Question

Given that x has a Poisson distribution with

Answer 1

The Poisson probability distribution function is
$P(x;\mu)= \frac{e^{-\mu}\mu ^{x}}{x!}$
where
μ = mean number of successes
x =  actual or expected number of successes

Given:
μ = 13
x = 5

Therefore the probability that x=5 is
P(x = 5) = (e⁻¹³*13⁵)/5!
             = 0.8392/120
             = 0.006994
             = 0.0070  (to 4 dec. places)

Answer: 0.0070  (to 4 decimal places)

It is interesting to observe P(x) as x varies, as in the graph shown below.