1. The mean amount purchased by a typical customer at Churchill’s Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. 1. What is the likelihood the sample mean is at least $25.00? 2. What is the likelihood the sample mean is greater than $22.50 but less than $25.00? 3. Within what limits will 90 percent of the sample means occur?
2. 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. 1. Based on this sample information, develop a 90 percent confidence interval for the population mean yearly premium. 2. How large a sample is needed to find the population mean within $250 at 99 percent confidence? Given the following data sets: