Question

For the past 102 ​years, a certain state suffered 25 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 2005 hurricane season in this state was​ unusual?

Answer 1

Number of years observed = 102

Number of times hurricane hit = 25

Average number of hurricane per year,

Poisson distribution:

​(a) probability that the state will not be hit by any major hurricanes in a single​ year, P(X=0) =

​(b) probability that the state will be hit by at least one major hurricane in a single​ year, P(X >=1) =

No, it is not unusual.

​(c) probability that the state will be hit by at least three major hurricanes in a single​ year, P(X >=3) =

d) Yes, it is unusual.