The mean amount purchased by typical customer at Churchill's Grocery Store is $23.50 with standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For sample of 50 customers, answer the following questions.
a. Determine the likelihood sample mean is at least $25.00?
b. Determine the likelihood sample mean is greater than $22.50 but less than $25.00?
c. In what limits will 90 percent of the sample means occur?