Areas Under the Normal Curve

The normal distribution, also called the Gaussian distribution, is a probability distribution that arises in many different natural processes. For example, the height of adult organisms in most species follows a normal distribution. The normal distribution is important in statistics because many estimators have sampling distributions that are asymptotically normal; this includes means, medians, proportions, and all maximum likelihood estimators. This means that the null distribution for many hypothesis tests is a normal distribution and that the p value for these tests is given by the area under a normal curve.

This entry first discusses the general definition of probability as area, providing both a formal calculus-based definition and a less formal intuitive explanation. Then it discusses the relationship between the area under the normal curve ...