Question

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.2 per year. a. Find the probability that, in a year, there will be 4 hurricanes. b. In a 45 -year period, how many years are expected to have 4 hurricanes? c. How does the result from part (b) compare to a recent period of 45 years in which 7 years had 4 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 4 hurricanes is nothing. (Round to one decimal place as needed.) c. The result from part (b) is ▼ close to very OR different from the number of hurricanes in the recent period of 45 years, so the Poisson distribution ▼ does OR does not appear to work well in the given situation.

Answer 1

Here, we have Poisson distribution with = 5.2

Probability mass function of Poisson distribution is :

Let X denote the number of hurricanes in a certain area.

a.

Probability that, in a year, there will be 4 hurricanes = P(X=4)

Probability that, in a year, there will be 4 hurricanes = 0.168

b.

In a 45 -year period, The expected number of years with 4 hurricanes is = 45 * P(X=4) = 45 * 0.168 = 7.6

c.

The result from part (b) is very close to the number of hurricanes in the recent period of 45 years, so the Poisson distribution does appear to work well in the given situation.