Eddie's Bicycle Shop has a thriving business repairing bicycles. Trisha runs the reception area where customers check in their bicycles to be repaired and then later pick up their bicycles and pay their bills. She estimates that the time required to serve a customer on each visit has a uniform distribution between 3 minutes and 8 minutes. Apply the inverse transformation method as indicated below to simulate the service times for five customers by using the following five uniform random numbers: 0.6505, 0.0740, 0.8443, 0.4975, 0.8178.
(a) Apply this method graphically.
(b) Apply this method algebraically.
(c) Calculate the average of the five service times and compare it to the mean of the service-time distribution.
(d) Use Excel to generate 500 random observations and calculate the average. Compare this average to the mean of the service-time distribution.