A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be approximately bell-shaped with a mean of $9004 and a standard deviation of $5629 (based on data from the U.S. Department of Transportation).

a. Construct the 95% confidence interval for the mean of all such costs.

b. If you are a manager for an insurance company that provides lower rates for drivers who wear seat belts and you want a conservative estimate for a worst-case scenario, what amount should you use as the possible hospital cost for an accident victim who wears a seat belt?