For the past 107 years, a certain state suffered 34 direct hits from major (cate

Question

For the past 107 years, a certain state suffered 34 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 (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 (Round to four decimal places as needed.) Is this unusual? O No O Yes (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 (Round to four decimal places as needed.) Does this indicate that the 2004 hurricane season in this state was unusual? O No O Yes

Explanation / Answer

Average = 34/107 = 0.32

So from Poisson distribution calculator:

a) P(X = 0) = 0.7278

b) P(At least one hurricane) = P(X > 0) = 0.2722

No

c) P(At least three hurricanes) = P(X > 2) = 0.0042

Yes

d) P(At least two hurricanes) = P(X > 1) = 0.0410

Yes

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