Deck 5: The Normal Curve and Standard Scores

Question 1

A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The proportion of scores between 300 and 400 is _________.

A) 0.3665
B) 0.4868
C) 0.8533
D) 0.1203

Answer 1

0.1203

Question 2

The mean of the z distribution equals _________.

A) 1
B) 0
C) S X
D) N

Answer 2

0

Question 3

An economics test was given and the following sample scores were recorded: The mean of the distribution is _________.

A) 12.00
B) 10.00
C) 9.00
D) 8.00

Answer 3

10.00

Question 4

An economics test was given and the following sample scores were recorded: The standard deviation of the distribution is _________.

A) 10.20
B) 2.10
C) 2.11
D) 10.74

Question 5

A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The proportion of scores that lie above 650 is _________.

A) 0.4535
B) 0.9535
C) 0.0475
D) 0.0485

Question 6

The standard deviation of the z distribution equals _________.

A) 1
B) 0
C) ΣX
D) N

Question 7

A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. What percentage of the distribution lies below $7.42.

A) 17.72%
B) 32.28%
C) 82.28%
D) 31.92%

Question 8

The z score corresponding to a raw score of 120 is _________.

A) 1.2
B) 2.0
C) 1.0
D) impossible to compute from the information given

Question 9

A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. The stock price beyond which 0.05 of the distribution falls is _________.

A) $ 4.60
B) $12.47
C) $ 4.57
D) $12.44

Question 10

A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The proportion of scores that lie between 460 and 600 is _________.

A) 0.4394
B) 0.5365
C) 0.4406
D) 0.4635

Question 11

A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The raw score that lies at the 90th percentile is _________.

A) 615.20
B) 384.80
C) 616.10
D) 383.90

Question 12

A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. The percentile rank of a price of $13.87 is _________.

A) 48.78%
B) 1.22%
C) 98.78%
D) 51.22%

Question 13

A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. The percentage of scores that lie between $9.00 and $10.00 is _________.

A) 15.31%
B) 31.17%
C) 23.24%
D) 7.93%

Question 14

A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. What percentage of the distribution lies between $5 and $11?

A) 21.48%
B) 78.41%
C) 49.41%
D) 57.98%

Question 15

An economics test was given and the following sample scores were recorded: The z score for individual E is _________.

A) 0.47
B) 9.00
C) 4.27
D) - 0.47

Question 16

A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The percentile rank of a score of 667 is _________.

A) 3.14%
B) 96.78%
C) 3.22%
D) 96.86%

Question 17

The z score corresponding to the mean of a raw score distribution equals _________.

A) the mean of the raw scores
B) 0
C) 1
D) N

Question 18

An economics test was given and the following sample scores were recorded: The z score for individual D is _________.

A) 1
B) 0
C) 10
D)

Question 19

In a normal curve, the inflection points occur at _________.

A) µ ± 1 s
B) ±1 s
C) µ ± 2 s
D) µ

Question 20

The normal curve is _________.

A) linear
B) rectangular
C) bell-shaped
D) skewed

Question 21

If a population of scores is normally distributed, has a mean of 45 and a standard deviation of 6, the most extreme 5% of the scores lie beyond the score(s) of _________.

A) 35.13
B) 45.99
C) 56.76 and 33.24
D) 45.99 and 35.13

Question 22

Would you rather have an income (assume a normal distribution and you are greedy) _________.

A) with a z score of 1.96
B) in the 95th percentile
C) with a z score of -2.00
D) with a z score of 0.000

Question 23

On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percentage of scores fall between 70 and 80?

A) 75.66
B) 70 23
C) 24.34
D) 23.57
E) 12.17

Question 24

The standard deviation of the z distribution equals _________.

A) 0
B) 1
C) the variance of the z distribution
D) 0 and the variance of the z distribution

Question 25

A distribution has a mean of 60.0 and a standard deviation of 4.3. The raw score corresponding to a z score of 0.00 is _________.

A) 64.3
B) 14.0
C) 4.3
D) 60.0

Question 26

On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what is the percentile rank of a score of 56?

