If *X* is distributed as
,
then the standardized variable
has the standard normal distribution. This
property of the normal distribution allows us to cast a probability problem
concerning *X* into one concerning *Z*. To find the probability that *X* lies in
a given interval, convert the interval to the z-scale and then calculate the
probability by using the standard normal table.

If *X* is distributed as
,
then

where *Z* has the standard normal distribution.

- δΎ‹
- The number of calories in a salad on the lunch menu is normally distributed
with mean=200 and sd=5. Find the probability that the salad you select will
contain

- (a)
- More than 208 calories.
- (b)
- Between 190 and 200 calories.

Letting

*X*denote the number of calories in the salad, we have the standardized variable- (a)
- The z-value corresponding to x=208 is
.
Therefore,

- (b)
- The z-values corresponding to x=190 and x=200 are
and
respectively. We calculate