During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10 miles. A

Question

During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10 miles. A certain county is responsible for repairing potholes in a 10-mile stretch of the interstate (thus the average potholes are 3 * 1.6 = 4.8 for the 10-mile stretch). Let Y denote the number of potholes the county will have to repair at the end of next winter.

a. What is the distribution? What is/are its parameter(s)?

b. What is the expected value (mean), variance, and standard deviation?

c. What is the probability of finding exactly 5 potholes over the 10-mile stretch by the end of winter? That is find P(Y = 5)

d. What is the probability that there are more than 4 but no more than 9 potholes? That is, find P(4 < Y =< 9)

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Explanation / Answer

a. The distribution of Y is Poisson with parameter = 4.8.

b. The mean and the variance is 4.8. The standard deviation is 2.19.

c. P(Y=5) = 0.17

d. P(4<Y<=9) = P(Y=5) + P(Y=6) + ... + P(Y=9) = 0.49

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