Item$13$

$5$points

Item $13$

At a border inspection station, vehicles arrive at the 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 time that a vehicle must wait to get through the system?

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.