Assume that the poisson distribution applies and that the mean number of hurricanes in a certain area is 5.55.5 per year. a. find the probability that, in a year, there will be 44 hurricanes. b. in a 5555-year period, how many years are expected to have 44 hurricanes? c. how does the result from part (b) compare to a recent period of 5555 years in which 88 years had 44 hurricanes? does the poisson distribution work well here?

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.

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