A trucking firm has five trucks that each requires service at an average rate of once every 50 hours, according to an exponential distribution. The firm has a mechanic who needs five hours to complete the average job with exponential service times.
-Use the information in Scenario C.5.What is the average time a truck spends in the system?
A) Fewer than or equal to 6.5 hours
B) Greater than 6.5 hours but fewer than or equal to 7.0 hours
C) Greater than 7.0 hours but fewer than or equal to 7.5 hours
D) Greater than 7.5 hours

Question

Quizplus · Accepted Answer

The average time a truck spends in the system includes both the time spent waiting for service and the time spent being serviced. 
The average time between service requirements is 50 hours, so the arrival rate of trucks is λ = 1/50. 
The average service time is 5 hours, so the service rate is μ = 1/5.
Using Little's Law, the average time a truck spends in the system is L = λ/(μ-λ) = (1/50)/(1/5-1/50) = 7.14 hours.
Therefore, the answer is C: Greater than 7.0 hours but fewer than or equal to 7.5 hours.

A Trucking Firm Has Five Trucks That Each Requires Service