Deck 6: Z-Scores and the Normal Curve

Question 1

z-scores can be calculated from

A)any data.
B)interval or ratio scores.
C)nominal or ordinal scores.
D)the range.

Answer 1

interval or ratio scores.

Question 2

The z-score transformation is a useful statistical tool because it enables statisticians to

A)compare and interpret scores from virtually any distribution of interval or ratio scores.
B)determine which interval or ratio scores are the "best" scores.
C)transform interval or ratio data by multiplying by a constant.
D)revise the shape of distributions to be more useful.

Answer 2

compare and interpret scores from virtually any distribution of interval or ratio scores.

Question 3

Jason's z-score in the 10-K run was -3.If the raw score standard deviation was 5,and the mean running time for the competitors was 55 minutes,what was Jason's raw score running time?

A)60 minutes.
B)50 minutes.
C)40 minutes.
D)30 minutes.

Answer 3

40 minutes.

Question 4

Given a normal distribution,as z-scores' absolute values increase,those z-scores and the raw scores that correspond to them occur

A)more frequently.
B)less frequently.
C)more frequently at first and then less frequently.
D)less frequently at first and then more frequently.

Question 5

Pat's last statistics test score was 72.If the instructor tells Pat that the grade distribution was approximately normal,the class mean was 67,and the standard deviation was 3,which of the following is correct?

A)A score of 72 is never good.
B)Pat should be worried about this score,because many other students did better.
C)Pat should be fairly happy about this score,because many students did not do as well.
D)Pat should be ecstatic,because this is obviously one of the highest grades in the class.

Question 6

For a distribution with = 50 and = 5,find the z-scores for each of the following raw scores: 50;65;45;42

A)0;-3;1;1.6
B)0;6.71;-2.24;-3.58
C)0;3;-1;-1.6
D)0;-6.71;2.24;3.58

Question 7

The sample mean for a recent introductory psychology test was 78,and the sample variance was 9.If a student received a score of 82,what was this student's z-score?

A)0.44
B)1.33
C)-1.33
D)-0.44

Question 8

The sample mean for a recent introductory psychology test was 78,and the sample variance was 9.If a student's z-score = -2.0,what was this student's raw test score?

A)84
B)60
C)72
D)96

Question 9

Chris wants to calculate a z-score for his own height.The average height in the class is 66 inches,and Chris's height is 62 inches.Chris calculated his z-score to be +1.5.What's wrong with his calculation?

A)The z-score is an inappropriate calculation here.
B)The z-score should be a higher number.
C)He didn't have the standard deviation.
D)The z-score should be a negative number.

Question 10

When the standard deviation of a raw score distribution is large,the corresponding z-score distribution will be

A)relatively spread out.
B)relatively narrow.
C)positively skewed.
D)negatively skewed.

Question 11

Alicia scored a 70 on her psychology quiz,but the class as a whole averaged a 40.If the standard deviation was 10,what was Alicia's z-score?

A)-3
B)+3
C)-0.3
D)+0.3

Question 12

One way to measure the ability to find one's way in an environment is to use the Sense of Direction test scale.The scale ranges from 1 (poor)to 50 (good).In a sample of college students,including yourself,the mean rating of sense of direction is 30,with a standard deviation of 10.If your score was 20,what is your z-score?

A)0.57
B)-1.0
C)+1.5
D)-3.0

Question 13

For a distribution with = 50 and = 5,find the raw scores for the following z-scores: -1.2;-0.5;1.7;2.6

A)44.00;47.50;58.50;63.00
B)20.00;37.50;92.50;115.00
C)47.32;48.88;53.80;55.81
D)-20.00;-37.50;92.50;115.00

Question 14

A z-score of zero always means that

A)the raw score does not exist.
B)the raw score exists but is negligible.
C)the raw score almost never occurs.
D)the raw score is equal to the mean.

Question 15

Which of the following is not one of the things z-scores allow us to calculate for corresponding raw scores?

A)Relative frequency
B)Simple frequency
C)Percentile rank
D)Strength of relationship

Question 16

z-scores communicate a score's

A)absolute magnitude.
B)relative standing in a distribution.
C)distance from the population mean.
D)variability.

Question 17

In a normal distribution,large,positive z-scores occur with _______________ small,positive z-scores.

A)greater frequency than
B)less frequency than
C)equal frequency to
D)greater variability than

Question 18

For the following set of sample scores,what is the z-score for a raw score of 23? 22,23,19,25,26,22,19,25,22,20,21,23,23,24,18,20,22,24,21,21,20,24,22,21,23

A)1.25
B)0.50
C)0.34
D)0.68

Question 19

An evaluation of where a score is located in relation to the other scores in the distribution reflects its

A)absolute value.
B)relative standing.
C)standard deviation.
D)frequency.

Question 20

The absolute value of a number is the

A)measure of how much the number is worth.
B)size of a number only when it is a positive number.
C)size of a number only when it is a negative number.
D)size of a number,regardless of whether it is positive or negative.

