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Poisson distribution online calculator

Mean: Exact k Less than or equal to k Greater than or equal to k

You can see a sample solution below. Enter your data to get the solution for your question

$$\displaylines{\\ \\ \\ \\ Mean = \mu = 6 \\ \\ k = 5 \\ \\ formula\;for\;Poisson\;is\;P(k)= \frac{e^{- \mu}* \mu^{k}}{k!} \\ \\ P(X<=k)= \sum_{i=0}^{k}P(i) = \sum_{i=0}^{k}\frac{e^{- \mu}* \mu^{i}}{i!} \\ \\ P(X<=5)= \sum_{i=0}^{5}\frac{e^{- 6}* 6^{i}}{i!} \\ \\ = \frac{e^{- 6}* 6^{0}}{0!}+\frac{e^{- 6}* 6^{1}}{1!}+\frac{e^{- 6}* 6^{2}}{2!}+\frac{e^{- 6}* 6^{3}}{3!}+\frac{e^{- 6}* 6^{4}}{4!}+\frac{e^{- 6}* 6^{5}}{5!} \\ \\ = 0.002479+0.014873+0.044618+0.089235+0.133853+0.160623 \\ \\ 0.44568 \\ \\ = \mathbf{\color{Red}{0.44568}} }$$