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

140 CHAPTER 5 | z-Scores: Location of Scores and Standardized Distributions
s
F I G U R E 5.5
A visual presentation of the question
in Example 5.6. The 12-point distance
from 42–54 corresponds to 3 standard
deviations. Therefore, the standard deviation
must be σ = 4. Also, the score X = 42 is
below the mean by one standard deviation,
so the mean must be μ = 46.
–2 –1 0
42 m
54
X
12 points
1 2
z
EXAMPLE 5.7
In a population distribution, a score of X = 64 has a z-score of z = 0.50 and a score
of X = 72 has a z-score of z = 1.50. What are the values for the population mean and
standard deviation? You should obtain μ = 60 and σ = 8. Good luck
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LEARNING CHECK
1. A population of scores has μ = 44. In this population, an X value of 40 corresponds
to z = −0.50. What is the population standard deviation?
a. 2
b. 4
c. 6
d. 8
2. A population of scores has σ = 4. In this population, an X value of 58 corresponds
to z = 2.00. What is the population mean?
a. 54
b. 50
c. 62
d. 66
3. A population of scores has σ = 10. In this population, a score of X = 60 corresponds
to z = −1.50. What is the population mean?
a. −30
b. 45
c. 75
d. 90
ANSWERS
1. D, 2. B, 3. C