Ch5 – Normal Distributions And Standard (Z) + Test Bank Docx

MULTIPLE‑CHOICE TEST ITEMS

CHAPTER 5

NORMAL DISTRIBUTIONS AND STANDARD (z) SCORES

5.1 Many observed frequency distributions

a) coincide with the theoretical normal curve.

b) approximate the theoretical normal curve.

c) define the theoretical normal curve.

d) verify the theoretical normal curve.

5.2 The theoretical normal curve

a) ignores irregularities.

b) describes any observed frequency distribution.

c) defines those observations or behaviors that are normal.

d) all of the above

5.3 If the normal curve is used to describe the distribution of IQ scores for all currently enrolled students in U.S. colleges and universities, all students are identified with the

a) smooth normal curve.

b) total area under the normal curve.

c) maximum height of the normal curve.

d) horizontal axis.

5.4 It's most correct to view the normal curve as

a) a batch of observations.

b) a frequency distribution.

c) an observed frequency distribution.

d) a theoretical frequency distribution.

5.5 If a set of scores approximates a normal curve, scores having intermediate values will be

a) most prevalent.

b) least prevalent.

c) about as prevalent as scores having more extreme values.

d) none of the above

5.6 Since the normal curve never actually touches the horizontal axis,

a) most of the area is in its extremities.

b) the total area is infinitely large.

c) the normal tables are only approximate.

d) very extreme observations are possible.

5.7 The values of the mean, median, and mode for a normal curve are

a) usually the same.

b) always the same.

c) usually different.

d) always different.

5.8 If you have reason to believe that some frequency distribution approximates a normal curve,

a) use the normal curve.

b) use the normal curve if the observed frequency distribution consists of many observations.

c) use the normal curve if there aren't any minor irregularities in the observed frequency distribution.

d) use the normal curve if the observed frequency distribution is reasonably compact.

5.9 Use of the normal curve presumes that the data approximate a normal curve and that the mean and standard deviation

a) equal zero and one respectively.

b) each equals zero or some positive number.

c) are known.

d) all of the above

5.10 Any particular normal curve is transformed into a new normal curve whenever changes occur in

a) its mean.

b) its standard deviation.

c) both its mean and its standard deviation.

d) either its mean or its standard deviation.

5.11 NOTE: This question requires Greek letters. Since the normal curve is an idealized curve that is presumed to describe complete sets of observations or populations, the mean and standard deviation of the normal curve are represented by the symbols

a) and S, respectively.

b)and σ, respectively.

c) μ and S, respectively.

d) μ and σ, respectively.

5.12 Obvious differences in appearance among normal curves

a) are more apparent than real.

b) are not only real but very important.

c) cause difficulties in interpretation.

d) greatly complicate the use of the normal curve.

5.13 To calculate a z score,

a) divide by the standard deviation, then add the mean.

b) divide by the standard deviation, then subtract the mean.

c) add the mean, then divide by the standard deviation.

d) subtract the mean, then divide by the standard deviation.

5.14 A z score indicates

a) how many standard deviations an observation is above and below its mean.

b) the position of the corresponding original score relative to its mean and standard deviation.

c) both a and b

d) neither a nor b

5.15 The value of a z score could equal

a) some positive number.

b) some negative number.

c) zero.

d) all of the above

5.16 A negative z score signifies that the original score is

a) negative.

b) below the mean.

c) considerably below than the mean.

d) some small number.

5.17 On a reading comprehension test, it would be preferable to achieve a z score of

a) 2.34

b) ‑3.50

c) 0.00

d) 1.00

5.18 If the original distribution approximates a normal curve, the shift to z scores produces a new distribution that approximates

a) a new normal curve.

b) a new non‑normal curve.

c) a standard normal curve.

d) the original normal curve.

5.19 The standard normal curve retains

a) the units of measurement of the original normal distribution.

b) the mean and standard deviation of the original normal distribution.

c) the shape of the original normal distribution.

d) all of the above

5.20 The standard normal curve

a) appears in infinitely many different forms.

b) has a mean of 100 and a standard deviation of 7.

c) is unrelated to any other normal curve.

d) is the single normal curve for which tables are available.

5.21 The standard normal table consists of three columns, including column B, which indicates the

a) area between the mean and the z score.

b) area beyond the z score.

c) proportion of area between the mean and the z score.

d) proportion of area beyond the z score.

5.22 When working with the lower half of the normal curve, refer to ________________of the normal curve table.

a) the upper legend

b) the lower legend

c) column B

d) column C

5.23 For any z score, the corresponding proportions in columns B and C always sum to

a) 1.0000

b) 0.5000

c) 0.0000

d) the value of z.

