Deck 4: The Normal Curve and Z Score

Question 1

When a z score falls to the left of the mean

A) it must always be given a minus sign
B) it must always be greater than 1
C) it must always be less than 1
D) none of these, since z scores never fall to the left of the mean

Answer 1

A

Question 2

The normal curve is

A) symmetrical
B) unimodal
C) asymptotic to the abscissa
D) all of these

Answer 2

D

Question 3

Under the normal curve

A) the mean lies to the right of the median
B) the mode lies to the left of the mean
C) the median lies to the left of the mode
D) none of these

Answer 3

D

Question 4

If an IQ distribution is normal and has a mean of 100 and a standard deviation of 15, then 99% of all those taking the test scored between IQ's of

A) 0 and 150
B) 55 and 145
C) 85 and 115
D) 92.5 and 107.5

Question 5

When more than 34% of the cases under the curve fall between the mean and a z score of + 1, then

A) 68% of the cases fall below the mean
B) the curve cannot be symmetrical
C) the curve cannot be normal
D) none of these

Question 6

Under the normal curve, the percentage of cases falling above a z score of + 3, is

A) 68%
B) 95%
C) more than 1%
D) less than 1%

Question 7

Under the normal curve, when the z score is equal to + 1, then

A) the standard deviation of the distribution of raw scores must equal 15
B) the standard deviation of the distribution of raw scores must equal 10
C) the standard deviation of the distribution of raw scores must equal 0
D) none of these

Question 8

The normal curve is

A) a frequency distribution curve
B) leptokurtic
C) platykurtic
D) skewed to the left

Question 9

Under the normal curve the 50th percentile always falls at the

A) mean
B) median
C) mode
D) all of these

Question 10

Under the normal curve, if the mean of the distribution of raw scores is equal to 68, then its equivalent z score is equal to

A) 10
B) 1
C) 0
D) cannot tell, since the SD is not given

Question 11

When the normal curve is plotted according to standard deviation units, each having a value of 1.00, it is called

A) platykurtic
B) leptokurtic
C) the standard normal curve
D) the deviation curve

Question 12

A normal curve always has

A) a greater frequency of scores around the center than in the tails
B) a greater frequency of scores in the tails than around the center
C) a greater frequency of scores above the mean than below the mean
D) a greater frequency of scores below the mean than above the mean

Question 13

If an IQ distribution is normal and has a mean of 100 and a standard deviation of 15, then 68% of all those taking the test scored between IQ's of

A) 100 and 115
B) 85 and 100
C) 92.5 and 107.5
D) 85 and 115

Question 14

Under the normal curve, between the z scores of + 1 and + 2, there are always

A) 68% of the cases
B) 95% of the cases
C) 13.50% of the cases
D) sometimes a, and sometimes b, but never c

Question 15

Under the normal curve, 68% of the cases must always fall

A) above the mean
B) between + 1 standard deviation units from the mean
C) between + 2 standard deviation units from the mean
D) all of these, depending on the particular shape of the curve

Question 16

Under the normal curve, between z scores of + 10, there are always

A) 100% of the cases
B) 95% of the cases
C) 68% of the cases
D) more than 99% but less than 100% of the cases

Question 17

The creation of the normal curve concept is popularly credited to

A) Blaise Pascal
B) Henry Gossett
C) Sir Bryant McKenna
D) Karl Gauss

Question 18

A bimodal distribution may never be

A) symmetrical
B) a frequency distribution
C) normal
D) all of these

Question 19

Under the normal curve, 50% of the cases must always fall

A) below the mean
B) above the mean
C) below the median
D) all of these

Question 20

When the mean and median do not coincide, then

A) the curve cannot be normal
B) the curve cannot be skewed
C) the curve cannot be unimodal
D) the curve cannot be a frequency distribution curve

Question 21

Under the normal curve, the only point where the frequency of cases is zero is

A) between the mean and a z score of + 1
B) beyond a z score of + 1
C) beyond a z score of + 3
D) none of these

Question 22

The z score provides direct information regarding how far a given raw score is

A) from the mean in units of standard deviation
B) from the mean in percentage units
C) from the lowest score in percentile units
D) from the highest score in percentile units