A) 58.30
B) 0.00
C) 25.27
D) 38.30
E) 11.70

Question 27

Assuming the z scores are normally distributed, what is the percentile rank of a z score of - 0.47?

A) 31.92
B) 18.08
C) 50.00
D) 47.00
E) 0.06

Question 28

If a distribution of raw scores is negatively skewed, transforming the raw scores into z scores will result in a _________ distribution.

A) normal
B) bell-shaped
C) positively skewed
D) negatively skewed

Question 29

S ( z - µz ) equals _________.

A) 0
B) 1
C) the variance
D) cannot be determined

Question 30

Which of the following z scores represent(s) the most extreme value in a distribution of scores assuming they are normally distributed?

A) 1.96
B) 0.0001
C) - 0.0002
D) - 3.12

Question 31

How much would your income be if its z score value was 2.58?

A) $10,000
B) $ 9,999
C) $ 5,000
D) cannot be determined from information given

Question 32

The proportion of scores less than z = 0.00 is _________.

A) 0.00
B) 0.50
C) 1.00
D) - 0.50

Question 33

In a normal distribution approximately _________ of the scores will fall within 1 standard deviation of the mean.

A) 14%
B) 95%
C) 70%
D) 83%

Question 34

A distribution has a mean of 60.0 and a standard deviation of 4.3. The raw score corresponding to a z score of - 1.51 is _________.

A) 53.5
B) 66.5
C) 66.4
D) 53.6

Question 35

The mean of the z distribution equals _________.

A) 0
B) 1
C) N
D) Depends on the raw scores.

Question 36

On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percentage of scores fall below a score of 83.8?

A) 55.00
B) 79.12
C) 20.88
D) 29.12
E) 70.88

Question 37

An economics test was given and the following sample scores were recorded: The z score for individual G is _________.

A) - 1.42
B) 13.00
C) 1.42
D) 6.16

Question 38

A standardized test has a mean of 88 and a standard deviation of 12. What is the score at the 90th percentile? Assume a normal distribution.

A) 90.00
B) 112.00
C) 103.36
D) 91.00

Question 39

In a normal distribution the z score for the mean equals _________.

A) 0
B) the z score for the median
C) the z score for the mode
D) all of these

Question 40

A distribution has a mean of 60.0 and a standard deviation of 4.3. The raw score corresponding to a z score of 2.02 is _________.

A) 51.3
B) 68.7
C) 51.4
D) 68.6

Question 41

If the original raw score distribution has a mean that is not equal to zero, the mean of the z transformed scores will not equal zero either.

Question 42

For any z distribution of normally distributed scores, P 50 is always equal to zero.

Question 43

You have just taken a standardized skills test designed to help you make a career choice. Your math skills score was 63 and your writing skills score was 45. The standardized math distribution is normally distributed, with m = 50, and s = 8. The writing skills score distribution is also normally distributed, with m = 30, and s = 10. Based on this information, as between pursuing a career that requires good math skills or one requiring good writing skills, you should chose _________.

A) neither, your skills are below average in both
B) the career requiring good math skills.
C) neither, this approach is bogus; dream interpretation should be used instead.
D) the career requiring good writing skills.

Question 44

A z score is a transformed score.

Question 45

Table A in your textbook has no negative z values, this means _________.

A) the table can only be used with positive z values
B) the table can be used with both positive and negative z values because it is symmetrical
C) the table can be used with both positive and negative z values because it is skewed
D) none of these

Question 46

A z score designates how many standard deviations the raw score is above or below the mean.

Question 47

The z distribution takes on the same shape as the raw scores.

Question 48

In a normal curve, the area contained between the mean and a score that is 2.30 standard deviations above the mean is 0.4893 of the total area.

Question 49

You have just received your psychology exam grade and you did better than the mean of the exam scores. If so, the z transformed value of your grade must

A) be greater than 1.00
B) must be greater than 0.00
C) have a percentile rank greater than 50%
D) can't determine with information given
E) must be greater than 0.00 and have a percentile rank greater than 50%.

