Ch 5 z-scores: Location of Scores and Standardized Distributions

In a distribution with μ = 100 and σ = 15, a score X=130 would be transformed into a z-score of what value?

z= +2.00

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

A

For a population with μ = 100 and σ = 20, what is the z-score corresponding to X = 105? a. +0.25 b. +0.50 c. +4.00 d. +5.00

A

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

A

t/f the z-score distribution will always have a mean of 0

true

t/f the distribution of z-scores will have the same shape as the original distribution of scores

true; transforming a distribution of x-values to z values does not move the scores from one position to another

z score formula

z = (x - μ)/σ

A distribution of scores has a mean of μ = 86 and a standard deviation of σ = 7. What z-score corresponds to a score of X = 95 in this distribution?

z = +1.29

What are the 2 main purposes of a z-score?

1. Each z-score tells the exact location of the original X value within the distribution. 2. The z-scores form a standardized distribution that can be directly compared to other distributions that also have been transformed into z-scores.

A distribution with μ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be μ = 50 and σ = 10. In the new, standardized distribution your score is X = 60. What was your score in the original distribution? a. X = 45 b. X = 43 c. X=1.00 d. impossible to determine without more information

B

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

B

A population with μ = 85 and σ = 12 is transformed into z-scores. After the transformation, the population of z-scores will have a standard deviation of _____ a. σ = 12 b. σ = 1.00 c. σ=0 d. cannot be determined from the information given

B

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

C

Using z-scores, a population with μ = 37 and σ = 6 is standardized so that the new mean is μ = 50 and σ = 10. How does an individual's z-score in the new distribu- tion compare with his/her z-score in the original population? a. new z = old z+13 b. new z = (10/6)(old z) c. new z =old z d. cannot be determined with the information given

C

standardized distribution

Composed of scores that have been transformed to create predetermined values for μ and σ. They are used to make dissimilar distributions comparable.

A distribution with μ = 47 and σ = 6 is being standardized so that the new mean and standard deviation will be μ = 100 and σ = 20. What is the standardized score for a person with X = 56 in the original distribution? a. 110 b. 115 c. 120 d. 130

D

A population has μ = 50 and σ = 10. If these scores are transformed into z-scores, the population of z-scores will have a mean of ____ and a standard deviation of ____. a. 50 and 10 b. 50 and 1 c. 0 and 10 d. 0 and 1

D

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

D

Which of the following is an advantage of transforming X values into z-scores? a. All negative numbers are eliminated. b. The distribution is transformed to a normal shape. c. All scores are moved closer to the mean. d. None of the other options is an advantage.

D

For a distribution with a mean of μ=60 and σ=8, what x-value corresponds with a z-score of z=-1.50?

X = 48

How do you determine a raw score (X) from a z-score

X= μ + zσ

z-score

specifies the precise location of each X value within a distribution.The sign of the z-score (+ or −) signifies whether the score is above the mean (positive) or below the mean (negative). The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and μ.