Question

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?

Answer 1

Answer:

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

$P(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}$

In this case we have $\lambda=5.4$. The probability that, in a year, there will be 3 hurricanes is:

$P(x=3)=\frac{5.4^3e^{-5.4}}{3!}=\frac{0.71}{6}=0.12$

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:

$Y=45*0.12=5.4$

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.