The distance between major cracks in a highway
follows an exponential distribution with a mean of five miles.
(a) What is the probability that there are no major cracks in a
10-mile stretch of the highway?
(b) What is the probability that there are two major cracks in a
10-mile stretch of the highway?
(c) What is the standard deviation of the distance between
major cracks?
(d) What is the probability that the first major crack occurs
between 12 and 15 miles of the start of inspection?
(e) What is the probability that there are no major cracks in
two separate five-mile stretches of the highway?
(f) Given that there are no cracks in the first five miles
inspected, what is the probability that there are no major
cracks in the next 10 miles inspected?
