Normal distribution

The normal distribution is a probability distribution. It is also called Gaussian distribution because it was first discovered by Carl Friedrich Gauss.

For the normal distribution, the values less than one standard deviation away from the mean account for 68.27% of the set; while two standard deviations from the mean account for 95.45%; and three standard deviations account for 99.73%.

The normal distribution is very important in many fields because many things take this form.[1] It is often called the bell curve, because the graph of its probability density looks like a bell.

• The mean ("average") of the distribution defines its location.
• The standard deviation ("variability") defines the scale.

These two parameters are represented by the symbols ${\displaystyle \mu }$ and ${\displaystyle \sigma }$, respectively.[2]

The standard normal distribution (also known as the Z distribution) is the normal distribution with a mean of zero and a standard deviation of one (the green curves in the plots to the right).[2]

Many values follow a normal distribution.[3][4] Some examples include:[5]

• Height
• Test scores
• Measurement errors
• Light intensity as in laser light)
• Intelligence is normally distributed.
• Insurance companies use normal distributions to model certain average cases.