11. (12 points) Suppose that the amount of time AUS students spend daily at student center is normally distributed with standard deviation of 40 minutes. A random sample of 15 AUS students was drawn, and each reported the amount of time spent at the student center (in minutes). These are as follows: 180,130,150,165,90,130,120,60,200,180, 80, 240,210, 150,and125. a. b. c. (1. Estimate with 95% confidence the average time spent at student center. Determine the 90% condence interval estimate of the population mean. At 99% condence level, what is the bound on the error of estimation (i.e. margin of error)? How large of a sample must be taken in order to be 96% confident that the bound on the error of estimation (i.e. margin of error) will not exceed 5 minutes