The Agency for Healthcare Research and Quality reports that medical errors are responsible for injury to 1 out of every 25 hospital patients in the United States. (Data extracted from M. Ozan-Rafferty, "Hospitals: Never Have a Never Event," The Gallup Management Journal, gmj. gallup.com, May 7, 2009.) These errors are tragic and expensive. Preventable health care-related errors cost an estimated $29 billion each year in the United States. Suppose that you select a sample of 100 U.S. hospital patients.
a. What is the probability that the sample percentage reporting injury due to medical errors will be between 5% and 10%?
b. The probability is 90% that the sample percentage will be within what symmetrical limits of the population percentage?
c. The probability is 95% that the sample percentage will be within what symmetrical limits of the population percentage?
d. Suppose you selected a sample of 400 U.S. hospital patients. How does this change your answers in (a) through (c)?