## The Normal Approximation to the Binomial Distribution - The Continuity Correction

The binomial distribution, written hasExpectation Value Thisis the expected number of successes in n attempts. The variance isgiven by Ifwe want to use the normal distribution as an approximation toestimate forexample – 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 areestimating maybe equal to 5, when we use the normal approximation Suppose and Thenormal approximation is  Look up the probability corresponding to andsubtract from 1. This returns a probability of 0.0080. maybe equal to 7, when we use the normal approximation  Asabove and Thenormal approximation is  Look up the probability corresponding to andsubtract from 1 twice. This returns a probability of 0.9798. maybe equal to 5, when we use the normal approximation  Asabove and Thenormal approximation is  Look up the probability corresponding to andsubtract from 1. This returns a probability of 0.0026 maybe equal to 5, when we use the normal approximation  Asabove and Thenormal approximation is  Look up the probability corresponding to andsubtract from 1 twice. This returns a probability of 0.9222. 