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.