**Answer:**

**a) **9.52% probability that, in a year, there will be 4 hurricanes.

**b) **4.284 years are expected to have 4 hurricanes.

**c) **The value of 4 is very close to the expected value of 4.284, so 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 time interval.

**6.9 per year.**

This means that

**a. Find the probability that, in a year, there will be 4 hurricanes. **

This is P(X = 4).

So

9.52% 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? **

For each year, the probability is 0.0952.

Multiplying by 45

45*0.0952 = 4.284.

4.284 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 4 years had 4 hurricanes? Does the Poisson distribution work well here? **

The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.