The z distribution is rigorously called the standard normal distribution in probability and statistics textbooks and in the literature. A random variable with a standard normal distribution is called a standard normal random variable. Because Z is usually used to represent a standard normal random variable, the standard normal distribution is sometimes called the z distribution for convenience by practitioners. In the following, the convention of representing a random variable with a capital letter and a specific value of the random variable with the corresponding lowercase letter is used.
The standard normal distribution is one of the most important probability distributions in probability theory and statistics. Many random phenomena follow a normal distribution or approximately a normal distribution and can be represented by a normal random ...
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