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 trucks 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
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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 trucks 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 distribution 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.
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What is the
probability that all three inspection units will be idle at the same time? -
What proportion of trucks traveling this section of Interstate 81 will be inspected?
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On average, how many trucks will be pulled over for inspection each hour?
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