The Normal Approximation to the Geometric Distribution - The Continuity Correction

The geometric distribution, writtenhasExpectation ValueThevariance is given byIfwe want to use the normal distribution as an approximation toestimateforexample we must make modifications since the binomial distribution isa discrete distribution but the normal approximation is continuous.

In order to take account of this, and that if we areestimatingmaybe equal to 80, when we use the normal approximationSupposeThenormal approximation is

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

maybe equal to 110, when we use the normal approximationAs aboveThenormal approximation is

Look up the probability corresponding toThisreturns a probability of 0.8315. To find wesubtract from 1 to obtain 0.1685.

maybe not be equal to 120. When we use the normal approximationAs aboveThenormal approximation is

Look up the probability corresponding toThisreturns a probability of 0.9808. We subtract this from 1 to obtain0.0192.

maynot be equal to 114, when we use the normal approximationAsaboveThenormal approximation is

Look up the probability corresponding toThis returns a probability of 0.8962.