LESSON 4

Question 1

“z = (x-μ)/σ”

The formula for calculating a _______ is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the ______ is simply the raw score minus the population mean, divided by the population standard deviation.

Answer 1

Z - Score

Question 2

A distribution of scores has a mean of μ = 100 and a standard deviation of
σ = 10. What z-score corresponds to a score of X = 130 in this distribution?

“z = (x-μ)/σ”

Answer 2

z = 3

Question 3

If your exam score is X = 60, which set of
parameters would give you the best grade?
a. μ = 65 and σ = 5
b. μ = 65 and σ = 2
c. μ = 70 and σ = 5
d. μ = 70 and σ = 2

Answer 3

a. μ = 65 and σ = 5

Question 4

For a distribution of exam scores with μ = 70,
which value for the standard deviation would
give the highest grade to a score of X = 75?
a. σ = 1
b. σ = 2
c. σ = 5
d. σ = 10

Answer 4

a. σ = 1

Question 5

Last week Sarah had a score of X = 43 on a Spanish
exam and a score of X = 75 on an English exam. For
which exam should Sarah expect the better grade?
a. Spanish
b. English
c. The two grades should be identical.
d. Impossible to determine without more information

Answer 5

d. Impossible to determine without more information

Question 6

“x = µ + Zσ”

where µ equals the mean, Z equals the z score, and σ equals the standard deviation.

Answer 6

Z - Score to Raw Score

Question 7

A population has a mean of μ = 60 and a standard deviation of σ = 12. For this population, find the raw score for each of the following z values.

a. -0.50
b. 2.50

Answer 7

a. 54
b. 90

Question 8

Formula of :

σ = x - µ/Z

Answer 8

Standard Deviation

Question 9

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

Answer 9

d. 8

Question 10

Formula for :

µ = x - Zσ

Answer 10

Population Mean

Question 11

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

Answer 11

b. 50

Question 12

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

Answer 12

c. 75

Question 13

A ________ is composed of scores that have been transformed to create predetermined values for μ and σ. ________ are used to make dissimilar distributions comparable.

Answer 13

Standardized Distribution