Final answer:
A customer should expect to leave a motor at the repair shop for approximately 2.5833 hours. To reduce the expected waiting time to 6.5 hours, the variance of the repair time would need to be controlled to reduce the average repair time to 2.5 hours.
Step-by-step explanation:
To calculate the number of working hours a customer should expect to leave a motor at the repair shop, we need to find the average repair time and add it to the average waiting time. The average repair time is given as 2.5 hours. To find the average waiting time, we need to calculate the reciprocal of the arrival rate, which is 1 divided by 12 (since there are 12 motors arriving per week). This gives us 1/12 = 0.0833. Therefore, the average waiting time is 0.0833 hours per motor. Adding the average repair time of 2.5 hours to the average waiting time of 0.0833 hours gives us a total of 2.5833 hours that a customer should expect to leave a motor at the repair shop.
To reduce the expected waiting time to 6.5 hours, we can use the formula for the average waiting time of a Poisson process, which is 1/λ. In this case, λ is the arrival rate. We can solve for λ using the formula λ = 1/μ, where μ is the average repair time. By plugging in the given average repair time of 2.5 hours, we can find λ = 1/2.5 = 0.4 (arrivals per hour). To calculate the new average waiting time, we use the formula 1/λ. Plugging in the new arrival rate of 0.4, we find the new average waiting time to be 1/0.4 = 2.5 hours. Therefore, in order to reduce the expected waiting time to 6.5 hours, the variance of the repair time would need to be controlled such that the average repair time is reduced to 2.5 hours.