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 problems.

a. What is the likelihood the sample mean is at least $25.00?

b. What is the likelihood the sample mean is greater than $22.50 but less than $25.00?

c. Within what limits will 90 percent of the sample means occur?