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

PROBLEMS 157
16. A distribution of exam scores has a mean of μ = 78.
a. If your score is X = 70, which standard deviation
would give you a better grade: σ = 4 or σ = 8?
b. If your score is X = 80, which standard deviation
would give you a better grade: σ = 4 or σ = 8?
17. For each of the following, identify the exam score that
should lead to the better grade. In each case, explain
your answer.
a. A score of X = 70, on an exam with M = 82 and
σ = 8; or a score of X = 60 on an exam with
μ = 72 and σ = 12.
b. A score of X = 58, on an exam with μ = 49 and
σ = 6; or a score of X = 85 on an exam with
μ = 70 and σ = 10.
c. A score of X = 32, on an exam with μ = 24 and
σ = 4; or a score of X = 26 on an exam with
μ = 20 and σ = 2.
18. A distribution with a mean of μ = 38 and a standard
deviation of σ = 5 is transformed into a standardized
distribution with μ = 50 and σ = 10. Find the new,
standardized score for each of the following values
from the original population.
a. X = 39
b. X = 43
c. X = 35
d. X = 28
19. A distribution with a mean of μ = 76 and a standard
deviation of σ = 12 is transformed into a standardized
distribution with μ = 100 and σ = 20. Find the new,
standardized score for each of the following values
from the original population.
a. X = 61
b. X = 70
c. X = 85
d. X = 94
20. A population consists of the following N = 5 scores:
0, 6, 4, 3, and 12.
a. Compute μ and σ for the population.
b. Find the z-score for each score in the population.
c. Transform the original population into a new population
of N = 5 scores with a mean of μ = 100 and
a standard deviation of σ = 20.
21. A sample has a mean of M = 30 and a standard
deviation of s = 8. Find the z-score for each of the
following X values from this sample.
X = 32 X = 34 X = 36
X = 28 X = 20 X = 18
22. A sample has a mean of M = 25 and a standard
deviation of s = 5. For this sample, find the X value
corresponding to each of the following z-scores.
z = 0.40 z = 1.20 z = 2.00
z = −0.80 z = −0.60 z = −1.40
23. For a sample with a standard deviation of s = 8, a
score of X = 65 corresponds to z = 1.50. What is
the sample mean?
24. For a sample with a mean of M = 51, a score of
X = 59 corresponds to z = 2.00. What is the sample
standard deviation?
25. In a sample distribution, X = 56 corresponds to
z = 1.00, and X = 47 corresponds to z = −0.50.
Find the mean and standard deviation for the sample.
26. A sample consists of the following n = 7 scores: 5, 0,
4, 5, 1, 2, and 4.
a. Compute the mean and standard deviation for the
sample.
b. Find the z-score for each score in the sample.
c. Transform the original sample into a new sample
with a mean of M = 50 and s = 10.