Practice Questions for Business Statistics

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Chapter: Probability Distributions

Contents:

31-2 A probability function is a rule of correspondence

31-3 What is a synonym or example of a variable?

38-3 Define the following term

45-1 "Which of the following ""probability mass functions"" "

56-1 Find P(T <= 0)

63-1 The random numbers generator

119-2 Approximately how many A's were there

120-1 A standard normal distribution has

121-2 What proportion of samples would have 4800 cells

131-2 find K so that the probability that a sample value is

135-1 variance = 0.000052. What is the probability

136-3 "normal variable, then the area to the left "

137-1 What area under the standard normal curve falls outside

137-2 "and a variance of 9, what percent of the population"

138-1 then P(Z > -0.38) is

138-2 then P(XBAR > 15) is

139-1 Find the 33rd percentile of the distribution of lifetimes

141-1 A Z-Score is a

141-3 Z-scores provide information about the location of

142-1 standard deviation = 10. Her Z-score is

142-2 Charlie's raw score on the test is

143-1 below approximately what percent of the students taking the test

144-1 better than what percent of the persons taking the test

144-2 will have a standard deviation equal to

145-2 A score of 85 from this population has a Z-score

146-2 The Z-score corresponding to the 52nd percentile is

147-1 number of students scoring between 70 and 82 is

149-1 Pr(-.25 < Z) is

149-2 what score will be associated with a standard Z score of 1.5

150-1 Pr(Z <= 1.65 or Z > 3.0) is

150-2 Pr(Z > +1.96 or Z < -1.65) is

155-2 then P(69.5 <= X <= 75)

166-1 of cases are likely to be between 86 and 93 in a normal

166-2 percentile rank does a score of 42 fall

167-1 What score has a percentile rank of 33%

167-2 scores for the middle 50% of the data

168-1 What percentage of the scores are above 78?

168-2 has an X value equal to

169-2 In a frequency distribution with a median of 50

170-1 21% of the observations lie below it?

171-1 what is the percentage of scores likely to fall below 550?

172-2 and variance 4 will fall between -9 and -4?

173-1 The probability that a value between 7 and 9 is obtained is

176-1 The standard normal score Z is:

176-2 what percentage of his students will earn an A?

177-1 Rods are too long to be useable

177-2 "are too short, what is the cut off length between ""too"

185-1 how much time should we give them?

189-1 "600 yard run-walk represent a normal distribution, how"

190-1 the monthly food expenditures of families

193-2 guarantees the battery to last 30 months.

200-1 The average weekly food expenditure was $70.00

202-1 a floor manager of a large department store

206-2 a floor manager of a large department store is studying

207-1 A floor manager of a large department store is studying the buying

213-1 If 91% of the bike-commuters take longer to reach campus than you

213-2 P(-1 < X < 5) = _______________

529-2 Which of the following random variables are continuous

530-3 What is the principal distinction between a discrete

531-2 The number of individuals in a family is a continuous variable.

531-3 Variables in which measurement is always approximate because

532-2 A continuous variable:

743-1 The breaking strength of a cable is a discrete variable.

1776-4 "If each score is raised by 7 points, what percentage"

1859-3 "If the mean depth of a river is 2 feet, it would be safe "

1860-1 The mean number of children per family in LA is quoted as 2.2.

2035-1 What percent of the area of a distribution lies between the first and

2054-1 The 70th percentile of the distribution of a random variable X

2054-2 Not more than 10% of a set of measurements can be above the 95th

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Questions:

31-2

    Q:  A probability function is a rule of correspondence or equation that:

        a)  Finds the mean value of the random variable.
        b)  Assigns values of x to the events of a probability experiment.
        c)  Assigns probablities to the various values of x.
        d)  Defines the variability in the experiment.
        e)  None of the above is correct.

