Question

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.8 per year. a. Find the probability​ that, in a​ year, there will be 5 hurricanes. b. In a 35​-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 35 years in which 3 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 ▼ close to very different from the number of hurricanes in the recent period of 35 ​years, so the Poisson distribution ▼ does does not appear to work wellin the given situation

Answer 1

Solution:

a. We are required to find:

Using the Poisson distribution model, we have:

Therefore, the probability is 0.0986

b. The expected number of years with 5 hurricanes is:

c. The result from part​ (b) is close to the number of hurricanes in the recent period of 35 ​years, so the Poisson distribution does appear to work well in the given situation.