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The Normal Approximation to the Poisson Distribution - The Continuity Correction

The Poisson distribution, writtenhas Expectation ValueThis is the expected number of successes in n attempts. The variance is given byIf we want to use the normal distribution as an approximation to estimatefor example – which is very useful whenandare 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 estimatingmay be equal to 5, when we use the normal approximationSupposeThe normal approximation is

Look up the probability corresponding toand subtract it from 1. This returns a probability of 0.0778..

may be equal to 7, when we use the normal approximationAs aboveThe normal approximation is

Look up the probability corresponding toand subtract from 1 twice. This returns a probability of 0.6335

may not be equal to 5, when we use the normal approximationAs abovethe normal approximation is

Look up the probability corresponding toand subtract it from 1. This returns a probability of 0.0409.

may not be equal to 7, when we use the normal approximationAs aboveThe normal approximation is

Look up the probability corresponding toand subtract it from one twice. This returns a probability of 0.7148.