Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

172 CHAPTER 6 | Probability
and exactly 0.3000 to the left. Each of these sections corresponds to the proportion listed
in column D. Begin by scanning down column D, looking for a value of 0.3000. Again,
this exact proportion is not in the table, but the closest value is 0.2995. Reading across the
row to column A, you should find a z-score value of z = 0.84. Looking again at the sketch
(Figure 6.9(b)), the right-hand line is located at z = +0.84 and the left-hand line is located
at z = –0.84.
■
You may have noticed that we have sketched distributions for each of the preceding
problems. As a general rule, you should always sketch a distribution, locate the mean with
a vertical line, and shade in the portion you are trying to determine. Look at your sketch. It
will help you determine which columns to use in the unit normal table. If you make a habit
of drawing sketches, you will avoid careless errors when using the table.
LEARNING CHECK
1. What proportion of a normal distribution is located in the tail beyond a z-score
of z = –1.50?
a. –0.0668
b. –0.9332
c. 0.0668
d. 0.9332
2. A vertical line is drawn through a normal distribution at z = –1.00. How much of
the distribution is located between the line and the mean?
a. 15.87%
b. 34.13%
c. 84.13%
d. –15.87%
3. What z-score separates the lowest 10% of the distribution from the rest?
a. z = 0.90
b. z = –0.90
c. z = 1.28
d. z = –1.28
ANSWERS
1. C, 2. B, 3. D
6.3 Probabilities and Proportions for Scores
from a Normal Distribution
LEARNING OBJECTIVES
3. Calculate the probability for a specific X-value.
4. Calculate the score (X-value) corresponding to a specific proportion in a distribution.
In the preceding section, we used the unit normal table to find probabilities and
proportions corresponding to specific z-score values. In most situations, however,