# Confidence Intervals for the Binomial Distribution

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A confidence interval for estimating a parameter of a probability distribution must show two basic properties. First, it must contain the value of the parameter with a prescribed probability, and second, it must be as short as possible in order to be useful. Confidence intervals may be derived in different ways. In the case of a binomial distribution with trials and probability parameter , the conventional method for estimating uses the normal approximation and produces an interval centered at the point *, *where* ** *is the number of successes obtained in the* ** *trials.

Contributed by: Tomas Garza (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The article on Binomial proportion confidence interval* *in Wikipedia gives the details for Wilson's method. Implementation of the Clopper–Pearson method is due to the author of this presentation.

## Permanent Citation

"Confidence Intervals for the Binomial Distribution"

http://demonstrations.wolfram.com/ConfidenceIntervalsForTheBinomialDistribution/

Wolfram Demonstrations Project

Published: March 7 2011