Question

For the past 104 ​years, a certain state suffered 27 direct hits from major​ (category 3 to​ 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts​ (a) through​ (d). a) What is the probability that the state will not be hit by any major hurricanes in a single​ year? The probability is nothing.​ (Round to four decimal places as​ needed.) ​(b) What is the probability that the state will be hit by at least one major hurricane in a single​ year? The probability is nothing. ​(Round to four decimal places as​ needed.) Is this​ unusual? Yes No ​(c) What is the probability that the state will be hit by at least three major hurricanes in a single​ year, as happened last​ year? The probability is nothing. ​(Round to four decimal places as​ needed.) Does this indicate that the 2004 hurricane season in this state was​ unusual?

Answer 1

Let X be the random variable representing the number of hits by major hurricances in a year.

given,

total number of hits in last 104 years = 27

that implies the rate of hit by a major hurricane per year = 27/104

and it is given that the number of hits per year follows a poisson distribution,

a)

The probability that the State will not hit by any major hurricane in a single year,

b)

The probability that the state will be hit by at least one major hurricane in a single year,

c)

The probability that the state will be hit by atleast three major hurricanes in a single year,

this show the probability that the state will be hit by atleast three major hurricanes in a single year is very very small.This indicate that the 2004 hurricane season in this state was​ unusual.