[PDF] The Normal Distribution as an Approximation to the Binomial

29623_6normal_bd.pdf

Middlesex Community College | Prepared by: Stephen McDonald The Normal Distribution as an Approximation to the Binomial Distribution

For a large enough number of trials (n) the area under normal curve can be used to approximate the probability of a binomial distribution. Requirements: The number of trials is fixed. Each trial is independent of the others. There are only two outcomes, success (p) and failure (q). The probability of each outcome remains constant between trials. ݊ ή݌ ൒ͷ

݊ ήݍ ൒ͷ To use the normal distribution to approximate the binomial, we must also define a mean

ሺߤ standard deviation ሺߪ ߤ ߪ ඥ݊ ή݌ ήݍ

Continuity Correction Factor:

Since the binomial distribution is not continuous whereas the normal distribution is continuous, we must apply the continuity correct factor to account for this. This is as simple as adding or subtracting 0.5 from the discrete x-value in question. For the discrete value: ݔ ൏Ǣݏݑܾݐݎܿܽ-Ǥͷ ܽ݊݀ ݑݏ݁ ܽ

ݔ ൐Ǣܽ݀݀ -Ǥͷ ܽ݊݀ ݑݏ݁ ܽሾࡳࡾࡱ࡭ࢀࡱࡾ ࢀࡴ࡭ࡺሿ

ݔ ൑Ǣܽ݀݀ -Ǥͷ ܽ݊݀ ݑݏ݁ ܽ ݔ ൒Ǣݏݑܾݐݎܿܽ-Ǥͷ ܽ݊݀ ݑݏ݁ ܽ ݔ ൌǢܽ݀݀ ࢇ࢔ࢊ ݏݑܾݐݎܿܽݐ -Ǥͷ ܽ ܽ