Let X1,..., Xn be a random sample from a n(, 2) population, where 2 is known. Show

Let X1,..., Xn be a random sample from a n(θ, σ2) population, where σ2 is known. Show that the usual one-sided 1 - α upper confidence bound {θ: θ <  + zασ /√n} is unbiased, and so is the corresponding lower confidence bound.