 | 0.7916 | 0.5760 | 0.3585 | 0.2676 |
13 | 0.9964 | 0.9929 | 0.9872 | 0.9784 | 0.9658 | 0.9486 | 0.9261 | 0.8981 | 0.8645 | 0.7813 | 0.8645 | 0.6815 | 0.4644 | 0.3632 |
14 | 0.9986 | 0.9970 | 0.9943 | 0.9897 | 0.9827 | 0.9726 | 0.9585 | 0.9400 | 0.9165 | 0.8540 | 0.9165 | 0.7720 | 0.5704 | 0.4657 |
15 | 0.9995 | 0.9988 | 0.9976 | 0.9954 | 0.9918 | 0.9862 | 0.9780 | 0.9665 | 0.9513 | 0.9074 | 0.9513 | 0.8444 | 0.6694 | 0.5681 |
16 | 0.9998 | 0.9996 | 0.9990 | 0.9980 | 0.9963 | 0.9934 | 0.9889 | 0.9823 | 0.9730 | 0.9441 | 0.9730 | 0.8987 | 0.7559 | 0.6641 |
17 | 0.9999 | 0.9998 | 0.9996 | 0.9992 | 0.9984 | 0.9970 | 0.9947 | 0.9911 | 0.9857 | 0.9678 | 0.9857 | 0.9370 | 0.8272 | 0.7489 |
18 | 1.0000 | 0.9999 | 0.9999 | 0.9997 | 0.9993 | 0.9987 | 0.9976 | 0.9957 | 0.9928 | 0.9823 | 0.9928 | 0.9626 | 0.8826 | 0.8195 |
19 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9997 | 0.9995 | 0.9989 | 0.9980 | 0.9965 | 0.9907 | 0.9965 | 0.9787 | 0.9235 | 0.8752 |
20 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9998 | 0.9996 | 0.9991 | 0.9984 | 0.9953 | 0.9984 | 0.9884 | 0.9521 | 0.9170 |
21 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9998 | 0.9996 | 0.9993 | 0.9977 | 0.9993 | 0.9939 | 0.9712 | 0.9469 |
22 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9997 | 0.9990 | 0.9997 | 0.9970 | 0.9833 | 0.9673 |
23 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9999 | 0.9995 | 0.9999 | 0.9985 | 0.9907 | 0.9805 |
24 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9998 | 1.0000 | 0.9993 | 0.9950 | 0.9888 |
25 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 1.0000 | 0.9997 | 0.9974 | 0.9938 |
26 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9987 | 0.9967 |
27 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 0.9994 | 0.9983 |
28 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9997 | 0.9991 |
29 | 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 | 0.9996 |
30 | 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 | 0.9998 |
31 | 1.0000 | 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 |
32 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |