Deck 5: Z Scores, T Scores and Other Normal Curve Transformations

Question 1

If the standard deviation of a normal distribution were equal to 15 and someone had a raw score of 122, which fell at the 90th percentile, then the mean

A) must be greater than 122
B) must be less than 122
C) must be between 90 and 122
D) could not be found from the above information

Answer 1

B

Question 2

A percentile rank of 85 indicates that

A) 15% of the distribution is below it
B) 35% of the distribution is below it
C) 35% of the distribution is between it and the mean
D) it is below the mean

Answer 2

C

Question 3

When converting a z score into a raw score, anytime the z score is positive in sign

A) so too will be the raw score
B) so too will be the mean
C) the value of the raw score will be greater than the mean
D) none of these, since the conversion can only be made when z is negative

Answer 3

C

Question 4

Whenever the value of the standard deviation is positive, then

A) the z score must be positive
B) the percentile must be greater than 50
C) the raw score must be above the mean
D) none of these, since the standard deviation is always positive

Question 5

On a normal distribution, the value of the standard deviation can be found from a knowledge of the

A) mean, median and mode
B) mean, z score and raw score
C) z score, raw score and percentile
D) curve's kurtosis

Question 6

When converting a z score into a raw score, anytime the z score is negative in sign

A) so too will be the raw score
B) so too will be the mean
C) so too will be the standard deviation
D) the value of the raw score will be less than the mean

Question 7

A percentile rank of 45 indicates that

A) it is 5 percentage points below the mean
B) it is 45 percentage points below the mean
C) it is 95 percentage points below the mean
D) it is above the mean

Question 8

On a normal distribution, percentiles may be converted into raw scores

A) by first translating the percentile into a z score
B) by first translating the mean into a standard score
C) by first translating the percentile into its decile equivalent
D) all of these

Question 9

If someone were to score at the 84th percentile, the resulting z score would be approximately

A) .50
B) 1.00
C) .34
D) none of these, since a percentile never yields a z score

Question 10

Whenever the percentage values in the z score table indicate an absolute tie

A) use the higher of the two z scores
B) use the lower of the two z scores
C) use the z score which is closest to the mean
D) the z score cannot be used

Question 11

Whenever the value of the z score is positive, then

A) the percentile must be greater than 50
B) the raw score must be greater than the mean
C) neither of these, since the z score is always positive
D) both a and b, but not c

Question 12

A percentile rank of 95 indicates that

A) 95% of the distribution is above it
B) 47 and a half % of the distribution is above it
C) 95% of the distribution is below it
D) 47 and a half % of the distribution is below it

Question 13

Whenever the z score equation is used in order to calculate the mean, the mean must always be greater than the raw score

A) when the raw score has a percentile value of less than 50
B) when the raw score has a percentile value of greater than 50
C) when the raw score is negative
D) when the z score is positive

Question 14

Any percentile which is greater than 50 will convert into a raw score

A) which is greater than 50
B) which is to the left of the mean
C) which is greater than the mean
D) which is larger than the value of the percentile

Question 15

When converting percentiles into z scores, it is essential to know

A) the value of the mean
B) the value of the standard deviation
C) the value of the raw score
D) the percentage of cases falling between the given percentile and the mean

Question 16

All z scores falling to the left of the mean

A) must be given negative signs
B) must result in negative percentiles
C) must result in negative raw scores
D) none of these

Question 17

A z score of +3.00, means that

A) the raw score is exactly 3 standard deviation units above the mean
B) the raw score is exactly 3 percentage points above the mean
C) the raw score is exactly 3 raw score units above the mean
D) none of these

Question 18

If someone were to score at the 16th percentile, the resulting z score would be approximately

A) -.50
B) 1.00
C) -.34
D) none of these, since a percentile never yields a z score

Question 19

If the mean of a normal distribution were equal to 100, and a raw score of 99 was found to be at the 10th percentile, then

A) the standard deviation must be extremely small
B) the standard deviation must be extremely large
C) the standard deviation must be less than the z score
D) the standard deviation could not be calculated from this information

