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
to show that the transformationtransformsonto