At the california border inspection station vehicles arrive, Operation Management

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At the california border inspection station vehicles arrive

At the California border inspection station, vehicles arrive at the rate of 12 per minute following a Poisson distribution. For simplicity, assume that there is only one lane and one inspector, who can consider vehicles at the rate of 14 per minute also according to a Poisson distribution.

What is the average length of the waiting line?

What is the average time that a vehicle must wait to get through the system?

What is the utilization of the inspector?

What is the probability that when you arrive there will be three or more vehicles ahead of you?

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