Question

The mean amount purchased by a typical customer at Churchill's Grocery Store is $21.00 with a standard deviation of $7.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 42 customers, answer the following questions.





(a)


What is the likelihood the sample mean is at least $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)





Probability







(b)


What is the likelihood the sample mean is greater than $20.00 but less than $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)





Probability







(c)


Within what limits will 99 percent of the sample means occur? (Round your answers to 2 decimal places.)





Sample mean



and