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31-3

    Q:  What is a synonym or example of a variable?

        a)  constant
        b)  characteristic which takes on different values
        c)  number of ears on humans
        d)  parameter

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38-3

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.
        Constant

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45-1

    Q:  A sample space consists of the following elementary events:

          - the traffic-light is red
          - the traffic-light is orange
          - the traffic-light is green

        Upon this a random variable X is defined as follows:

             red = 1
          orange = 2
           green = 3

        Which of the following "probability mass functions" of the discrete
        random variable X is absolutely wrong?

        a.        5/6 |                      b.        5/6 |
                      |                                    |
                  4/6 |                                4/6 |  *     *
            p(X)      |                          p(X)      |  *     *
                  3/6 |                                3/6 |  *     *
                      |                                    |  *     *
                  2/6 |  *  *  *                       2/6 |  *     *
                      |  *  *  *                           |  *     *
                  1/6 |  *  *  *                       1/6 |  *  *  *
                      |  *  *  *                           |  *  *  *
                      ---+--+--+------> X                  ---+--+--+------>  X
                         1  2  3                              1  2  3

        c.        5/7 |                      d.        5/7 |        *
                      |                                    |        *
                  4/7 |                                4/7 |        *
            p(X)      |                          p(X)      |        *
                  3/7 |  *     *                       3/7 |        *
                      |  *     *                           |        *
                  2/7 |  *     *                       2/7 |        *
                      |  *     *                           |        *
                  1/7 |  *  *  *                       1/7 |  *  *  *
                      |  *  *  *                           |  *  *  *
                      ---+--+--+------>  X                 ---+--+--+------>  X
                         1  2  3                              1  2  3

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56-1

    Q:  Suppose that the random variable T has the following probability
        distribution:

            t    |   0   1   2
        ----------------------
        P(T = t) |  .5  .3  .2

        a.  Find P(T <= 0)
        b.  Find P(T >= 0 and T < 2)
        c.  Compute E(T), the mean of the random variable T.

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63-1

    Q:  The random numbers generator of a computer produces values that are
        uniformly distributed from zero to one.  A programmer doesn't want
        his program to print the same message everytime that a user reaches
        a certain point in the program.  He wants the program to print:

                Hooray]         20% of the time,
                Yep.            40% of the time,
                Bullseye]        5% of the time, and
                Fantastic]      35% of the time.

        He can do this by including in the program an instruction that
        tells the program to do different things depending on the random
        number generated.

        a.  Sketch the distribution of random numbers and indicate areas and
            boundary values so that the 4 comments will appear as desired.

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119-2

    Q:  One hundred students took a test on which the mean score was 73
        with a variance of 64.  A grade of A was given to all who
        scored 85 or better.  Approximately how many A's were there, assuming
        scores were normally distributed?  (Choose the closest.)

        1.  42
        2.  7
        3.  58
        4.  5
        5.  22

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120-1

    Q:  A standard normal distribution has:

        a.  the mean equal to the variance
        b.  mean equal 1 and variance equal 1
        c.  mean equal 0 and variance equal 1
        d.  mean equal 0 and standard deviation equal 0
        e.  none of these

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121-2

    Q:  Use the model that the number of cells in a sample of kidney tissue
        is normally distributed with a mean of 4200 and a standard deviation
        of 300 to answer the following questions:

        (a)  What proportion of samples would have 4800 cells or more?
        (b)  What proportion of samples would have from 3700 to 4400 cells?

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131-2

    Q:  If a normal distribution has mean 200 and standard deviation 20, find
        K so that the probability that a sample value is less than K is .975.

        a.  239      b.  204      c.  210      d.  215      e.  220
        E. 220    F. 230    G. 239    H. 250

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135-1

    Q:  The thickness of the individual cards produced by a certain
        playing card manufacturer is normally distributed with mean =
        0.01 inches and variance = 0.000052.  What is the probability
        that a deck of 52 cards is more than 0.65 inches in thickness?

