Special property of Normal distributions
If X has a Normal(mean=
) distribution then
has a Normal(mean=0, SD=1) distribution.
Equivalently, if Z has a Normal(mean=0, SD=1) distribution then
has a Normal(mean=
Using this property, a probability for any Normal distribution can be
converted into a probability for a Normal (mean=0, SD=1) distribution.
Tables of probabilities for the Normal(mean=0, SD=1) distribution are
This is often called the standard Normal distribution.
Let X = plasma glucose and suppose the distribution of X amongst
obese 40-49 year old men is Normal (
What proportion of obese 40-49 year old men have X>10.5?
Since the distribution of X is Normal(
0.5 - 0.3944
from table for Normal
So, 10.56% of men in this population have plasma glucose
value greater than 10.5.