Customers arrive every three minutes governed by a Poisson distribution.A single server is capable of handling twenty-five customers per hour and this service time is exponentially distributed.About how many minutes per hour is the server not helping customers?
A)less than or equal to 7
B)greater than 7 but less than or equal to 10
C)greater than 10 but less than or equal to 13
D)greater than 13

Question

Quizplus · Accepted Answer

The arrival rate is 20 customers per hour (60/3), and the service rate is 25 customers per hour. The utilization rate is 20/25 = 0.8, meaning the server is busy 80% of the time and idle 20% of the time. Therefore, the server is not helping customers for 0.2 * 60 = 12 minutes per hour.

Customers Arrive Every Three Minutes Governed by a Poisson Distribution