Normal Approximation To The Binomial Distribution

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 this in a fairly elegant way. In the problem situations following this introduction the normal distribution is used to avoid very tedious arithmetic while at the same time giving a very good approximate solution.