We have already seen that the Poisson distribution can be used to approximate the binomial distribution for large values of and small values of 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.
- be familiar with the normal distribution and the standard normal distribution
- be able to calculate probabilities using the standard normal distribution
- 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
1.1 A typical problem