5.24 The total area under the normal curve always equals

a) 1.0000

b) 0.5000

c) 0.0000

d) the value of z.

5.25 Proportions of area under the normal curve are

a) either positive or negative.

b) always negative.

c) always positive.

d) none of the above

5.26 When working normal curve problems, you should first decide whether

a) a proportion or score is to be found.

b) the upper or lower half of the curve is involved.

c) to use column B or column C.

d) a single answer or two answers are required.

5.27 When working normal curve problems,

a) memorize solutions to particular problems.

b) search for a formula.

c) concentrate on the logic of the solution.

d) all of the above

5.28 When working normal curve problems, the solution can be obtained in

a) only one way.

b) more than one way.

c) a very large number of ways.

d) an infinite number of ways.

5.29 The area to the left of a given score (along the base of a normal curve) represents the proportion of

a) negative scores.

b) positive scores.

c) smaller or lower scores.

d) larger or higher scores.

5.30 When solving normal curve problems that involve two z scores,

a) enter the tables twice, once for each z score.

b) subtract one z score from the other, then enter the table for the difference between z scores.

c) add one z score to the other, then enter the table for the sum of the two z scores.

d) do any of the above, depending on the logic of the problem.

5.31 When solving normal curve problems, you must attend closely to the wording of problems. Within 30 points of the mean translates into

a) two target areas, one in each tail of the normal curve.

b) two target areas, each sharing a common boundary at the mean, with one area extending above the mean and the other extending below the mean.

c) a single target area above the mean.

d) a single target area below the mean.

5.32 When finding scores, we use the normal curve table in the following fashion:

a) enter columns A or A' and read out the proportions from columns B, C, B', or C'.

b) enter columns A or A' and read out the z scores from columns B, C, B', or C'.

c) enter columns B, C, B', or C' and read out the proportions from columns A or A'.

d) enter columns B, C, B', or C' and read out the z scores from columns A or A'.

5.33 When finding scores, it's crucial that the target score be placed on the correct side of the mean. Otherwise,

a) the wrong sign might be assigned to the z score read from the tables.

b) the wrong value of z might be read from the tables.

c) the wrong value of z might be calculated.

d) all of the above

5.34 When finding the unknown score associated with the 80th percentile, we should locate the target proportion of

a) .8000 in column B.

b) .3000 in column B.

c) .8000 in column C.

d) .3000 in column C.

5.35 In many statistical applications, we wish to distinguish between _______________ events.

a) true and false

b) real and imaginary

c) controlled and uncontrolled

d) common and rare

5.36 Assume that the anxiety scores for college students approximate a normal distribution with a mean of 25 and a standard deviation of 7. To find the proportion of college students with anxiety scores of 40 or more, convert to a z score and consult

a) column B.

b) column C.

c) column B'.

d) column C or B', depending on the sign of z.

5.37 Assume that the anxiety scores for college students approximate a normal distribution with a mean of 25 and a standard deviation of 7. To find the proportion of college students with anxiety scores that deviate more than 10 points either above or below the mean, convert to z scores and consult

a) columns B and C.

b) columns B'and C'.

c) columns B and B'.

d) columns C and C'.

5.38 Assume that the anxiety scores for college students approximate a normal distribution with a mean of 25 and a standard deviation of 7. To find the proportion of college students with anxiety scores between 40 and 45 points, convert to z scores and after reading the appropriate entries from the standard normal table, subtract the

a) first entry from the second.

b) second entry from the first.

c) larger entry from the smaller.

d) smaller entry from the larger.

5.39 Assume that the anxiety scores for college students approximate a normal distribution with a mean of 25 and a standard deviation of 7. To find the anxiety score for a college student at the 90th percentile, first look in

a) column A for a z score of 0.90.

b) column A for a z score of .4000.

c) column B for the target proportion of .1000.

d) column B for the target proportion of .4000.

NOTE: 5.40 to 5.46 require access to the standard normal table.

