Binomial distribution: Difference between revisions

Revision as of 22:56, 2 June 2006

Revision as of 04:26, 3 June 2006

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[[image:BinDistApprox_large.png|right|250px|thumb|Binomial PDF and normal approximation for ''n'' = 6 and ''p'' = 0.5.]]

*If ''n'' is large enough, the skew of the distribution is not too great, and a suitable [[continuity correction]] is used, then an excellent approximation (sometimes provided a suitable [[continuity correction]] is used) to B(''n'', ''p'') is given by the [[normal distribution]]

::<math> N(np, np(1-p)).\,</math>

:Various [[Rule of thumb|rules of thumb]] may be used to decide whether ''n'' is large enough. One rule is that both ''np'' and ''n''(1 &minus; ''p'') must be greater than 5. However, the specific number varies from source to source, and depends on how good an approximation one wants; some sources give 10. Another commonly used rule holds that the above normal approximation is appropriate only if