We are given
λ = mean = 5.5 hurricanes per year
and Poisson distribution applies.
P(k, λ ) = λ ^k * e^(- λ ) / k!
a) 4 hurricanes in a year
P(4,5.5)=5.5^(4)*e^(-5.5)/4!
=0.1558
b) In 55 years, the expected number of years with 4 hurricanes
= 55*0.1558 = 8.57, could be rounded to the nearest integer, 9.
c) Records show that in 55 years had 8 years had 4 hurricanes each year.
This compares very closely with the expected number 8.57.
