Assume that the Poisson distribution applies and that the mean number of hurrica
ID: 3369871 • Letter: A
Question
Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.7 per year. a. Find the probability? that, in a? year, there will be 6 hurricanes. b. In a 55?-year ?period, how many years are expected to have 6 ?hurricanes? c. How does the result from part? (b) compare to a recent period of 55 years in which 7 years had 6 ?hurricanes? Does the Poisson distribution work well? here? a. The probability is nothing. ?(Round to three decimal places as? needed.) b. The expected number of years with 6 hurricanes is nothing. ?(Round to one decimal place as? needed.) c. The result from part? (b) is ? close to very different from the number of hurricanes in the recent period of 55 ?years, so the Poisson distribution ? does not does appear to work well in the given situation.
Explanation / Answer
a) probability? that, in a? year, there will be 6 hurricanes =P(X=6)=e-7.7*7.76/6! =0.131
b) expeced periods =np=55*0.131=7.2
c)The result from part? (b) is close to from the number of hurricanes in the recent period of 55 ?years, so the Poisson distribution appear to work well in the given situation.