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

The Poisson distribution, written has Expectation Value This 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 estimate for example – which is very useful when and are large - we must make modifications since the Poisson distribution is a discrete distribution but the normal approximation is continuous.

In order to take account of this, and that if we are estimating may be equal to 5, when we use the normal approximation Suppose The normal approximation is  Look up the probability corresponding to and subtract it from 1. This returns a probability of 0.0778.. may be equal to 7, when we use the normal approximation As above The normal approximation is  Look up the probability corresponding to and subtract from 1 twice. This returns a probability of 0.6335 may not be equal to 5, when we use the normal approximation As above the normal approximation is  Look up the probability corresponding to and subtract it from 1. This returns a probability of 0.0409. may not be equal to 7, when we use the normal approximation As above The normal approximation is  Look up the probability corresponding to and subtract it from one twice. This returns a probability of 0.7148.