Question 23

The closer a given z score is to 0, then the closer it is

A) to the tails of the curve
B) to the mean of the distribution
C) to the 68th percentile
D) to a 0% frequency

Question 24

The 49th percentile must be below a raw score of

A) 500
B) 400
C) 300
D) 200

Question 25

Under the normal curve, if a given raw score falls at the 84th percentile, then its equivalent z score must be equal to

A) the mean
B) 0
C) + 1
D) + 2

Question 26

On any normal distribution the 50th percentile corresponds with a z score of

A) 0
B) 50
C) 68
D) + 1

Question 27

Approximately 68% of all the scores would fall

A) between raw scores of 400 and 600
B) between raw scores of 200 and 500
C) between raw scores of 500 and 600
D) above a raw score of 700

Question 28

Under the normal curve, the mean falls below the 50th percentile only when

A) the mean of the raw score distribution is equal to 50
B) the mean of the raw score distribution is equal to 100
C) the mean of the raw score distribution is unknown
D) none of these, since under the normal curve the mean must fall at the 50th

Question 29

Between the raw scores of 400 and 600, there must be

A) 50% of the scores
B) 34% of the scores
C) 68% of the scores
D) 95% of the scores

Question 30

Assume a normal distribution of height scores, with a mean of 68" and a standard deviation of 3", then

A) 68% of the cases must fall between 65" and 71"
B) 50% of the cases must fall below 68"
C) 68% of the cases must fall at exactly 68"
D) a and b, but not c

Question 31

The higher a given point on the ordinate of the normal curve, then

A) the higher the frequency of scores below that point
B) the lower the frequency of scores below that point
C) the closer the point is to the abscissa
D) the higher the resulting raw score

Question 32

Under the normal curve, any percentile of less than 50 must correspond to a

A) negative z score
B) raw score of less than 50
C) z score of less than 1
D) z score of 0

Question 33

The 84th percentile corresponds with a raw score of

A) 250
B) 500
C) 600
D) 800

Question 34

A z score of + 1 corresponds with a raw score of

A) 200
B) 400
C) 500
D) 600

Question 35

Under the normal curve, the relationship between a specific z score and the percentage of cases falling between it and the mean

A) depends on the size of the standard deviation
B) depends on the value of the mean
C) depends on the value of the raw score
D) is a constant

Question 36

A raw score of 500 would translate into a z score of

A) -3
B) -1
C) -.01
D) 0

Question 37

The 50th percentile would yield a raw score of

A) 400
B) 450
C) 500
D) 568

Question 38

The larger the absolute value of the z score (regardless of its sign), then

A) the higher its equivalent raw score
B) the lower its equivalent raw score
C) the further it is from the mean
D) the closer its equivalent raw score must be to the mean

Question 39

A negative z score means that

A) the raw score is below the mean
B) the mean is below the raw score
C) the distribution is skewed left
D) none of these, since it is impossible to get a negative z score

Question 40

A raw score of 200 would translate into a z score of

A) -3
B) -1
C) +1
D) +2

Question 41

The percentage values on the z score table are only valid when

A) the z scores are positive
B) the raw score mean equals 50
C) the raw score mean is greater than 50
D) the distribution is normal

Question 42

The only time a z score can be negative is when

A) the raw score is higher than the mean
B) the raw score is lower than the mean
C) the standard deviation is negative
D) the standard deviation is equal to 0

Question 43

Whenever a given raw score coincides exactly with the mean, the resulting z score, regardless of the size of the standard deviation, must be
C) True or False: For the following, indicate T (True) or F (False)

A) equal to 0
B) positive
C) equal to 50
D) none of these, since in this case, the z score cannot be found
48

Question 44

When a given point under the normal curve is 1.54 standard deviation units above the mean, then

A) its percentile is 15.4
B) its percentile is 1.54
C) its z score is +1.54
D) both a and c, but not b

Question 45

Every distribution of z scores has a

A) mean of zero and a standard deviation of 1
B) mean of 50 and a standard deviation of 10
C) mean of 100 and a standard deviation of 15
D) none of these, since every distribution of z scores is different

Question 46

The fact that the normal distribution is asymptotic to the abscissa means that

A) its curve must be symmetrical
B) its curve must yield both positive and negative values
C) its curve may never touch the abscissa
D) its curve must always touch the abscissa

