Question

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.8 per year. a. Find the probability that, in a year, there will be 5 hurricanes. b. In a 35-year period, how many years are expected to have 5 hurricanes? c. How does the result from part (b) compare to a recent period of 35 years in which 3 years had 5 hurricanes? Does the Poisson distribution work well here?

a. The probability is . (Round to three decimal places as needed.)

b. The expected number of years with 5 hurricanes is (Round to one decimal place as needed.)

c. The result from part (b) is ▼ close to very different from the number of hurricanes in the recent period of 35 years, so the Poisson distribution ▼ does does not appear to work wellin the given situation

Answer #1

**Solution:**

**a. We are required to find:**

**Using the Poisson distribution model, we
have:**

**Therefore, the probability is 0.0986**

b. The expected number of years with 5 hurricanes is:

**c. The result from part (b) is close to the number of
hurricanes in the recent period of 35 years, so the Poisson
distribution does appear to work well in the given
situation.**

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