Assume that the poisson distribution applies and that the mean number of hurricanes in a certain area is 5.4 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) There is a probability of 12% that 3 hurricanes happens in any year.

b) It is expected that 5.4 years in a period of 45 years have 3 hurricanes.

c) The Poisson distribution work well in predicting this kind of events.

Step-by-step explanation:

The Poisson distribution has the following expression

In this case we have . The probability that, in a year, there will be 3 hurricanes is:

There is a probability of 12% that 3 hurricanes happens in any year.

If we take a period of 45 years, the expected amount of years with 3 hurricanes can be estimated as:

It is expected that 5.4 years in a period of 45 years have 3 hurricanes.

The Poisson distribution work well in predicting this kind of events.