### Introduction

We have already seen that the Poisson distribution can be used to approximate the binomial distribution for large values of $n$ and small values of $p$ provided that the correct conditions exist. The approximation is only of practical use if just a few terms of the Poisson distribution need be calculated. In cases where many - sometimes several hundred - terms need to be calculated the arithmetic involved becomes very tedious indeed and we turn to the normal distribution for help. It is possible, of course, to use high-speed computers to do the arithmetic but the normal approximation to the binomial distribution negates the necessity of this in a fairly elegant way. In the problem situations which follow this introduction the normal distribution is used to avoid very tedious arithmetic while at the same time giving a very good approximate solution.

#### Prerequisites

• be familiar with the normal distribution and the standard normal distribution
• be able to calculate probabilities using the standard normal distribution

#### Learning Outcomes

• recognise when it is appropriate to use the normal approximation to the binomial distribution
• solve problems using the normal approximation to the binomial distribution.
• interpret the answer obtained using the normal approximation in terms of the original problem

1.2 Discussion