Z-Score of Normal Distribution

A normal distribution with mean $\mu = 0$ and standard deviation $\sigma = 1$ is called the standard normal distribution, and the variable following it is called a standard normal variate; the distribution is also referred to as the Z-distribution.

Every normal variate, regardless of its own mean and standard deviation, can be converted into a standard normal variate. This is done by computing the Z-score (or standard score) of each data value — a transformation that puts values from different normal distributions onto the same scale, making them directly comparable.