Question 20

A z score of -1.50 indicates that the raw score is

A) one and one-half percentage points below the mean
B) one and one-half standard deviation units below the mean
C) one and one-half raw score units below the mean
D) negative

Question 21

The range of the T score distribution always equals approximately

A) 50
B) 60
C) 30
D) the same value as the range of the raw score distribution

Question 22

A T score of 30 is equal to a z score of

A) -2
B) +2
C) +1
D) 0

Question 23

The value of the standard deviation of the T distribution is equal to

A) the standard deviation of z
B) the standard deviation of the raw score distribution
C) the standard deviation of the raw score distribution, divided by 10
D) 10

Question 24

A T score of 60 is exactly

A) one standard deviation unit above the mean
B) ten standard deviation units above the mean
C) ten standard deviation units below the mean
D) the same as a percentile rank of 60

Question 25

When a raw score translates into a negative z score, then the mean of the distribution

A) must be higher than the raw score
B) must be lower than the raw score
C) must fall above the 50th percentile
D) must fall below the 50th percentile

Question 26

A T score of 60 is equal to a z score of

A) 0
B) +2
C) +1
D) 50

Question 27

The T score distribution always assumes a

A) mean of 50 and an SD of 10
B) mean of 100 and an SD of 15
C) mean of 0 and an SD of 1
D) none of these

Question 28

When a raw score translates into a negative z score, the resulting percentile must be

A) negative
B) greater than 50
C) less than 50
D) none of these

Question 29

The z score distribution always assumes a

A) mean of 50 and an SD of 10
B) mean of 100 and an SD of 15
C) mean of 0 and an SD of 1
D) none of these

Question 30

The value of the mean of the T score distribution is always equal to

A) the value of the raw score mean
B) the value of the z score mean
C) the value of the standard deviation
D) 50

Question 31

When the standard deviation of the raw score distribution equals 10, then the mean of the raw score distribution must equal

A) 50
B) 100
C) 15
D) cannot tell from information given

Question 32

The percentile value for a given raw score must always be at least 50 or above whenever

A) the mean is greater than the raw score
B) the raw score is more than 1 percentage point away from the mean
C) the equivalent z score is greater than 50
D) the equivalent z score is positive

Question 33

The T score can only be used

A) when the mean of the raw score distribution equals 50
B) when the z score distribution is no longer normal
C) when the mean of the raw score distribution is 100
D) when the distribution is normal

Question 34

In a normal distribution, the mean falls above the 50th percentile only when

A) the z score is positive
B) the raw score is negative
C) the raw score is below the 50th percentile
D) none of these

Question 35

If the mean of the raw score distribution equals 68 with a standard deviation of 3, then a person with a raw score of 65 would have a T score of

A) 60
B) 50
C) 47
D) 40

Question 36

Whenever the z score equation is used in order to calculate the mean, the mean must always be less than the raw score

A) when the raw score has a percentile value of less than 50
B) when the raw score is positive
C) when the z score is negative
D) when the raw score has a percentile value of greater than 50

Question 37

The raw score distribution always assumes a

A) mean of 50 and an SD of 10
B) mean of 100 and an SD of 15
C) mean of 0 and an SD of 1
D) none of these

Question 38

When a raw score converts to a percentile of greater than 50, then the resulting T score must be

A) negative
B) equal to 10
C) equal to the z score
D) greater than 50

Question 39

A raw score which is at the 50th percentile translates into a T score of

A) 50
B) 10
C) 70
D) cannot tell from information given

Question 40

If the mean of the raw score distribution equals 120 with a standard deviation of 5, then a raw score of 130 would have a T score of

A) 55
B) 60
C) 70
D) 30

Question 41

If one knows the mean, the raw score and the z score, then the z score equation can be used to calculate the standard deviation.

