### Introduction

In some situations, it is possible to easily describe a problem in terms of sums and differences of random variables. Consider a typical situation in which shafts are fitted to cylindrical sleeves. One random variable is used to describe the variability of the diameter of the shaft, and one is used to describe the variability of the sleeves. Clearly, we need to know how the total variability involved affects the fitting of shafts and sleeves. In this Section, we will confine ourselves to cases where the random variables are normally distributed and independent.

#### Prerequisites

- be familiar with the results and concepts met in the study of probability
- be familiar with the normal distribution

#### Learning Outcomes

- describe a variety of problems in terms of sums and differences of normal random variables
- solve problems described in terms of sums and differences of normal random variables