A random sample of 5792 physicians in Colorado showed that 3139 provide at least some charity care (i.e., treat poor people at no cost). These data are based on information from State Health Care Data: Utilization, Spending, and Characteristics (American Medical Association).
(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p.
(b) Find a 99% confidence interval for p. Give a brief explanation of the meaning of your answer in the context of this problem.
(c) Is the normal approximation to the binomial justified in this problem? Explain.