5.40 Given that IQs are normally distributed with a mean of 100 and a standard deviation of 15, what proportion of IQs are below 110?

a) .25

b) .75

c) .50

d) none of the above

5.41 Given that IQs are normally distributed with a mean of 100 and a standard deviation of 15, what proportion of IQs are above 115?

a) .16

b) .34

c) .84

d) none of the above

5.42 Given that IQs are normally distributed with a mean of 100 and a standard deviation of 15, what proportion of IQs are above 95?

a) .13

b) .37

c) .63

d) none of the above

5.43 Given that IQs are normally distributed with a mean of 100 and a standard deviation of 15, what IQ corresponds to 5th percentile?

a) 70

b) 80

c) 90

d) none of the above

5.44 Given that IQs are normally distributed with a mean of 100 and a standard deviation of 15, what proportion of IQs fall between 130 and 145?

a) .02

b) .05

c) .08

d) none of the above

5.45 Given that IQs are normally distributed with a mean of 100 and a standard deviation of 15, what pair of IQs separate the middle 95 percent from the remainder of the distribution?

a) 71 and 129

b) 79 and 121

c) 68 and 132

d) none of the above

5.46 Given that IQs are normally distributed with a mean of 100 and a standard deviation of 15, what IQ score exceeds 99 percent of all IQ scores?

a) 125

b) 130

c) 135

d) none of the above

5.47 Distributions of z scores can be obtained from _____ distribution of original scores.

a) any

b) any normal

c) any standard normal

d) any symmetrical

5.48 If a positively skewed distribution of incomes is transformed into a distribution of z scores, the shape of the new distribution will be

a) normal.

b) positively skewed.

c) intermediate between normal and positively skewed.

d) standard normal.

5.49 The shift to z scores always produces a distribution with

a) a mean and standard deviation whose values depend on the original mean and standard deviation.

b) a mean of 0 and a standard deviation of 1.

c) a mean of 50 and a standard deviation of 7.

d) a mean of 500 and a standard deviation of 100.

5.50 If Kristen earned z scores of 2.50, 1.00, and -0.50 on her final exams in statistics, literature, and philosophy, respectively, she performed most poorly in

a) statistics.

b) literature.

c) philosophy.

d) one of these classes, but we need more information.

5.51 If Kristen earned z scores of 2.50, 1.00, and -0.50 on her final exams in statistics, literature, and philosophy, respectively, she performed above average -- that is, above the mean -- in

a) none of the above classes.

b) one of the above classes.

c) two of the above classes.

d) all three of the above classes.

5.52 Which of the following distributions would permit the most favorable interpretation of a raw score of 140 on a biology test?

a) mean of 100; standard deviation of 40

b) mean of 100; standard deviation of 20

c) mean of 120; standard deviation of 10

d) mean of 120; standard deviation of 5

5.53 Which of the following distributions would produce the least favorable interpretation of a raw score of 32 on a sociology exam?

a) mean of 40; standard deviation of 10

b) mean of 40; standard deviation of 4

c) mean of 36; standard deviation of 4

d) mean of 35; standard deviation of 3

5.54 Generally speaking, a standard score is any

a) original score.

b) z score.

c) score expressed relative to a known mean and standard deviation.

d) score expressed relative to some standard.

5.55 If you're told that you earned a z score of 1.50 on a social awareness test, this implies that you're about one and one‑half standard deviations

a) from the mean in a normal distribution of test scores.

b) from the mean in the distribution.

c) above the mean in a normal distribution of test scores.

d) above the mean in the distribution.

5.56 By far the most important standard score is a ____ score.

a) raw

b) z

c) T

d) IQ

5.57 For convenience, particularly when reporting test results, z scores can be transformed to other types of standard scores that lack

a) positive and negative values.

b) positively and negatively skewed shapes.

c) negative signs and decimal points.

d) very large and very small values.

5.58 Transformations from z scores to other types of standard scores

a) change the shape of the original distribution, but not the relative standing of any test score within the distribution.

b) change the relative standing of any test score within the original distribution, but not the shape of the distribution.

c) change both the shape of the original distribution and the relative standing of any test score within the distribution.

d) change neither the shape of the original distribution nor the relative standing of any test score within the distribution.

5.59 A test score located two standard deviations above the mean could be reported as a z score of 2.00. Or in a distribution of T scores with a mean of 50 and a standard deviation of 10, it could be reported as a T score of

a) 50

b) 52

c) 60

d) 70

5.60 A test score located one and one-third standard deviations below the mean could be reported as a z score of -1.33. Or in a distribution of transformed standard scores with a mean of 100 and a standard deviation of 15, it could be reported as a score of

a) 80

b) 85.7

c) 95.67

d) 120

5.61 Standard scores should be used only if

a) the distribution is normal.

b) the distribution is based on a large number of observations.

c) performance is being evaluated in terms of some absolute standard.

d) relative performance is being evaluated.

5.62 Although any desired mean and standard deviation could be used to generate a new distribution of transformed scores, values of the desired means and standard deviations are usually limited to pairs of

a) arbitrary numbers.

b) convenient numbers.

c) accurate numbers.

d) representative numbers.