Question 1: A normal population has a mean of 78 and a standard deviation of 6. You select a sample of 50. Evaluate the probability the sample mean is (Round z values to 2 decimal places and final answers to 4 decimal places):

(a) Less than 77.

(b) Between 77 and 79.

(c) Between 79 and 80.

(d) Greater than 80.

Question 2: CRA CDs Inc. wants the mean lengths of the "cuts" on a CD to be 150 seconds. This will allow the disk jockeys to have plenty of time for commercials within every 10-minute segment. Consider the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 9 seconds. Consider we select a sample of 24 cuts from various CDs sold by CRA CDs Inc.

(a) What can we say about the shape of the distribution of the sample mean?

(b) What is the standard error of the mean?

(c) What percent of the sample means will be greater than 155 seconds?

(e) What percent of the sample means will be greater than 142 but less than 155 seconds?

Question 3: The mean amount purchased by a typical customer at Churchill's Grocery Store is $21.00 with a standard deviation of $7.00. Suppose the distribution of amounts purchased follows the normal distribution. For a sample of 42 customers, answer the subsequent questions.

(a) What is the likelihood the sample mean is at least $22.50?

(b) What is the likelihood the sample mean is greater than $20.00 but less than $22.50?

(c) Within what limits will 99 percent of the sample means occur?