A suburban specialty restaurant has developed a single drive-thru window.Customers order,pay,and pick up their food at the same window.Arrivals follow a Poisson distribution while service times follow an exponential distribution.If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes,what proportion of the time is the server busy?
A)0.25
B)0.50
C)0.75
D)2.25
E)3.00

Question

Quizplus · Accepted Answer

First, we need to find the service rate in arrivals per hour to be able to compare it to the arrival rate per hour. If 2 customers are served every 15 minutes, then in one hour (60 minutes), 8 customers will be served. So the service rate is 8 customers per hour.
Next, we can use the following formula to find the proportion of time the server is busy:
P(server is busy) = (arrival rate)/(service rate)
P(server is busy) = (6)/(8)
P(server is busy) = 0.75
Therefore, the proportion of time the server is busy is 0.75 or 75%, which is answer choice C.

A Suburban Specialty Restaurant Has Developed a Single Drive-Thru Window