The distance between major cracks in a highway follows an exponential distribution with a mean of six miles.
i. Determine the probability that there are no major cracks in a 12-mile stretch of thehighway?
ii. Determine the probability that there are two major cracks in a 12-mile stretch of the highway?
iii. Determine the standard deviation of the distance between major cracks?
iv. Determine the probability that the first major crack occurs between 15 and 18 miles of the start of inspection?
v. Determine the probability that there are no major cracks in two separate six-mile stretches of the highway?
vi. Given that there are no cracks in the first six miles inspected, what is the probability that there are no major cracks in the next 12 miles inspected?