The standard normal distribution is the special case of a normal distribution with a mean of and a standard deviation of . The distribution has historical significance because it allows standardized values to be referenced in a look-up table rather than calculated by hand. The distribution is a probability density function with an area under the curve of the function equal to .

The standard normal distribution function is given in the equation above. This standardized form of the normal distrubtion allows for probabilities to be easily calculated or looked-up.

Variable | Description |
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The circle constant appears in the scaling factor that ensures the area under the distribution is equal to . | |

Euler’s Number is shorthand for the exponential function where and defines a family of exponential functions with useful properties and meaningful variable values. | |

Standardized input commonly referred to as a “-score value”. |