The article "The Functional Outcomes of Total Knee Arthroplasty" (R. Kane, K. Saleh, et al., Journal of Bone and Joint Surgery, 2005:1719-1724) reports that out of 10,501 surgeries, 859 resulted in complications within six months of surgery.
a. Find a 95% confidence interval for the proportion of surgeries that result in complications within six months.
b. Find a 99% confidence interval for the proportion of surgeries that result in complications within six months.
c. A surgeon claims that the rate of complications is less than 8.5%. With what level of confidence can this claim be made?