Mathematics

Mariela Perkins

10 May, 23:47

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 2 cracks per mile. Round your answers to four decimal places (e. g. 98.7654).

(a) What is the probability that there are no cracks that require repair in 15 miles of highway?

(b) What is the probability that at least one crack requires repair in 1/4 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 and other sections carry a light load, how do you feel about the assumption of a Poisson distribution for the number of cracks that require repair for all sections (1 denotes "is valid" and 0 otherwise) ?