Problem 3. (10 points) We measured LDL cholesterol levels of 150 patients given certain exercise regimen and the average cholesterol of this group is :T: : 114.73. The prior distribution of p for these measurements is a normal distribution with mean 120 with standard deviation of 40. Suppose the variance of the LDL cholesterol levels is 02 = 20. (a) Calculate the value of the Bayes estimator of cholesterol levels with respect to the squared loss. (You don't need to derive the posterior distribution again if it was derived in class). (b) Calculate the posterior probability that p is less than 115. (Use R code or check the Z table). (c) Calculate the 95% posterior credible interval for p