**Area Between Z Scores
(Both Z Scores + or Both Z Scores -)
**

**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
210 and 230?**

**II. What
is the proportion of people taking this test that score between 180 and 175?**

I. The proportion of people taking the test that score between 210 and 230

A. Using the Z score formula convert both 210 and 230 to Z scores

B. 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

C. Next we will find the area between the mean and Z (Col. 2) for .20.

The area between the mean and Z for .20 = .0793

D. Finally, because both the Z scores are
positive

we subtract the
Column 2 areas to find the area between the Z scores.

Area between = .2257 - .0793 = .1464

II. The proportion of people taking the test that score between 180 and 175

A. Using the Z score formula convert both 220 and 260 to Z scores

B. Next we will use Table Z to 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 find the area between the mean and Z (Col. 2) for -.40.

The area between the mean and Z for -.40 = .1554

D. Finally, because both the Z scores are
negative

we subtract the
Column 2 areas to find the area between the Z scores.

Area between = .1915 - .1544 = .0371

Hint: Remember that even though the Z
scores are negative **the areas that you find in
Table Z are always
positive values**. Therefore when you are finding the area between

two Z scores the result will always be positive.

Copyright © 2004 by Mark W. Vernoy