Question: Problem At a border inspection station, vehicles arrive at a rate of 10 per hour in a Poisson distribution. There is only one lane and

Problem At a border inspection station, vehicles arrive at a rate of 10 per hour in a Poisson distribution. There is only one lane and one inspector, who can inspect vehicles within 5 minutes each in an exponentially distributed fashion. a. Calculate the arrival rate and the service rate.

b. Calculate the percentage of time the inspector is free (idle).

c. Calculate the average number of vehicles in the station.

d. Calculate the average time that a vehicle must wait in line.

e. What is the probability of having 10 vehicles in the station?

f. What is the probability of having more than 2 vehicles in the station?

g. During the weekend, a vehicle arrives every 4 minutes. By how much the average waiting time of a vehicle in the line would increase?

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