Question 50

A testing service has 1000 raw scores. It wants to transform the distribution so that the mean = 10 and the standard deviation = 1. To do so, _________.

A) do a z transformation for each raw score and add 10 to each z score.
B) do a z transformation for each raw score and multiply each by 10
C) divide the raw scores by 10
D) compute the deviation score for each raw score. Divide each deviation score by the standard deviation of the raw scores. Take this result for all scores and add 10 to each one.
E) a and d

Question 51

A set of raw scores has a rectangular shape. The z transformed scores for this set of raw scores has a _________ shape.

A) rectangular
B) normal (bell-shaped)
C) it depends on the number of scores in the distribution
D) none of these

Question 52

A z distribution always is normally shaped.

Question 53

All standard scores are z scores.

Question 54

Given the following set of sample raw scores, X: 1, 3, 4, 6, 8. What is the z transformed value for the raw score of 3?

A) -0.18
B) -0.48
C) -0.15
D) -0.52

Question 55

All bell-shaped curves _________.

A) are normal curves
B) have means = 0
C) are symmetrical
D) a and c

Question 56

A distribution of raw scores is positively skewed. You want to transform it so that it is normally distributed. Your friend, who fancies herself a statistics whiz, advises you to transform the raw scores to z scores; that the z scores will be normally distributed. You should _________.

A) ignore the advice because your friend flunked her last statistics test
B) ignore the advice because z distributions have the same shape as the raw scores.
C) take the advice because z distributions are always normally distributed
D) take the advice because z distributions are usually normally distributed

Question 57

Makaela took a Spanish exam; her grade was 79. The distribution was normally shaped with = 70 and s = 12. Juan took a History exam; his grade was 86. The distribution was normally shaped with = 80 and s = 8. Which did better on their exam relative to those taking the exam?

A) Makaela.
B) Juan.
C) Neither, they both did as well as each other.
D) Makaela, because her exam was harder
E) a and d.

Question 58

z scores allow comparison of variables that are measured on different scales.

Question 59

The normal curve reaches the horizontal axis in 4 standard deviations above and below the mean.

Question 60

If you transformed a set of raw scores, and then added 15 to each z score, the resulting scores _________.

A) would have a standard deviation = 1
B) would have a mean = 0
C) would have a mean =15
D) would have a standard deviation > 1
E) would have a standard deviation =1 and a mean of =15

Question 61

The area under the normal curve represents the proportion of scores that are contained in the area.

Question 62

A raw score that is 1 standard deviation above the mean of the raw score distribution will have a z score of 1.

Question 63

Define asymptotic.

Question 64

In the standard normal curve, 13.59% of the scores will always be contained between the mean ( µ ) and +1 s .

Question 65

A z transformation will allow comparisons to be made when units of distributions are different.

Question 66

To do a z transformation, one must know only the population mean and the value of the raw score to be transformed.

Question 67

The normal curve never touches the X axis.

Question 68

It is impossible to have a z score of 30.2.

Question 69

The normal curve is a symmetric, bell-shaped curve.

Question 70

The area beyond a z score of +2.58 is 0.005.

Question 71

The area under the normal curve represents the percentage of scores contained within the area.

Question 72

If the original raw score distribution is not normally distributed, the mean of the z transformation scores of the raw data will not equal 0.

Question 73

One cannot reasonably do z transformations on ratio data.

Question 74

In a plot of the normal curve, frequency is plotted on the X axis.

Question 75

The area beyond a z score of -1.12 is the same as the area beyond a z score of 1.12.

Question 76

The standard deviation of the z distribution is always equal to 1.0.

Question 77

If the raw score distribution is very positively skewed, the standard deviation of the z transformed scores will not equal 1.

Question 78

To calculate the score at the 97.5th percentile, one would apply the formula X = µ + ( s )(1.96).

Question 79

It is impossible to have a z score of 23.5.

Question 80

The z score and the z distribution are the same thing.