The mean amount purchased by 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.
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?