A statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken. This test was taken by a large...

A statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken. This test was taken by a large group of students,and the average score was 78.5. A random sample of eight students was asked to predict this average score. Their predictions were:72, 83, 78, 65, 69, 77, 81, 71.Assume a Normal population with variance (σ1)^2 = 2 and a N(70, 5) prior for the mean. (a) Provide a 95% Bayesian credible interval for the mean.(b) Based on the sample of 8 students, what is the prediction that another student will provide an average score greater than 75?