# Engineering Tables/Normal Distribution

The **normal distibution** is an extremely important family of continuous probability distributions. It has applications in every engineering discipline. Each member of the family may be defined by two parameters, *location* and *scale*: the mean ("average", *μ*) and variance (standard deviation squared, *σ*^{2}) respectively.

The probability density function, or pdf, of the distribution is given by:

The cumulative distribution function, or cdf, of the normal distribution is:

These functions are often impractical to evaluate quickly, and therefore tables of values are used to allow fast look-up of required data. The family of normal distributions is infinite in size, but all can be "normalised" to the case with mean of 0 and SD of 1:

- Given a normal distribution , the standardised normal distribution, Z, is:

Due to this relationship, all tables refer to the standardised distribution, Z.