Poisson Probability Calculator
Answer:
$ P(7) $ Probability of exactly 7 occurrences: 0.11252824952692
Solution:
$P(7)$ Probability of exactly 7 occurrences
If using a calculator, you can enter $ \lambda = 5.2 $ and $ x = 7 $ 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 = 7 $ and $ \lambda = 5.2 $, we have $$ P(7) = \frac{{e^{-5.2}} \cdot {5.2^7}}{7!} $$ Evaluating the expression, we have $$ P(7) = 0.11252824952692 $$