For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of5616physicians in Colorado showed that3170provided at least some charity care (i.e., treated poor people at no cost).

(a) Letprepresent the proportion of all Colorado physicians who provide some charity care. Find a point estimate forp. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval forp. (Round your answers to three decimal places.)

lower limit

upper limit

Give a brief explanation of the meaning of your answer in the context of this problem.

99% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.

1% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.

1% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.

99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.

(c) Is the normal approximation to the binomial justified in this problem? Explain.

No;np< 5 andnq> 5.

Yes;np< 5 andnq< 5.

No;np> 5 andnq< 5.

Yes;np> 5 andnq> 5.