# Normal Approximation to The Binomial Distribution and the Continuity Correction

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The binomial distribution, writtenhas Expectation ValueThis is the expected number of successes in n attempts. The variance is given by If we want to use the normal distribution as an approximation to estimatefor example – which is very useful when n is large – we must make modifications since the binomial distribution is a discrete distribution but the normal approximation is continuous.

In order to take account of this, and that if we are estimatingmay be equal to 5, when we use the normal approximationSupposeand The normal approximation is

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

may be equal to 7, when we use the normal approximation As aboveandThe normal approximation is

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

may be equal to 5, when we use the normal approximation As aboveandThe normal approximation is

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

may be equal to 5, when we use the normal approximation As aboveandThe normal approximation is

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