Poisson Probability Calculator

Answer:

$ P(8) $ Probability of exactly 8 occurrences: 0.11881525306021

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Solution:

$P(8)$ Probability of exactly 8 occurrences

If using a calculator, you can enter $ \lambda = 6.5 $ and $ x = 8 $ 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 = 8 $ and $ \lambda = 6.5 $, we have $$ P(8) = \frac{{e^{-6.5}} \cdot {6.5^8}}{8!} $$ Evaluating the expression, we have $$ P(8) = 0.11881525306021 $$