Poisson Probability Calculator

Answer:

$ P(6) $ Probability of exactly 6 occurrences: 0.12373365507425

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Solution:

$P(6)$ Probability of exactly 6 occurrences

If using a calculator, you can enter $ \lambda = 4.4 $ and $ x = 6 $ 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 = 6 $ and $ \lambda = 4.4 $, we have $$ P(6) = \frac{{e^{-4.4}} \cdot {4.4^6}}{6!} $$ Evaluating the expression, we have $$ P(6) = 0.12373365507425 $$