Question 47

Percentiles always indicate

A) the percentage of cases falling below a given point
B) the percentage of cases falling above a given point
C) the percentage of cases falling between a given z score and the mean
D) the percentage of cases falling above a given z score

Question 48

The numerical difference between the raw score and the mean, when divided by the standard deviation, yields the

A) normal curve
B) percentile
C) first moment of the curve
D) z score

Question 49

Between two negative z scores there must always be

A) fewer than 50% of the cases
B) more than 50% of the cases
C) exactly 50% of the cases
D) none of these, since 0% must always fall between negative z scores

Question 50

The 50th percentile would yield a z score of

A) -1
B) +500
C) above +1
D) 0

Question 51

The z score table always gives, as a direct read-out, the percentage of cases falling

A) between a given z score and the mean
B) below a negative z score
C) above a positive z score
D) none of these

Question 52

When the standard deviation of the raw score distribution is negative, the resulting z score must be

A) negative
B) equal to 0
C) positive
D) none of these, since the standard deviation can never be negative

Question 53

Anytime a z score yields a percentile which is greater than 50, then

A) the z score must be positive
B) the raw score must be higher than the mean
C) the z score must be greater than 0
D) all of these

Question 54

All percentiles of less than 50 must necessarily

A) fall below the raw score mean
B) yield negative z scores
C) fall to the left of the z score mean
D) all of these

Question 55

The z score for any raw score may be found by

A) subtracting the mean from the raw score and dividing by the standard deviation
B) subtracting the raw score from the mean and dividing by the standard deviation
C) subtracting the raw score from 100 and dividing by 15
D) none of these, since raw scores cannot be converted into z scores

Question 56

Over 50% of all the scores would fall above a raw score of

A) 568
B) 534
C) 501
D) 499

Question 57

A z score of +3 corresponds with a

A) percentile of 3
B) percentile of 53
C) percentile of 103
D) raw score which is 3 standard deviation units above the mean

Question 58

A positive z score must always yield a percentile which is

A) above 50
B) below 50
C) between 40 and 60
D) above 100

Question 59

For a z score of 1.35 the z score table indicates a percentage value of 41.15. This means that

A) 41.15% of the cases fell below a z score of +1.35
B) 41.15% of the cases fell above a z score of +1.35
C) 41.15% of the cases fell between z scores of +1.35
D) 41.15% of the cases fell between a z score of +1.35 and the mean

Question 60

The difference between z scores and standard scores is that

A) z scores can never be negative, whereas standard deviation scores always are
B) z scores can only be calculated with reference to the mean, whereas standard scores relate to the median
C) z scores can only be calculated with reference to the standard deviation, whereas standard scores relate to the variance
D) none of these, since z scores are standard scores

Question 61

Raw scores may never be converted into z scores unless the raw score mean is equal to 0.

Question 62

A negative z score always means that the raw score is less than the mean.

Question 63

A negative z score always yields a percentile of less than 50.

Question 64

A positive z score may only occur when the mean of the raw score distribution is greater than 50.

Question 65

Fewer than 50% of the cases may ever fall between two z scores of the same sign.

Question 66

Whenever the mean of a raw score distribution is less than 50, the z score must be negative.

Question 67

Between z scores of + 3 over 99% of the cases will be found.

Question 68

Regardless of the size of the raw score mean of standard deviation, a z score of +1 always means that the raw score is exactly one, full standard deviation unit about the mean.

Question 69

On a normal distribution the mean always lies to the right of the mode.

Question 70

Under the normal curve, the further to the right on the abscissa, the greater the number of cases.

Question 71

All percentiles above 50 must yield negative z scores.

Question 72

When any frequency distribution curve is symmetrical, it must, by definition, also be normal.

Question 73

A percentile of greater than 50 may only occur when the mean of the raw score distribution is greater than 50.

Question 74

A positive z score always results when the raw score is greater than the mean.

Question 75

The mean of the z score distribution must always equal 0.

Question 76

The standard score is synonymous with the raw score.

Question 77

The normal curve is mesokurtic.

Question 78

A frequency distribution curve may be symmetrical without being normal.

Question 79

There are more cases which fall above a z score of +2 than there are falling below it.

Question 80

The normal distribution curve is unimodal.