2. Conduct Bayesian analysis for the following problem. Normal distribution with unknown mean: a random sample of n students is drawn from a large population, and their weights are measured. The average weight of the n sampled students is y = 150 pounds. Assume the weights in the population are normally distributed with unknown mean 0 and known standard deviation 20 pounds. Suppose your prior distribution for A is normal with mean 180 and standard deviation 40. a) Give your posterior distribution for 0. (Your answer will be a function of n.) b) A new student is sampled at random from the same population and has a weight of y pounds. Give a posterior predictive distribution for 7. (Your answer will still be a function of n.) c) For n = 10, give a 95% posterior interval for 6 and a 95% posterior predictive interval for y. d) Do the same for n = 100