The Normal Approximation to the Binomial Distribution - The Continuity Correction

The binomial distribution, writtenhasExpectation ValueThisis the expected number of successes in n attempts. The variance isgiven by Ifwe want to use the normal distribution as an approximation toestimateforexample – which is very useful when n is large - we must makemodifications since the binomial distribution is a discretedistribution but the normal approximation is continuous.

In order to take account of this, and that if we areestimatingmaybe equal to 5, when we use the normal approximationSupposeandThenormal approximation is

Look up the probability corresponding toandsubtract from 1. This returns a probability of 0.0080.

maybe equal to 7, when we use the normal approximationAsaboveandThenormal approximation is

Look up the probability corresponding toandsubtract from 1 twice. This returns a probability of 0.9798.

maybe equal to 5, when we use the normal approximationAsaboveandThenormal approximation is

Look up the probability corresponding toandsubtract from 1. This returns a probability of 0.0026

maybe equal to 5, when we use the normal approximationAsaboveandThenormal approximation is

Look up the probability corresponding toandsubtract from 1 twice. This returns a probability of 0.9222.