The mean amount purchased by a typical customer at Churchill's Grocery Store is $21.50 with a standard deviation of $7.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 44 customers, answer the following questions.
What is the likelihood the sample mean is at least $24.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)
What is the likelihood the sample mean is greater than $19.50 but less than $24.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Within what limits will 90 percent of the sample means occur? (Round your answers to 2 decimal places.)