Deck 5: Z-Scores

Question 1

What position in the distribution corresponds to a z-score of z = -1.00?

A)Below the mean by 1 point
B)Below the mean by a distance equal to 1 standard deviation
C)Above the mean by 1 point
D)Above the mean by a distance equal to 1 standard deviation

Answer 1

B

Question 2

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

A)σ = 2
B)σ = 4
C)σ = 8
D)Cannot determine from the information given

Answer 2

A

Question 3

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

Answer 3

B

Question 4

A population has μ = 50.What value of σ would make X = 55 an extreme value out in the tail of the distribution?

A)σ = 1
B)σ = 5
C)σ = 10
D)Cannot determine with the information given

Question 5

For a population with µ = 40 and σ = 8,what is the z-score corresponding to X = 34?

A)-0.50
B)-0.75
C)-1.00
D)-1.50

Question 6

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 7

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 8

For a population with µ = 80 and σ = 10,what is the X value corresponding to z = -2.00?

A)78
B)75
C)70
D)60

Question 9

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

Question 10

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

A)σ = 2
B)σ = 4
C)σ = 8
D)Cannot determine from the information given

Question 11

For a population with µ = 70 and σ = 8,what is the z-score corresponding to X = 82?

A)+0.25
B)+0.75
C)+1.25
D)+1.50

Question 12

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 13

Which of the following z-score values represents the location farthest from the mean?

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

Question 14

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

A)σ = 1
B)σ = 5
C)σ = 10
D)Cannot determine with the information given

Question 15

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

A)2 points above the mean
B)2 points below the mean
C)12 points above the mean
D)12 points below the mean

Question 16

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 17

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

Question 18

For a population with a standard deviation of σ = 10,what is the z-score corresponding to a score that is 5 points below the mean?

A)z = 0.50
B)z = 1.00
C)z = -0.50
D)z = -1.00

Question 19

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 20

What z-score corresponds to a score that is above the mean by 2 standard deviations?

A)+2
B)+10
C)+20
D)Impossible to determine without knowing the value of the standard deviation

Question 21

In a population with a standard deviation of σ = 5,a score of X = 44 corresponds to a z-score of z = 2.00.What is the population mean?

A)49
B)54
C)39
D)34

Question 22

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 23

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 24

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)There is not enough information to compare last year with the average.

Question 25

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 26

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) $\mu$ = 85 and $\sigma$ = 4
B) $\mu$ = 85 and $\sigma$ = 2
C) $\mu$ = 81 and $\sigma$ = 4
D) $\mu$ = 81 and $\sigma$ = 6

Question 27

A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 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 28

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

A)0
B)1
C)N
D)Cannot be determined from the information given

Question 29

Last week Sarah had exams in math and in Spanish.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 σ = 8,and Sarah had a score of X = 68.For which class should Sara expect the better grade?

A)Math
B)Spanish
C)The grades should be the same because the two exam scores are in the same location.
D)There is not enough information to determine which is the better grade.

Question 30

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 = 45.What was your score in the original distribution?

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

Question 31

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

A)0
B)1
C)N
D)Cannot be determined from the information given

Question 32

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 33

Last week Tim got a score of X = 54 on a math exam with µ = 60 and σ = 8.He also got X = 49 on an English exam with µ = 55 and σ = 3,and he got X = 31 on a psychology exam with µ = 37 and σ = 4.For which class should Tim expect the best grade?

A)Math
B)English
C)Psychology
D)All 3 grades should be the same.

Question 34

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

A)0; 1
B)60; 1
C)0; 8
D)60; 8 (unchanged)

Question 35

Using z-scores,a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 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)Cannot be determined with the information given

Question 36

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

A)Math
B)Spanish
C)The grades should be the same because the two exam scores are in the same location.
D)There is not enough information to determine which is the better grade.

Question 37

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

A)σ = 12
B)σ = 1.00
C)σ = 0
D)Cannot be determined from the information given

Question 38

For a sample of n = 30 scores,a score that is 6 points above the mean has a z-score of z = 1.50.What is the sample standard deviation?

A)4
B)6
C)8
D)12

Question 39

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 40

In a population of scores,X = 44 corresponds to z = +0.50 and X = 50 corresponds to z = +2.00.What are the values for the population mean and standard deviation?

A) $\mu$ = 42 and $\sigma$ = 4
B) $\mu$ = 43 and $\sigma$ = 2
C) $\mu$ = 40 and $\sigma$ = 8
D) $\mu$ = 41 and $\sigma$ = 6

Question 41

A positive z-score always corresponds to a score that is greater than the mean.

Question 42

A sample of n = 20 scores is transformed into z-scores.What is the value of SS,the sum of squared deviations,for the set of 20 z-scores?

A)0
B)19
C)20
D)Cannot be determined without more information

Question 43

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

Question 44

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 45

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 46

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

Question 47

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 48

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 49

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 50

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

Question 51

For a sample of n = 100 scores,X = 45 corresponds to z = 0.50 and X = 52 corresponds to z = +1.00.What are the values for the sample mean and standard deviation?

A)M = 31 and s = 7
B)M = 31 and s = 14
C)M = 38 and s = 7
D)M = 38 and s = 14

Question 52

A score that is 6 points above the mean corresponds to a z-score of z = +0.50.For this population,the standard deviation is σ = 3.

Question 53

A score that is 2 points higher than the sample mean has a z-score of z = 0.50,and a score of X = 44 has a z-score of -1.00.What is the sample mean?

A)M = 40
B)M = 46
C)M = 48
D)M = 50

Question 54

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 55

For a population with a mean of μ = 60 and a standard deviation of σ = 8,a score of X = 56 corresponds to z = -0.50.

Question 56

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 57

A sample of n = 20 scores is transformed into z-scores.What is the mean for the set of 20 z-scores?

A)0
B)1
C)10
D)Cannot be determined without more information

Question 58

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

Question 59

A z-score of z = +1.00 always indicates a location exactly 1 standard deviation above the mean.

Question 60

For a population with μ = 50 and σ = 10,a score of X = 45 corresponds to z = +0.50.

Question 61

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 62

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

Question 63

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

Question 64

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 σ = 6.

Question 65

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 66

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

Question 67

For a population with μ = 34,a score of X = 31 corresponds to z = -1.00.The standard deviation for the population is σ = 6.

Question 68

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 69

Transforming an entire distribution of scores into z-scores will not change the shape of the distribution.

Question 70

A population with μ = 54 and σ = 12 is standardized to create a new distribution with μ = 100 and σ = 20.After the transformation,an individual receives a new score of X = 95.The original score for this individual was X = 51.

Question 71

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

Question 72

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 73

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

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 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 76

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

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

Question 79

In a sample with s = 6,a score of X = 53 corresponds to z = -0.50.The mean for this sample is M = 56.

Question 80

A population with μ = 41 and σ = 4 is standardized to create a new distribution with μ =
50 and σ = 10.In this transformation,a score of X = 39 from the original distribution will be
transformed into a score of X = 55.