Suppose that X is normally distributed with mean /x and variance a2 = 400.

The prior distribution of n is normally distributed with mean M' — — 60 and variance e/2 = 40. Furthermore, a sample of size 20 is taken, with sample mean M = —69.

(a) Find the posterior distribution of /x.

(b) Find a 68 percent credible interval for ix.

(c) Find P(H0) from the posterior distribution, where H0 is the hypothesis that ix is greater than or equal to —70.