Question: Explain whether or not you think the sampling distribution for the sample mean would be approximately normal in each of the following scenarios. If it would be, specify the population of interest and the measurement of interest. If it would not be, explain why not.

a. A researcher wants to know what the average cholesterol level would be if people restricted their fat intake to 30% of calories. He gets a group of patients who have had heart attacks to volunteer to participate, puts them on a restricted diet for a few months, and then measures their cholesterol and calculates the mean value.

b. A large corporation would like to know the average income of its workers' spouses. Rather than going to the trouble to collect a random sample, they post someone at the exit of the building at 5:00 P.M. Everyone who leaves between 5:00 P.M. and 5:30 P.M. is asked to complete a short questionnaire on the issue. There are 70 responses.

c. A university wants to know the average income of its alumni. They select a random sample of 200 alumni and mail them a questionnaire. The university follows up with a phone call to those who do not respond within 30 days.

d. An automobile manufacturer wants to know the average price for which used cars of a particular model and year are selling in a certain state. It is able to obtain a list of buyers from the state motor vehicle division, from which a random sample of 20 buyers is selected. The manufacturer makes every effort to find out what those people paid for the cars and is successful in doing so.