The three most common treatments for blocked coronary arteries are medication; bypass surgery; and angioplasty, which is a medical procedure that involves clearing out arteries and that leads to higher profits for doctors than do the other two procedures. The highest rate of angioplasty in the United States is in Elyria, a small city in Ohio. A 2006 article in the New York Times stated that “the statistics are so far off the charts—Medicare patients in Elyria receive angioplasties at a rate nearly four times the national average—that Medicare and at least one commercial insurer are starting to ask questions.” The rate, in fact, is three times as high as that of Cleveland, Ohio, which is located just 30 miles from Elyria. 

a. What is the populati on in this example? What is the sample? 

b. How did probability play a role in the decision of Medicare and the commercial insurer to begin investigations? 

c. How might the z distribution help the investigators to detect possible fraud in this case? 

d. If the insurers determine that physicians in Elyria are committing fraud, but the insurers are wrong, what kind of error would they have made? Explain. 

e. Does Elyria’s extremely high percentile mean that the doctors in town are committing fraud? Cite two other possible reasons for Elyria’s status as an outlier.