Chapter 16, Problem 67E

The service history of the Prego SUV is as follows: 50% will need no repairs during the first year, 35% will have repair costs of $\$500$ during the first year, 12% will have repair costs of $\$1500$ during the first year, and the remaining SUVs (the real lemons) will have repair costs of $\$4000$ during their first year. Determine the price that the insurance company should charge for a one-year extended warranty on a Prego SUV if it wants to make an average profit of $\$50$ per policy.