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 5 hurricanes. b. In a 45-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 45 years in which 4 years had 5 hurricanes? Does the Poisson distribution work well here? a. The probability is. (Round to three decimal places as needed.) b. The expected number of years with 5 hurricanes is (Round to one decimal place as needed.) c. The result from part (b) is V the number of hurricanes in the recent period of 45 years, so the Poisson distribution V appear to work well in the given situation.

(a) The mean number of hurricanes in a certain area is 7.7 per year. Given the mean number of success (λ) that occur in a specified region, we can compute the Poisson probability based on the following formula: P(X) =(e-l λx )/x! where, 'x' is the actual number of successes, λ is the mean number of success occurred in a specified region. (a) The probability that, in a year, there will be 5 hurricanes is obtained as follows: P(5)=(e-7.7 ×7.75 )/5! = 0.1021 Thus, probability that, in a year, there will be 5 hurricanes is 0.102. (b) The probability that, in a year, there will be 5 hurricanes is 0.102. So, the number of expected years out of 45 to have 5 hurricanes can be calculated as: µ=np= 45×0.102= 4.6 thus, we expect about 5 years with hurricanes. (c) Yes, Poisson distribution can be applied here. We expect about 5 years with hurricanes and 4 is very close to that value. The result from part (b) is very close to the number of hurricanes in the recent period of 45 years. so, the Poisson distribution appears to work well in the situation.