Deck 5: Z-Scores: Location of Scores and Standardized Distributions

Question 1

A population of scores has µ = 80.In this population,a score of X = 86 corresponds to z = +2.00.What is the population standard deviation?​

A)​2
B)​3
C)​6
D)​12

Answer 1

​3

Question 2

In a population with σ = 8,a score of X = 44 corresponds to a z-score of z = -0.50.What is the population mean?​

A)μ = 36​
B)​μ = 40
C)​μ = 48
D)​μ = 52

Answer 2

​μ = 48

Question 3

On an exam with μ = 52,you have a score of X = 44.Which of the following values for the standard deviation would give you the highest position in the class distribution?​

A)​σ = 2
B)​σ = 4
C)​σ = 8
D)​σ = 10

Answer 3

​σ = 10

Question 4

For a population with µ = 80 and σ = 10,what is the X value corresponding to z = -0.50?​

A)​-5
B)​85
C)​75
D)​79.5

Question 5

Which of the following z-score values represents the location closest to the mean?​

A)​z = +0.50
B)​z = +1.00
C)​z = -1.00
D)​z = -2.00

Question 6

On an exam with μ = 52,you have a score of X = 56.Which of the following values for the standard deviation would give you the highest position in the class distribution?​

A)​σ = 2
B)​σ = 4
C)​σ = 8
D)​σ = 10

Question 7

For a population with µ = 80 and σ = 6,what is the z-score corresponding to X = 68?​

A)-0.50​
B)​-2.00
C)​+2.00
D)​-12.00

Question 8

Which of the following represents the deviation score?​

A)​x- µ
B)​Z
C)​s
D)​(x- µ)/s

Question 9

Last week Sarah had exams in Math,Spanish and English.On the Math exam,the mean was µ = 40 with σ = 5 and Sarah had a score of X = 45.On the Spanish exam,the mean was µ = 60 with s = 8 and Sarah had a score of X = 68.On the English exam,the mean was µ = 70 with s = 8 and Sarah had a score of X = 78.For which class should Sara expect the better grade?​

A)​Math
B)​Spanish
C)​English
D)​Grades are the same.

Question 10

For a population with µ = 40 and σ = 8,what is the z-score corresponding to X = 46?​

A)​+0.50
B)​+0.75
C)​+1.00
D)​+1.50

Question 11

Last week,Sarah had exams in Math,Spanish,and English.On the Math exam,the mean was µ = 30 with s = 5,and Sarah had a score of X = 45.On the Spanish exam,the mean was µ = 60 with s = 8 and Sarah had a score of X = 68.On the English exam,the mean was µ = 70 with s = 8 and Sarah had a score of X = 70.For which class should Sara expect the better grade?​

A)​Math
B)​Spanish
C)​English
D)​Grades are the same.

Question 12

What position in the distribution corresponds to a z-score of z = +2.00?​

A)Above the mean by 2 points​
B)​Above the mean by a distance equal to 2 standard deviations
C)​Below the mean by 2 points
D)​Below the mean by a distance equal to 2 standard deviations

Question 13

The direct,unchanged scores that are the direct result of measurement are called:​

A)​standardized scores
B)​deviation scores
C)​z-scores
D)​raw scores

Question 14

For a population with µ = 40 and σ = 8,what is the X value corresponding to z = 1.50?​

A)​44
B)​50
C)​52
D)​58

Question 15

For a population with µ = 80 and σ = 10,what is the z-score corresponding to X = 95?​

A)​+0.25
B)​+0.50
C)​+0.75
D)​+1.50

Question 16

A population of scores has µ = 44.In this population,a score of X = 40 corresponds to z = -0.50.What is the population standard deviation?​

A)2​
B)​4
C)​8
D)​-8

Question 17

For a population with µ = 100 and σ = 20,what is the X value corresponding to z = -0.75?​

A)85​
B)​95
C)​105
D)​115

Question 18

For a population with a standard deviation of σ = 6,what is the z-score corresponding to a score that is 12 points above the mean?​

A)​z = 1
B)​z = 2
C)​z = 6
D)​z = 12

Question 19

A population distribution has σ = 6.What position in this distribution is identified by a z-score of z = +2.00?​

A)​two points above the mean
B)​two points below the mean
C)​twelve points above the mean
D)​twelve points below the mean

Question 20

In a population of scores,X = 83 corresponds to z = -0.50 and X = 93 corresponds to z = +2.00.What are the values for the population mean and standard deviation?​

A)m = 85 and s = 4​
B)​m = 85 and s = 2
C)​m = 81 and s = 4
D)​m = 81 and s = 6

Question 21

For a sample with M = 80,a score of X = 88 corresponds to z = 2.00.What is the sample standard deviation?​

A)​2
B)​4
C)​8
D)​16

Question 22

A sample of n = 20 scores has a mean of M = 45 and a standard deviation of s = 8.In this sample,what is the z-score corresponding to X = 57?​

A)​z = 12/20 = 0.60
B)​z = 1.00
C)​z = 1.50
D)​z = 2.00

Question 23

Using z-scores,a population with µ = 37 and s = 6 is standardized so that the new mean is µ = 50 and s = 10.After the standardization,one individual has a score of X = 55.What was this individual's score in the original distribution?​

A)​X = 40
B)​X = 42
C)​X = 43
D)​It cannot be determined with the information given.

