The article “application of surgical navigation to total hip arthroplasty” (t. ecker and s. murphy, journal of engineering in medicine, 2007: 699–712) reports that in a sample of 121 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes. (a) find a 99% confidence interval for the mean surgery time for this procedure. (5 points) (b) approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes? assume σ = s. (4 points) (c) approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes? assume σ = s. (4 points)