Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 44 / 3 / b / Solution

Let $z_{0.999}={\Phi }^{-1}(0.999)$ be the standard normal distribution quantile. Standardizing the prediction in part (a) givesThis is a one-sided predictive limit; its upper-tail probability is $0.001$ under the specified model.