The standard normal distribution, commonly denoted , is a normal distribution such that and .
In other words, if a random variable is such that , we say that it follows a standard normal distribution, and commonly denote it .
The values of ’s distribution function are well known and can be easily found in tables. We can use these tables to facilitate our calculations with any other normal distribution , since we can standardise as follows:
Let be a random variable with a standard normal distribution. Then: