Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000.
a. Based on this sample information, develop a 90% confidence interval for the population mean yearly premium.
b. How large a sample is needed to find the population mean within $250 at 99% confidence?