Question 21

The proportion of the total area under a normal curve between two z-scores corresponds to the ______ of that range of scores.

A)numeric magnitude
B)variability
C)frequency
D)relative frequency

Question 22

The average score on the statistics quiz was a 70,and there was a standard deviation of 10 points.If Enrique had a z-score of -1.0,his raw score would be ______ and his percentile rank would be ______.

A)40;2%
B)50;16%
C)60;16%
D)60;34%

Question 23

When two normal z-distributions are plotted on the same graph,what can we say about the relative frequency of each z-score?

A)It will always be the same.
B)It will always be different.
C)It depends on the raw score mean.
D)It depends on the raw score standard deviation.

Question 24

If there were 500 students in Jamal's class,approximately how many actual students scored higher than Jamal on the quiz if Jamal had a z-score of -1?

A)250
B)340
C)420
D)490

Question 25

A perfect normal curve,which serves as a model of any approximately normal z-distribution,is called the

A)sampling distribution of means.
B)standard,normalized z-distribution.
C)standard normal curve.
D)standard mean score distribution.

Question 26

If only the upper 30% of a normally distributed class passed a quiz for which the mean was 70 and the standard deviation was 10,what was the lowest score a student could have received and still have passed?

A)80.0
B)64.8
C)70.0
D)75.2

Question 27

Your sense of direction puts you at the 39th percentile,relative to a raw score distribution with a mean of 3.5 and a standard deviation of 1.What is your z-score?

A)-0.28
B)+0.28
C)+1.23
D)-1.23

Question 28

Only the upper 30% of a normally distributed class passed a quiz for which the mean was 70 and the standard deviation was 10.In this class,76.7 and 78.4 are the boundary limits for students who scored between what percentiles?

A)75th and 80th
B)80th and 85th
C)77th and 80th
D)67th and 80th

Question 29

Which of the following is NOT a way we apply the standard normal curve?

A)finding relative frequency
B)measuring variability
C)finding simple frequency
D)calculating the raw score for a specific percentile

Question 30

The mean of a z-score distribution is always ______,and the standard deviation is always ______.

A)0;10
B)1;0
C)100;20
D)0;1

Question 31

In a z-distribution,the standard deviation will always be

A)greater than 1.
B)less than 1.
C)equal to 1.
D)equal to 0.

Question 32

The distribution of z-scores is always

A)positively skewed.
B)negatively skewed.
C)the same as the distribution of raw scores.
D)more spread out than the distribution of raw scores.

Question 33

How accurately the standard normal curve model predicts the actual relative frequency of raw scores depends on three aspects of the data:

A)The raw scores form an approximately normal distribution;there is a large sample N;and the raw scores are theoretically continuous scores measured on an interval or ratio scale.
B)50% of the raw scores are above and below the median;there is a large sample N;and the raw scores are measured on an ordinal,interval,or ratio scale.
C)50% of the raw scores are above and below the median;there is a moderately large sample N;the raw scores are theoretically continuous scores measured on an interval or ratio scale.
D)The raw scores form an approximately normal distribution;there is a moderately large sample N;and the raw scores are measured on an ordinal,interval,or ratio scale.

Question 34

If a class's scores are normally distributed,with a mean of 70 and a standard deviation of 10,what are the upper and lower limits of the middle 68% of the class?

A)50 and 90
B)40 and 100
C)60 and 80
D)32 and 68

Question 35

Your sense of direction puts you at the 79th percentile,relative to a raw score distribution with a mean of 3.5 and a standard deviation of 1.What is your z-score?

A)+0.13
B)+0.50
C)+0.81
D)-0.81

Question 36

If raw scores ranging from 1 to 50 represented all the corresponding negative z-scores on the distribution,and raw scores ranging from 50 to 100 represented all the corresponding positive z-scores,what would be the total relative frequency of 50 to 100?

A)1.00
B)0.75
C)0.50
D)0.25

Question 37

On a recent paper,Maria's score,transformed to a z-score,was +1.If the cutoff mark is the upper 10% of the class for As,the upper 10% to 20% for Bs,the upper 20% to 30% for Cs,and the upper 30% to 40% for Ds (below 60% being a failure),what grade did Maria receive on the quiz?

A)A
B)B
C)C
D)F

Question 38

To evaluate a person for possible brain damage,a neuropsychologist gives the person a visual memory test and a reading test.To compare the person's performance across these two tests,what should the neuropsychologist do?

A)Graph the raw score distribution for each test on the same graph.
B)Calculate a z-score for each test.
C)Calculate z-scores for the sample means.
D)Find the simple frequency of the person's raw score for each test.

Question 39

If your sense of direction,relative to a sample of college students,gave you a z-score of +1.5,what is your percentile?

A)6th
B)7th
C)43rd
D)93rd

Question 40

We can use the standard normal curve as our model for

A)perfectly normal distributions only.
B)perfectly normal distributions only,when transformed to z-scores.
C)any approximately normal distribution,when transformed to z-scores.
D)any approximately normal distribution,when transformed to percentiles.

