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

222 CHAPTER 7 | Probability and Samples: The Distribution of Sample Means
σ = 20. What is the probability of obtaining a sample
mean greater than M = 65 for each of the following:
a. a sample of n = 16 students
b. a sample of n = 25 students
c. a sample of n = 100 students
14. IQ scores form a normal distribution with a mean of
μ = 100 and a standard deviation of σ = 15. What
is the probability of obtaining a sample mean greater
than M = 103,
a. for a random sample of n = 9 people?
b. for a random sample of n = 25 people?
c. for a random sample of n = 100 people?
15. A normal distribution has a mean of μ = 54 and a
standard deviation of σ = 6.
a. What is the probability of randomly selecting a
score less than X = 51?
b. What is the probability of selecting a sample of
n = 4 scores with a mean less than M = 51?
c. What is the probability of selecting a sample of
n = 36 scores with a mean less than M = 51?
16. A population has a mean of μ = 30 and a standard
deviation of σ = 8
a. If the population distribution is normal, what is
the probability of obtaining a sample mean greater
than M = 32 for a sample of n = 4?
b. If the population distribution is positively skewed,
what is the probability of obtaining a sample mean
greater than M = 32 for a sample of n = 4?
c. If the population distribution is normal, what is
the probability of obtaining a sample mean greater
than M = 32 for a sample of n = 64?
d. If the population distribution is positively skewed,
what is the probability of obtaining a sample mean
greater than M = 32 for a sample of n = 64?
17. For random samples of size n = 25 selected from a normal
distribution with a mean of mean of μ = 50 and a
standard deviation of σ = 20, find each of the following:
a. The range of sample means that defines the middle
95% of the distribution of sample means.
b. The range of sample means that defines the middle
99% of the distribution of sample means.
18. The distribution ages for students at the state college
is positively skewed with a mean of μ = 21.5 and a
standard deviation of σ = 3.
a. What is the probability of selecting a random sample
of n = 4 students with an average age greater
than 23? (Careful: This is a trick question.)
b. What is the probability of selecting a random
sample of n = 36 students with an average age
greater than 23?
c. For a sample of n = 36 students, what is the probability
that the average age is between 21 and 22?
19. Jumbo shrimp are those that require 10–15 shrimp
to make a pound. Suppose that the number of jumbo
shrimp in a 1-pound bag averages μ = 12.5 with a
standard deviation of σ = 1, and forms a normal distribution.
What is the probability of randomly picking
a sample of n = 25 1-pound bags that average more
than M = 13 shrimp per bag?
20. Callahan (2009) conducted a study to evaluate the
effectiveness of physical exercise programs for
individuals with chronic arthritis. Participants with
doctor-diagnosed arthritis either received a Tai Chi
course immediately or were placed in a control group
to begin the course 8 weeks later. At the end of the
8-week period, self-reports of pain were obtained for
both groups. Data similar to the results obtained in the
study are shown in the following table.
Self-Reported Level of Pain
Mean
Tai Chi course 3.7 1.2
No Tai Chi course 7.6 1.7
a. Construct a bar graph that incorporates all of the
information in the table.
b. Looking at your graph, do you think that participation
in the Tai Chi course reduces arthritis pain?
21. A normal distribution has a mean of μ = 60 and a
standard deviation of σ = 18. For each of the following
samples, compute the z-score for the sample mean
and determine whether the sample mean is a typical,
representative value or an extreme value for a sample
of this size.
a. M = 67 for n = 4 scores
b. M = 67 for n = 36 scores
22. A random sample is obtained from a normal population
with a mean of μ = 95 and a standard deviation
of σ = 40. The sample mean is M = 86.
a. Is this a representative sample mean or an extreme
value for a sample of n = 16 scores?
b. Is this a representative sample mean or an extreme
value for a sample of n = 100 scores?
23. A normal distribution has a mean of μ = 65 and a
standard deviation of σ = 20. For each of the following
samples, compute the z-score for the sample mean
and determine whether the sample mean is a typical,
representative value or an extreme value for a sample
of its size.
a. M = 74 for a sample of 4 scores
b. M = 74 for a sample of 25 scores
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