12.1 A statistician buys a pack of 10 new golf balls, drops each golf ball from a height of one meter, and measures the height in centimeters it returns on the first bounce. The ten values are:

79.9 80.0 78.9 78.5 75.6 80.5 82.5 80.1 81.6 76.7 Assume that y, the height (in cm) a golf ball bounces when dropped from a one-meter height, is normal (p, a’), where the standard deviation a = 2.

(a) Assume a normal (75, lo2) prior for p. Find the posterior distribution of

(b) Calculate a 95% Bayesian credible interval for p?