Deck 5: Z-Scores

Question 1

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

Answer 1

A

Question 2

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

Answer 2

$\mu$ = 85 and $\sigma$
= 4

Question 3

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

Answer 3

C

Question 4

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 5

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

Question 6

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 7

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 8

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 9

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 10

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 11

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 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

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 14

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 15

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 16

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 17

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 18

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 19

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 20

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 21

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 22

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 23

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 24

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 25

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 26

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 27

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 28

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 29

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 30

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 31

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 32

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 33

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

Question 34

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 35

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 36

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 37

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 38

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 39

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 40

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.