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 mean
and variance
and the quantity
takes values
then the transformation
transforms each value
onto a standard normal score
Every value ofcorresponds to a probability
and
We can use the transformation properties of the mean and variance
and
to show that the transformationtransforms
onto