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: