The Normal Approximation to The Geometric Distribution and the Continuity Correction

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The geometric distribution, writtenhas Expectation ValueThe variance is given byIf we want to use the normal distribution as an approximation to estimatefor example 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 80, when we use the normal approximationSupposeThe normal approximation is

Look up the probability corresponding toand subtract from 1. This returns a probability of 0.0244.

may be equal to 110, when we use the normal approximation As aboveThe normal approximation is

Look up the probability corresponding toThis returns a probability of 0.8315. To find we subtract from 1 to obtain 0.1685.

may be not be equal to 120. When we use the normal approximation As aboveThe normal approximation is

Look up the probability corresponding toThis returns a probability of 0.9808. We subtract this from 1 to obtain 0.0192.

may not be equal to 114, when we use the normal approximationAs aboveThe normal approximation is

Look up the probability corresponding to This returns a probability of 0.8962.

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