Poisson distribution online calculator
You can see a sample solution below. Enter your data to get the solution for your question
$$ \displaylines{\\ \\
\\ \\ Mean = \mu = 6
\\ \\ k = 5
\\ \\
formula\;for\;Poisson\;is\;P(k)=
\frac{e^{- \mu}* \mu^{k}}{k!}
\\ \\
P(X<=k)=
\sum_{i=0}^{k}P(i)
= \sum_{i=0}^{k}\frac{e^{- \mu}* \mu^{i}}{i!}
\\ \\
P(X<=5)=
\sum_{i=0}^{5}\frac{e^{- 6}* 6^{i}}{i!}
\\ \\
=
\frac{e^{- 6}* 6^{0}}{0!}+\frac{e^{- 6}* 6^{1}}{1!}+\frac{e^{- 6}* 6^{2}}{2!}+\frac{e^{- 6}* 6^{3}}{3!}+\frac{e^{- 6}* 6^{4}}{4!}+\frac{e^{- 6}* 6^{5}}{5!}
\\ \\
=
0.002479+0.014873+0.044618+0.089235+0.133853+0.160623
\\ \\
0.44568
\\ \\
= \mathbf{\color{Red}{0.44568}}
} $$