In a service centre, cars arrive according to Poisson distribution with a mean of two cars per hour. The time of servicing a car is exponential with a mean of 15 minutes. The expected waiting time (in minute) in the queue is A. 10 B. 15 C. 25 D. 30

[amp_mcq option1=”10″ option2=”15″ option3=”25″ option4=”30″ correct=”option1″]

The correct answer is A. 10.

The expected waiting time in the queue is equal to the reciprocal of the arrival rate times the service rate. The arrival rate is 2 cars per hour, which is equal to 1/30 cars per minute. The service rate is 1 car per 15 minutes, which is equal to 4/60 cars per minute. Therefore, the expected waiting time in the queue is 1/30 * 4/60 = 10 minutes.

Option B is incorrect because it is the mean service time. Option C is incorrect because it is the mean time between arrivals. Option D is incorrect because it is the mean of the sum of the service time and the waiting time.