Given z-scores, now you can take
a whole bunch of data like life expectancies and instantly find
values for people that express where they rank with respect to others.
In other words, the z-score formula gives you a way of normalizing
or collapsing the data to a common standard based on how many
standard deviations values lie from the mean. To put it another way.
Subtracting the value of the mean from each one of the
values and dividing each of these differences by its standard
deviation parametizes the original distribution so that it
has a mean of 0 all the time and a standard deviation of 1.
So, given the shape of the distribution, you can build one table
for it. In other words, no matter what your data looks like,
no matter what the mean value is, you can reduce
it to one standard table by reformulating your data using the z-score
formula. You then can take all kinds of experiments
and build tables for them because you can normalize it or
reduce it by doing things like forming a z-value.

Another way to illustrate this is to present the following
problem, "Suppose
you have two people. One has an IQ of 130 on the WAIS IQ test
which has a mean of 100 and a standard deviation of approximately 10. The
other has an IQ of 145 on the Stanford Binet IQ test which also has a
mean of 100, but has a standard deviation of approximately 15. According
to the IQ tests, who is the smartest?" Given no knowledge of statistics
the answer is far from obvious. On the other hand, with z-scores you
can quickly calculate that each person has an IQ 3 standard deviations
above the mean. In other words, you can quickly use
z-scores to find that both have approximately the same intelligence.

*Lesson 1: Summary Measures of Data 1.6 - 3*

#####
*Biostatistics for the Clinician*

Statisticians know a great deal about the standard
normal distribution. Consequently, they also know a great deal about
the entire family of Gaussian distributions. All of the previous properties
of z-score distributions hold for the standard normal distribution.
But, in addition, probability values for all sample values are known
and tabled. So, for example, it is known then that for any normal
distribution, approximately 68% of
values lie within one standard deviation of the mean. Approximately
95% of values lie with 2 standard deviations of the mean. Approximately
2.1% of values lie below 2 standard deviations below the mean.
Approximately 2.1% of values lie above 2 standard deviations above the
mean. In general, all probabilities associated with the normal
distribution have already been computed and are tabled (see Figure below).