A certain area of the US is hit by six hurricanes per year F

A certain area of the U.S. is hit by six hurricanes per year. Find the probability that in a given

year that area will experience between 5 to 9 hurricanes inclusively.

Solution

Given X follows Poisson distribution with mean =6

P(X=x)=(6^x)*exp(-6)/x! for x=0,1,2,...

So the probability is

P(5<=X<=9) = P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)

=(6^5)*exp(-6)/5!+....+(6^9)*exp(-6)/9!

=0.6310195