Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 6.9 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 4 years had 4 hurricanes? Does the Poisson distribution work well here? a. The probability is nothing. (Round to three decimal places as needed.)

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.

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get