Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.3 per year. a. Find the probability that in a year, there will be 3 hurricanes. b. in a 45-year period, how many years are expected to have 3 hurricanes ? c. How does the result from part (b) compare to a recent period of 45 years in which 5 years had 3 hurricanes? Does the Poisson distribution work well here?

a) 0.12386 = 12.386% probability that in a year, there will be 3 hurricanes.

b) 5.57 years are expected to have 3 hurricanes, that is, between 5 and 6 years.

c) 5 years is very close to the mean of 5.57, which means that the Poisson distribution works well here.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

The mean number of hurricanes in a certain area is 5.3 per year.

This means that

a. Find the probability that in a year, there will be 3 hurricanes.

This is P(X = 3).

0.12386 = 12.386% probability that in a year, there will be 3 hurricanes.

b. in a 45-year period, how many years are expected to have 3 hurricanes ?

0.12386 each year. So, for 45 years:

45*0.12386 = 5.57

5.57 years are expected to have 3 hurricanes, that is, between 5 and 6 years.

c. How does the result from part (b) compare to a recent period of 45 years in which 5 years had 3 hurricanes? Does the Poisson distribution work well here?

5 years is very close to the mean of 5.57, which means that the Poisson distribution works well here.

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed