Given that x has a poisson distribution with
mu
μ
equals
=
13
13, what is the probability that x
equals
=
5
5?
p(
5
5)
almost equals
≈
0.9930
0.9930 (round to four decimal places as needed.)

The Poisson probability distribution function is

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)

0.0070  (to 4 decimal places)

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