Question 24

A population with µ = 85 and s = 12 is transformed into z-scores.After the transformation,what is the standard deviation for the population of z-scores?​

A)​s = 12
B)​s = 1.00
C)​s = 0
D)​s = 4.

Question 25

In a sample with M = 40 and s = 8,what is the z-score corresponding to X = 38?​

A)​z = -0.25
B)​z = -0.50
C)​z = 0.25
D)​z = 0.50

Question 26

If an entire population with μ = 60 and s = 8 is transformed into z-scores,then the distribution of z-scores will have a mean of ____ and a standard deviation of ____.​

A)0 and 1​
B)​60 and 1
C)​0 and 8
D)​60 and 8 (unchanged)

Question 27

For a sample of n = 30 scores,X = 45 corresponds to z = 1.50 and X = 40 corresponds to z = +1.00.What are the values for the sample mean and standard deviation?​

A)​M = 35 and s = 10
B)​M = 30 and s = 15
C)​M = 35 and s = 15
D)​M = 30 and s = 10

Question 28

For a sample with M = 50 and s = 12,what is the X value corresponding to z = -0.25?​

A)47​
B)​53
C)​46
D)​54

Question 29

For an exam with a mean of M = 74 and a standard deviation of s = 8,Mary has a score of X = 80,Bob's score corresponds to z = +1.50,and Sue's score is located above the mean by 10 points.If the students are placed in order from smallest score to largest score,what is the correct order?​

A)Bob, Mary, Sue​
B)​Sue, Bob, Mary
C)​Mary, Bob, Sue
D)​Mary, Sue, Bob

Question 30

Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean?​

A)​When the population mean is much larger than 15
B)​When the population standard deviation is much larger than 15
C)​When the population mean is much smaller than 15
D)​When the population standard deviation is much smaller than 15

Question 31

Under what circumstances is a score that is located 5 points above the mean a central value,relatively close to the mean?​

A)​When the population mean is much less than 5
B)​When the population mean is much greater than 5
C)​When the population standard deviation is much less than 5
D)​When the population standard deviation is much greater than 5

Question 32

A distribution with µ = 35 and s = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and s = 10.In the new,standardized distribution your score is X = 45.What was your score in the original distribution?​

A)​X = 30
B)​X = 31
C)​X = 39
D)​X = 45

Question 33

A sample has M = 72 and s = 4.In this sample,what is the X value corresponding to z = -2.00?​

A)X = 70​
B)​X = 68
C)​X = 64
D)​X = 60

Question 34

For any distribution,what is the z-score corresponding to the mean?​

A)0​
B)​1
C)​N
D)​Z

Question 35

In N = 25 games last season,the college basketball team averaged µ = 76 points with a standard deviation of σ = 6.In their final game of the season,the team scored 89 points.Based on this information,the number of points scored in the final game was ____.​

A)a little above average​
B)​far above average
C)​above average, but it is impossible to describe how much above average
D)​impossible to determine because there is not enough information to compare last year with the average

Question 36

A distribution with µ = 55 and s = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and s = 10.When the distribution is standardized,what value will be obtained for a score of X = 58 from the original distribution?​

A)​X = 53
B)​X = 55
C)​X = 58
D)​X = 61

Question 37

A sample with M = 85 and s = 12 is transformed into z-scores.After the transformation,what are the values for the mean and standard deviation for the sample of z-scores?​

A)M = 85 and s = 12​
B)​M = 0 and s = 12
C)​M = 85 and s = 1
D)​M = 0 and s = 1

Question 38

A population has μ = 50.What value of σ would make X = 55 a more central,representative score in the population?​

A)​σ = 1
B)​σ = 5
C)​σ = 10
D)​σ = 20

Question 39

You have a score of X = 65 on an exam.Which set of parameters would give you the best grade on the exam?​

A)​μ = 60 and σ = 10
B)​μ = 60 and σ = 5
C)μ = 70 and σ = 10​
D)​μ = 70 and σ = 5

Question 40

For a sample with s = 12,a score of X = 73 corresponds to z = 1.00.What is the sample mean?​

A)​M = 61
B)​M = 67
C)​M = 79
D)​M = 85

Question 41

On an exam,Tom scored 12 points above the mean and had a z-score of +2.00.The standard deviation for the set of exam scores must be s = 6.

Question 42

The process of transforming every x value in a distribution into a corresponding z-score to create a distribution of z-scores is called a z-score transformation.

