The Normal Approximation to the Geometric Distribution - The Continuity Correction
The geometric distribution, written
hasExpectation Value
Thevariance is given by
Ifwe want to use the normal distribution as an approximation toestimate
forexample 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 areestimating
maybe equal to 80, when we use the normal approximation
Suppose
Thenormal approximation is
Look up the probability corresponding to
andsubtract from 1. This returns a probability of 0.0244.
maybe equal to 110, when we use the normal approximation
As aboveThenormal approximation is
Look up the probability corresponding to
Thisreturns 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 approximation
As aboveThenormal approximation is
Look up the probability corresponding to
Thisreturns a probability of 0.9808. We subtract this from 1 to obtain0.0192.
maynot be equal to 114, when we use the normal approximation
AsaboveThenormal approximation is
Look up the probability corresponding to
This returns a probability of 0.8962.
