Many primary care doctors feel overworked and burdened by potential lawsuits. In fact, the Physicians' Foundation reported that 60% of all general practice physicians in the United States do not recommend medicine as a career (Reuters, Nov. 18, 2008). Let x represent the number of sampled general practice physicians who do not recommend medicine as a career.
a. Explain why x is approximately a binomial random variable.
b. Use the Physicians' Foundation report to estimate p for the binomial random variable.
c. Consider a random sample of 25 general practice physicians. Use p from part b to find the mean and standard deviation of x, the number who do not recommend medicine as a career.
d. For the sample of part c, find the probability that at least one general practice physician does not recommend medicine as a career.