Question 43

On an exam with s = 6,Tom's score of X = 54 corresponds to z = -1.00.The mean for the exam must be µ = 60.

Question 44

If an entire population of N = 20 scores is transformed into z-scores,the set of 20 z-scores will have SX = 0.

Question 45

For a population with μ = 30,a score of X = 24 corresponds to z = -2.00.The standard deviation for the population is s = 6.

Question 46

A population with μ = 59 and s = 8 is standardized to create a new distribution with μ = 100 and s = 20.After the transformation,an individual receives a new score of X = 90.The original score for this individual was X = 51.

Question 47

For a population of exam scores,a score of X = 83 corresponds to z = +0.50 and a score of X = 89 corresponds to z = +1.50.The population mean is μ = 80.

Question 48

For a population with a standard deviation of s = 12,a z-score of z = +0.50 corresponds to a score that is above the mean by 6 points.​

Question 49

In a distribution with µ = 80 and s = 20,a score of X = 95 corresponds to z = 1.50.

Question 50

For a population with a mean of μ = 80 and a standard deviation of σ = 12,a score of X = 77 corresponds to z = -0.50.

Question 51

For any distribution of scores,the location identified by z = +1 and the location identified by z = -1 are exactly the same distance from the mean.

Question 52

Because all z-score distributions have the same mean and standard deviation,the z-score distribution is called a standardized distribution.

Question 53

For a population with a mean of μ = 40,a score of X = 37 corresponds to z = -0.50.The standard deviation for the population is s = 3.

Question 54

Any individual with a positive z-score has a score greater than the mean.

Question 55

A population with μ = 45 and s = 8 is standardized to create a new distribution with μ = 100 and s = 20.In this transformation,a score of X = 41 from the original distribution will be transformed into a score of X = 110.

Question 56

For a population with a mean of μ = 80,any score greater than 80 will have a positive z-score.

Question 57

If two individuals in the same population have identical X scores,they also will have identical z-scores.

Question 58

In a population with s = 4,a score of X = 48 corresponds to z = 1.50.The mean for this population is µ = 42.

Question 59

A score with a value less than or equal to the mean will have a z-score that is less than or equal to zero.

Question 60

4 Using z-Scores to Standardize a Distribution

Question 61

In a distribution with s = 20,a score that is above the mean by 10 points will have a z-score of z = 0.50.

Question 62

Describe the general purpose of a z-score and explain how a z-score accomplishes this goal.

Question 63

On a psychology exam with µ = 76 and σ = 12,Tom scored 9 points below the mean,Mary had a score of X = 70,and Bill had a z-score of z = -1.00.Place these three students in order from lowest to highest score.____: Student with lowest score____: Student with middle score____: Student with highest score

Question 64

For a sample with a standard deviation of s = 10,a score with a deviation of +5 will have a z-score of z = 0.50.

Question 65

For a sample with a mean of M = 50 and a standard deviation of s = 10,a z-score of z = +2.00 corresponds to X = 70.

Question 66

Standardized scores are "simple" values for the mean and standard deviation that do not change any individual's location within the distribution.

Question 67

A professor standardizes exam scores so that all exams have μ = 50 and s = 10.If the original scores from an exam have μ = 42 and s = 6,then a student with an original exam score of X = 45 would receive a standardized score of X = 55.

Question 68

For a population with µ = 60 and σ = 12,find the z-score corresponding to each of the following X values: 66,78,57,48.

Question 69

For a population with µ = 48 and σ = 8,find the X value that corresponds to each of the following z-scores: -0.25,-1.50,0.50,2.00.

Question 70

For a sample with a mean of M = 76,a score of X = 72 corresponds to z = -0.50.The sample standard deviation is s = 8.

Question 71

A population of scores with µ = 73 and s = 20 is standardized to create a new population with µ = 50 and s = 10.What is the new value for each of the following scores from the original population?Scores: 63,65,77,83

Question 72

In a sample with s = 6,a score of X = 53 corresponds to z = -0.50.The mean for this sample is M = 50.​

Question 73

Describe what happens to the mean,the standard deviation,and the shape of a distribution when all of the scores are transformed into z-scores.

Question 74

For a sample with a standard deviation of s = 8,a score of X = 42 corresponds to z = -0.25.The mean for the sample is M = 40.

Question 75

For a sample with M = 50 and s = 8,z = 1.50 corresponds to X = 65.​

Question 76

In a sample of n = 40 scores,X = 31 corresponds to z = -1.50 and X = 39 corresponds to z = +0.50.The sample mean is M = 36.

Question 77

For a sample with a standard deviation of s = 6,a z-score of z = -1.50 corresponds to a location that is 9 points above the mean.

Question 78

For a distribution of scores,X = 40 corresponds to a z-score of z = +1.00,and X = 28 corresponds to a z-score of z = -0.50.What are the values for the mean and standard deviation for the distribution? (Hint: Sketch a distribution and locate each of the z-score positions.)