Area Between Z Scores
(One Z Score + and one Z Score -)
(A worked Problem:  Procedure explained in more detail in Chapter 7)

Problem:  Suppose that a personality test has:

    Mean = 200
    Standard Deviation = 50

I.  What is the proportion of people taking this test that score between 175 and 230?

I.  The proportion of people taking the test that score between 175 and 230

    A. Using the Z score formula convert both 175 and 230 to Z scores

    B.  Now we will find the area between the mean and Z (Col. 2) for -.50.

        The area between the mean and Z for -.50 = .1915

    C.  Next we will use Table Z to find the area between the mean and Z (Col. 2) for .60

        The area between the mean and Z for .60 = .2257

D.  Finally, because one Z scores is negative and the other Z score is positive
             we add the Column 2 areas to find the area between the Z scores.

        Area between = .2257 - .0793 = .1464

Hint:  Remember that even though the Z scores can be negative the areas that you find in
            Table Z are always positive values. Therefore in this case you are adding
             two positive areas.

Copyright © 2004 by Mark W. Vernoy