## Standardising a Normal Distribution

The standard normal distribution has meanand variance

It is a very convenient property of the normal distribution that any normal distribution, with any mean and any variance, can be transformed onto the standard normal distribution with a simple linear transformation.

If some quantityis normally distributed with meanand varianceand the quantity takes valuesthen the transformationtransforms each valueonto a standard normal score

Every value ofcorresponds to a probabilityand

We can use the transformation properties of the mean and variance

and

to show that the transformationtransformsonto