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

SECTION 7.3 | Probability and the Distribution of Sample Means 209
20
FIGURE 7.6
The middle 80% of the distribution
of sample means for n = 25.
Samples were selected from a normal
population with μ = 500 and
σ = 100.
10%
474.4
40% 40% 10%
500
m
525.6
21.28 0
11.28
M
z
sample of n = 25 students ought to have a mean SAT score around 500. More specifically,
we are 80% confident that the value of the sample mean will be between 474.4 and 525.6.
The ability to predict sample means in this way will be a valuable tool for the inferential
statistics that follow.
LEARNING CHECK
ANSWERS
1. A normal population has µ = 50 and σ = 8. A random sample of n = 16 scores
from this population has a mean of 54. What is the z-score for this sample mean?
a. +0.50
b. +1.00
c. +2.00
d. +4.00
2. A random sample of n = 9 scores is obtained from a population with µ = 50 and σ = 9.
If the sample mean is M = 53, what is the z-score corresponding to the sample mean?
a. z = 0.33
b. z = 1.00
c. z = 3.00
d. cannot determine without additional information
3. A random sample of n = 25 scores is selected from a normally distributed population
with μ = 500 and σ = 100. What is the probability that the sample mean will
be less than 490?
a. 0.4602
b. 0.3085
c. 0.1587
d. 0.0062
1. C, 2. B, 3. B