Poisson Probability Calculator

Answer:

$ P(5) $ Probability of exactly 5 occurrences: 0.10747670147956


Solution:

$P(5)$ Probability of exactly 5 occurrences

If using a calculator, you can enter $ \lambda = 3.1 $ 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 = 3.1 $, we have $$ P(5) = \frac{{e^{-3.1}} \cdot {3.1^5}}{5!} $$ Evaluating the expression, we have $$ P(5) = 0.10747670147956 $$