The employees of General Manufacturing Corp. receive health insurance through a group plan issued by Wellnet. During the past year, 40 percent of the employees did not file any health insurance claims, 40 percent filed only a small claim, and 20 percent filed a large claim. The small claims were spread uniformly between 0 and $2,000, whereas the large claims were spread uniformly between $2,000 and $20,000. Based on this experience, Wellnet now is negotiating the corporation’s premium payment per employee for the upcoming year. You are an OR analyst for the insurance carrier, and you have been assigned the task of estimating the average cost of insurance coverage for the corporation’s employees. Follow the instructions of Prob. 22.7-4, where the size of an employee’s health insurance claim (including 0 if no claim was filed) now plays the role that the repair time for a bicycle did in Prob. 22.7-4. [For part (), the true mean of the overall probability distribution of the size of an employee’s health insurance claim is $2,600.]
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.
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