Technically, this counts
82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105, 106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124, 125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142, 143,144,145,146,147,148,149,150,151,152
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.