At an automatic car wash,cars arrive randomly at a rate of 7 every 30 minutes.The car wash takes exactly 4 minutes (this is constant).On average,how long would each driver have to wait before receiving service?
A)28 minutes
B)32 minutes
C)17 minutes
D)24 minutes
E)None of the above

Question

Quizplus · Accepted Answer

The arrival rate is 7 cars per 30 minutes, or 1 car every 4.29 minutes. Since the service time is 4 minutes per car, the system is stable. The average wait time in a queue can be calculated using the formula: (arrival rate * service time^2) / (2 * (1 - utilization)), where utilization is the arrival rate times the service time. This results in an average wait time of approximately 28 minutes.

At an Automatic Car Wash,cars Arrive Randomly at a Rate