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.
Letting X denote the number of calories in the salad, we have the standardized variable