Question

NEED HELP PLEASE

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.8 per year.
a. Find the probability​ that, in a​ year, there will be 5 hurricanes.
b. In a ​55-year ​period, how many years are expected to have 5 ​hurricanes?
c. How does the result from part​ (b) compare to a recent period of 55 years in which 5 years had 5 ​hurricanes? Does the Poisson distribution work well​ here?

Answer 1

Explanation:

For this problem I'm gonna use the Excel function for the Poisson distribution. I'll leave the solutions in images attatched to this answer.

b. 55 * 0.0986= 5.423 years, or just 5 years.

c, It shows that the calculation of 5 years with 5 hurricanes in 55 years is accurate.

Does the Poisson distribution work well​ here? It does, because the calculations illusrate something very similar to the facts.