Interstate 81 through southwest Virginia is heavily traveled by long-distance truckers. To cut down on accidents, The

Question:

Interstate 81 through southwest Virginia is heavily traveled by long-distance truckers. To cut down on accidents, The Virginia State Patrol carries out random inspections of a truck’s weight and the condition of its brakes. On Fridays, trucks approach the inspection station at a rate of one every 45 seconds following a Poisson process. The time required to check a truck’s weight and brakes follows an exponential with an average inspection time of 5 minutes. The state troopers only pull over trucks when at least one of their three portable inspection units is available.
a. What is the probability that all three inspection units will be idle at the same time?
b. What proportion of trucks traveling this section of Interstate 81 will be inspected?
c. On average, how many trucks will be pulled over for inspection each hour?

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