Hurricanes. In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 6.1 per year, as in Example 1; and proceed to find the indicated probability.Hurricanesa. Find the probability that in a year, there will be 5 hurricanes.b. In a 55-year period, how many years are expected to have 5 hurricanes?c. How does the result from part (b) compare to the recent period of 55 years in which 8 years had 5 hurricanes? Does the Poisson distribution work well here?

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Asked Jan 12, 2020
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Hurricanes. In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 6.1 per year, as in Example 1; and proceed to find the indicated probability.

Hurricanes

a. Find the probability that in a year, there will be 5 hurricanes.

b. In a 55-year period, how many years are expected to have 5 hurricanes?

c. How does the result from part (b) compare to the recent period of 55 years in which 8 years had 5 hurricanes? Does the Poisson distribution work well here?

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Expert Answer

Step 1

Define the random variable x as the number of hurricanes in a year. Here, the occurrence of hurricanes is random and each hurricane is independent of the other. Also, the occurrences (hurricanes) are uniformly distributed for every year. Then, x follows Poisson distribution.

The Poisson distribution formula is,

Statistics homework question answer, step 1, image 1
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Step 2
Statistics homework question answer, step 2, image 1
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Step 3

b.

From part (a), the probability to have 5 hurricanes in a year is 0.158.

For a 55-year ...

Statistics homework question answer, step 3, image 1
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