The Poisson probability distribution function is
[tex]P(x;\mu)= \frac{e^{-\mu}\mu ^{x}}{x!} [/tex]
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.
