The normal distribution is a probability distribution that, when drawn on a graph, resembles a bell curve. A normal distribution has two parameters, a mean (denoted µ) and a standard deviation (denoted σ). The two parameters determine the location and spread of the distribution.
The mean determines the location of the distribution (where the peak of the curve sits) and the standard deviation determines how spread out (disperse) the distribution is.
Properties
- About 68% of the values drawn from a normal distribution are within 1 standard deviation of the mean; 95% are within two standard deviations; 99.7% are within three standard deviations
- A normal random variable can be 'standardized' as follows:
If
, then
has a normal distribution with a mean of 0 and a standard deviation of 1.
- The parameters of the normal distribution (the mean and variance) can be estimated from a random sample using the following formulas:
.