The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile.

(a) What is the probability that there are no cracks that require repair in 5 miles of highway?

(b) What is the probability that at least one crack requires repair in 1/2 mile of highway?

(c) If the number of cracks is related to the vehicle load on the highway and some sections of the highway have a heavy load of vehicles whereas other sections carry a light load, how do you feel about the assumption of a Poisson distri- bution for the number of cracks that require repair?