Forty-two percent of primary care doctors think their patients receive unnecessary medical care.

a. Suppose a sample of 300 primary care doctors was taken. Show the distribution of the sample proportion of doctors who think their patients receive unnecessary medical care.

b. Suppose a sample of 500 primary care doctors was taken. Show the distribution of the sample proportion of doctors who think their patients receive unnecessary medical care.

c. Suppose a sample of 1,000 primary care doctors was taken. Show the distribution of the sample proportion of doctors who think their patients receive unnecessary medical care.

d. In which of the preceding three cases, part (a) or part (b) or part (c), is the standard error of p smallest? Why?