Poisson Probability Calculator

Answer:

$ P(5) $ Probability of exactly 5 occurrences: 0.1376800842061

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Solution:

$P(5)$ Probability of exactly 5 occurrences

If using a calculator, you can enter $ \lambda = 3.6 $ and $ x = 5 $ into a poisson probability distribution function (PDF). If doing this by hand, apply the poisson probability formula: $$ P(x) = \frac{{e^{-\lambda}} \cdot {\lambda^x}}{x!} $$ where $x$ is the number of occurrences, $\lambda$ is the mean number of occurrences, and $e$ is the constant 2.718. Substituting in values for this problem, $ x = 5 $ and $ \lambda = 3.6 $, we have $$ P(5) = \frac{{e^{-3.6}} \cdot {3.6^5}}{5!} $$ Evaluating the expression, we have $$ P(5) = 0.1376800842061 $$