1) A normal population has a mean of 78 and the standard deviation of 6. You select a sample of 50.
Calculate the probability the sample mean is (Round z values to 2 decimal places andfinal answers to 4 decimal places):
(a) Less than 77.
(b) Between 77 and 79.
(c) Between 79 and 80.
(d) Greater than 80.
2) CRA CDs Inc. wants mean lengths of the "cuts" on a CD to be 150 seconds (2 minutes and 30 seconds). This would allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Suppose the distribution of the length of the cuts follows normal distribution with the population standard deviation of 9 seconds. Assume we choose a sample of 24 cuts from various CDs sold by CRA CDs Inc.
(a) What could we say about shape of the distribution of the sample mean?
(b) What is the standard error of the mean? (Round your answer to 2 decimal places.)
(c) What percent of the sample means would be greater than 155 seconds? (Round your answer to 2 decimal places.)
(d) What percent of the sample means would be greater than 142 but less than 155 seconds? (Round your answer to 2 decimal places.)
3) 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.)
(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.)
(c) Within what limits would 99 percent of the sample means occur? (Round your answers to 2 decimal places.)