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

168 CHAPTER 6 | Probability
■ The Unit Normal Table
Before we attempt any more probability questions, we must introduce a more useful tool
than the graph of the normal distribution shown in Figure 6.4. The graph shows proportions
for only a few selected z-score values. A more complete listing of z-scores and proportions
is provided in the unit normal table. This table lists proportions of the normal distribution
for a full range of possible z-score values.
The complete unit normal table is provided in Appendix B Table B.1, and part of the
table is reproduced in Figure 6.6. Notice that the table is structured in a four-column format.
The first column (A) lists z-score values corresponding to different positions in a normal
distribution. If you imagine a vertical line drawn through a normal distribution, then
the exact location of the line can be described by one of the z-score values listed in column
A. You should also realize that a vertical line separates the distribution into two sections: a
larger section called the body and a smaller section called the tail. Columns B and C in the
table identify the proportion of the distribution in each of the two sections. Column B presents
the proportion in the body (the larger portion), and column C presents the proportion
in the tail. Finally, we have added a fourth column, column D, that identifies the proportion
of the distribution that is located between the mean and the z-score.
(A)
z
(B)
Proportion
in body
(C)
Proportion
in ta il
(D)
Proportion
between
mean and z
B
0.00
0.01
0.02
0.03
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
0.33
0.34
.5000
.5040
.5080
.5120
0.5793
.5832
.5871
.5910
.5948
.5987
.6026
.6064
.6103
.6141
.6179
.6217
.6255
.6293
.6331
.5000 .0000
.4960 .0040
.4920 .0080
.4880 .0120
0.4207 .0120
.4168 .0832
.4129 .0871
.4090 .0910
.4052 .0948
.4013 .0987
.3974 .1026
.3936 .1064
.3897 .1103
.3859 .1141
.3821 .1179
.3783 .1217
.3745 .1255
.3707 .1293
.3669 .1331
Mean
Mean
D
z
C
z
Mean
z
FIGURE 6.6
A portion of the unit normal table. This table lists proportions of the normal distribution corresponding to each z-score
value. Column A of the table lists z-scores. Column B lists the proportion in the body of the normal distribution for that
z-score value and Column C lists the proportion in the tail of the distribution. Column D lists the proportion between the
mean and the z-score.