Question

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.2 per year.

a. Find the probability​ that, in a​ year, there will be 4 hurricanes.

b. In a 35​-year ​period, how many years are expected to have 4 ​hurricanes?

c. How does the result from part​ (b) compare to a recent period of 35 years in which 5 years had 4 ​hurricanes? Does the Poisson distribution work well​ here?

Answer 1

Let X denotes the number of hurricanes in a certain area in a randomly selected year.

X ~ Poisson(5.2)

The probability mass function of X is

a) The probability​ that, in a​ year, there will be 4 hurricanes

b) Let Y denotes the number of years when there will be 4 hurricanes in a 35 year period.

Y ~ Binomial( n = 35, p = 0.168063)

The probability mass function of Y is

The expected number of years to have 4 ​hurricanes = n*p = 35*0.168063 = 5.882205

c) The answers are quite close.