A newspaper article on salaries of college presidents reported compensations for a sample of 11 college presidents in area schools during the year 2002-2003, as well as compensations for the 10 highest-paid leaders of public universities in the entire United States. (Leaders of private universities, not included in the latter data set, have been known to receive more than $1 million in yearly pay.) The data, recorded in thousands of dollars, have been summarized with software.
a. Find the salary of a college president whose z-score for that area was approximately +2.
b. The same college president was also included in the list of the top 10 salaries for the entire United States; find his z-score in reference to this group.
c. Discuss the drawbacks in using the mean for college presidents in a particular area as an estimate for the mean salary of all college presidents.
d. Explain why the mean salary of top college presidents is useless as an estimate for any larger group.