4. (10%) Let X₁, X₂, ... , Xₙ, Xₙ₊₁ be a sample from normal population having an unknown mean μ and variance 1. Let
be the average of the first n of them.
(b) If
= 4, give an interval that, with 90 percent confidence, will contain the value of
Xₙ₊₁. (5%)