At a border inspection station, vehicles arrive at a rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there is only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion. What is the average length of the waiting line? Note: Round your answer to 2 decimal places. What is the average total time it takes for a vehicle to get through the system? Note: Round your answer to the nearest whole number. What is the utilization of the inspector? Note: Round your answer to 1 decimal place. What is the probability that when you arrive there will be three or more vehicles ahead of you? Note: Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.
At a border inspection station, vehicles arrive at a rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there is only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion.
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What is the average length of the waiting line?
Note: Round your answer to 2 decimal places.
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What is the average total time it takes for a vehicle to get through the system?
Note: Round your answer to the nearest whole number.
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What is the utilization of the inspector?
Note: Round your answer to 1 decimal place.
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What is the probability that when you arrive there will be three or more vehicles ahead of you?
Note: Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.
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