11. Let X1, . . . , Xn, Xn+1 be a sample from a normal population having an unknown mean and variance 1. Let

11. Let X1, . . . , Xn, Xn+1 be a sample from a normal population having an unknown mean μ and variance 1. Let ¯Xn = ni

=1 Xi /n be the average of the first n of them.

(a) What is the distribution of Xn+1 − ¯Xn?

(b) If ¯Xn = 4, give an interval that, with 90 percent confidence, will contain the value of Xn+1.