## What is a Normal Distribution?

Aliases: *gaussian distribution*

The normal distribution (a.k.a. Gaussian distribution, Bell Curve) is a very common continuous probability distribution which is characterized by being symmetric about its mean and having a non-zero value over the entire real line. The mean, median and mode coincide.

The normal distribution is useful because of the Central Limit Theorem (CLT) which states that under finite variance that the arithmetic means of a sample of independent observations of a random variable converge in distribution to the normal, that is, they become normally distributed when the number of observations is large. This allows us to perform an A/B test with a non-binomial metric such as average revenue per user or average order value under the assumption that the standard error of the mean is normally distributed even if the underlying distribution of values is highly skewed.

Statistics such as the z score are derived from a standard normal distribution while a t score is drawn from a T-distribution which converges to normal asymptotically (it is practically equivalent to the normal with more then ~30 samples).