During a typical Pennsylvania winter Interstate 80 averages 1.6 potholes per 10 miles. A certain county is responsible for repairing potholes in 30-mile stretch of the interstate. Let X denote the number of potholes the county will have to repair at the end of the next winter. a. The distribution of the random variable X is (choose one)
1. binomial
2. hypergeometric
3. negative binomial
4. Poisson.

b. Give the expected value and variance of X.
c. Find P(4 < X < =9).
d. The cost of repairing a pothole is $5000. If Y denotes the county's pothole repair expense for next winter, find the mean value and variance of Y.