Question 41

Which of the following statements accurately describes the sampling distribution of means?

A)The frequency distribution of several sample means that occurs when an infinite number of samples of the same size N are randomly selected from one raw score population
B)The frequency distribution of all possible sample means that occurs when a given finite number of samples of the same size N are randomly selected from one raw score population
C)The frequency distribution of all possible sample means that occurs when an infinite number of samples of variously sized Ns are randomly selected from several raw score populations
D)The frequency distribution of all possible sample means that occurs when an infinite number of samples of the same size N are randomly selected from one raw score population

Question 42

What raw score is at the 16th percentile (15.87 to be exact)when the mean of the distribution is 50 and the standard deviation is 4?

A)54
B)46
C)34
D)There is insufficient information to determine an answer.

Question 43

For each of the following z-scores,what is the area between the mean and each z-score? 0.40;1.01;-1.48;-1.89;2.53

A)0.3446;0.1562;0.0694;0.0294;0.0057
B)0.1554;0.3438;-0.4306;-0.4706;0.4943
C)0.1554;0.3438;0.4306;0.4706;0.4943
D)0.3446;0.1562;-0.0694;-0.0294;0.0057

Question 44

If the population variance of the raw scores equals 169 and the sample size is 121,what is the standard error of the mean?

A)0.11
B)1.18
C)1.40
D)15.36

Question 45

Bahatamy Academy has an outrageously intelligent student body.In a recent evaluation of all the high schools in the state,Bahatamy Academy received a z-score of +3 for its corresponding sample mean of SAT scores.With a population mean of 500 and a standard deviation (standard error)of 200 for the sampling distribution,what was Bahatamy's sample mean?

A)560
B)1,560
C)1,100
D)900

Question 46

Using the appropriate values from the z-table in the textbook appendix,find the z-score for which the area beyond z in the tail is 0.2546.

A)0.66
B)0.2454
C)-0.66
D)-0.2454

Question 47

For each of the following z-scores,what is the area beyond the z-score in the tail? 0.63;-1.65;1.94;-2.27;2.80

A)0.2643;0.0495;0.0262;0.0116;0.0026
B)0.2643;-0.0495;0.0262;-0.0116;0.0026
C)0.2357;0.4505;0.4738;0.4884;0.4974
D)0.2357;-0.4505;0.4738;-0.4884;0.4974

Question 48

What were the sample means that marked the middle 68% in the state if the population mean was 500 and the standard deviation (standard error)for the sampling distribution was 200?

A)350 and 650
B)300 and 700
C)400 and 600
D)450 and 550

Question 49

If a school's z-score for its sample mean was +3,its percentile rank in the state was

A)99.87%.
B)90.87%.
C)85.87%.
D)95.87%.

Question 50

Sampling distributions of means are always

A)approximately normally distributed.
B)positively skewed.
C)negatively skewed.
D)more variable than the population from which the samples were drawn.

Question 51

According to the central limit theorem,the sampling distribution of means always approximates a ______ distribution.

A)normal
B)positively skewed
C)negatively skewed
D)bimodal

Question 52

The mean of the sampling distribution of means is always

A)greater than the population mean.
B)less than the population mean.
C)equal to the population mean.
D)the population mean divided by the square root of N.

Question 53

A sampling distribution of means for samples of students taking the SAT exam has a population mean of 500 and a standard error of 200.What proportion of sample means would fall between the population mean and a sample mean of 800?

A)0.5000
B)0.3413
C)0.1915
D)0.4332

Question 54

The standard deviation of the sampling distribution of means is called the

A)percent error of the mean.
B)likely error of the mean.
C)standard error of the mean.
D)special error of the mean.

Question 55

For the following set of scores,what is the percentile for a score of 24? 22,23,19,25,26,22,19,25,22,20,21,23,23,24,18,20,22,24,21,21,20,24,22,21,23

A)84th percentile
B)34th percentile
C)16th percentile
D)50th percentile

Question 56

The size of depends on

A) and
B)N and
C) and
D)z and

Question 57

In sampling distributions,all the samples contain sets of raw scores

A)with the same variance.
B)from the same raw score population.
C)with the same mean.
D)that are representative of the population mean.

Question 58

The sample mean for a recent introductory psychology test was 78 and the sample variance was 9.Approximately what proportion of the scores was above 81?

A)0.50
B)0.68
C)0.16
D)0.34

Question 59

Using the appropriate values from the z-table in the textbook appendix,find the area above (beyond)z = +0.89.

A)0.3133
B)0.1867
C)-0.3133
D)-0.1867

Question 60

A sampling distribution of means is an approximately normal distribution

A)regardless of the shape of the raw score distribution.
B)only when the shape of the raw score distribution is approximately normal.
C)only when the raw score population mean is equal to the sample mean.
D)if an infinite number of samples is used.