Question 42

When T equals 50, then z must equal

A) 50
B) 10
C) 0
D) cannot tell from the above information

Question 43

If the T score equals 51, then the equivalent raw score

A) must be greater than 100
B) must be less than 100
C) must be greater than the raw score mean
D) must be greater than the T score mean

Question 44

On a T score distribution, 68% of the cases must fall between T scores of

A) 50 and 60
B) 0 and 10
C) 40 and 50
D) 40 and 60

Question 45

All T scores greater than 20 must coincide with percentiles which are greater than 50.

Question 46

Any raw score which has a percentile rank of 99, has a T score of at least

A) 10
B) 20
C) 80
D) 99

Question 47

When T=50, then z=0.

Question 48

A raw score which falls exactly at the second quartile, must convert to a T score of

A) 50
B) 100
C) 0
D) 10

Question 49

The standard deviation of the T score distribution is always equal to 10.

Question 50

When converting z to T, all positive z scores yield T scores

A) of greater than 50
B) of greater than 10
C) of greater than 0
D) none of these, since z cannot be converted to T

Question 51

When the value of T equals 40, the z score must be positive.

Question 52

All z scores greater than 0 must coincide with percentiles which are greater than 50.

Question 53

The standard deviation of the T distribution must always be greater than 50.

Question 54

When the value of the mean is less than the value of the raw score, then the raw score must convert to a T score of greater than 50.

Question 55

When T equals 50, then the raw score must equal

A) 50
B) 10
C) 0
D) cannot tell from the above information

Question 56

A raw score which falls exactly at the 5th decile, must convert to a T score of

A) 50
B) 100
C) 0
D) none of these

Question 57

A person with a T score of greater than 50, must have a negative z score.

Question 58

When the standard deviation of the raw score distribution is equal to less than 1.00, then

A) the standard deviation of the T distribution becomes less than 10
B) the standard deviation of the z distribution becomes less than 10
C) the standard deviation of the z distribution becomes less than 1
D) none of these

Question 59

The distribution of T scores is assumed to be

A) Gaussian
B) normal
C) mesokurtic
D) all of these

Question 60

If a distribution is normal, any percentile can be converted into its equivalent z score.

Question 61

With a mean of 100 and an SD of 20, what raw score would fall at the 27th percentile?

Question 62

When a given raw score value is less than the mean of the raw score distribution, its equivalent z score must be positive.

Question 63

With a mean of 105 and an SD of 6.30, what raw score falls at the 93rd percentile?

Question 64

The mean on a test is 90, with an SD of 20. What raw score would be equivalent to a percentile rank of 29?

Question 65

A z score of -1, indicates a point one standard deviation unit below the mean. 66 D: For the following questions, calculate the values. Assume a normal distribution in all questions.

Question 66

The mean is 100, with an SD of 15. What raw score would fall at the 11th percentile?

Question 67

Raw scores may never be converted into T scores unless the raw score distribution is normal.

Question 68

The mean on a test is 75 with an SD of 10. What is the raw score for a percentile rank of 80?

Question 69

The mean is 65, with an SD of 5.00. A raw score of 57 would fall at what percentile?

Question 70

The range of the T score distribution is approximately 10.

Question 71

The mean is 38.70 with an SD of 6.31. What score falls at the 11th percentile?

Question 72

The T score on a certain distribution is 28. The mean of the raw score distribution is 110, with an SD of 14.93. What is the value of the equivalent raw score?

Question 73

For a given raw score to be converted into a z score, one must know both the mean and standard deviation of the raw score distribution.

Question 74

If the mean of an IQ distribution equals 100, with a standard deviation of 15, then an IQ score of 85 is equivalent to a T score of 35.

Question 75

All T scores are positive in sign.

Question 76

With a mean of 100 and an SD of 20, what raw score would fall at the 75th percentile?

Question 77

When a T score is greater than 50, so too is its equivalent percentile.

Question 78

On the T score distribution the standard deviation always equals 10.

Question 79

On a test with a mean of 200 and an SD of 50, what raw score would fall at the 86th percentile?

Question 80

When the z score is negative, so too is the T score.