        A.  .001      B.  .006      C.  .023      D.  .036
        E.  .067      F.  .087      G.  .159      H.  .184

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136-3

    Q:  If Z is a standard normal variable, then the area to the left of
        Z = 0.65 is:

        a.  0.35        d.  0.2578
        b.  0.2242      e.  0.7422
        c.  0.65

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137-1

    Q:  What area under the standard normal curve falls outside the Z values
        -2.5 and 2.5?

        a.  .0062      b.  .9876      c.  .0124      d.  .4938      e.  .5062

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137-2

    Q:  If the life of wild pheasants follows a normal distribution with a
        mean of 9 months and a variance of 9, what percent of the population
        will be less than 11 months of age?
            (Note that MU = 9 and SIGMA(X)**2 = 9.)

        (a)  34.13                 (c)  74.86
        (b)  84.13                 (d)  62.93

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138-1

    Q:  If Z is the standard normal random variable, then P(Z > -0.38) is

        (a)  .1480              (c)  .3520
        (b)  .2960              (d)  .6480

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138-2

    Q:  If XBAR is the mean of a sample from a normal distribution with MU = 10,
        SIGMA(X)**2 = 25 and n = 9, then P(XBAR > 15) is:

        (a)  .001350              (c)  .98778
        (b)  .998650              (d)  .15866

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139-1

    Q:  The distribution of lifetimes for a certain type of light
        bulb is normally distributed with a mean of 1000 hours and a
        standard deviation of 100 hours.  Find the 33rd percentile of
        the distribution of lifetimes.

        a.  560
        b.  330
        c.  1044
        d.  1440
        e.  none of these

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141-1

    Q:  A Z-Score is a

        a.  raw score with a mean of zero;
        b.  raw score with a mean of 50;
        c.  standard score with a mean of zero;
        d.  standard score with a mean of 50.

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141-3

    Q:  Z-scores provide information about the location of raw scores

        a.  below the mean in units of the range of the distribution;
        b.  above the mean in units of the standard deviation of the
                distribution;
        c.  above and below the mean in units of the range of the
                distribution;
        d.  above and below the mean in standard deviation units from
                the mean.

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142-1

    Q:  Mary has a raw score of 40 in a distribution of scores with mean =
        30, range = 60, and standard deviation = 10.  Her Z-score is:

        a)  -1.00        d)  +1.00
        b)  -0.67        e)  +10.00
        c)  +0.67

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142-2

    Q:  Charlie's Z-score is 1.15 on a classroom examination.  The mean
        score for the class is 50, the range is 25, and the standard de-
       viation is 10.  Charlie's raw score on the test is:

        a)  11.15        c)  61.50
        b)  51.15        d)  77.75

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143-1

    Q:  A person with a Z-Score of -2.00 has performed below approximately
        what percent of the students taking the test?

        a)   2 percent        d)  84 percent
        b)  15 percent        e)  97 percent
        c)  50 percent

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144-1

    Q:  Suppose you were told that scores on an examination were converted
        to standard scores with a mean = 500, range of 800, and a standard
        deviation of 100.  A person with a score of 600 has performed bet-
        ter than what percent of the persons taking the test?

        a)  20 percent        d)  84 percent
        b)  50 percent        e)  97.5 percent
        c)  57 percent

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144-2

    Q:  If each of a set of raw scores is transformed into a Z-score, the new
        distribution will have a standard deviation equal to

        a.  zero.
        b.  one.
        c.  the mean of the original distribution.
        d.  the standard deviation of the original distribution.
        e.  a variable, depending upon the shape and spread of the original
            distribution.

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145-2

    Q:  In a population there are 60 scores; the distribution has a mean of
        45 and a standard deviation of 25.  A score of 85 from this population:

        a.  has a Z-score of 1.60.
        b.  has a Z-score of 1.00.
        c.  has a Z-score of -1.00.
        d.  it is impossible to compute Z without additional
            information
        e.  none of the above

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146-2

    Q:  The Z-score corresponding to the 52nd percentile is:
        a.  2.06
        b.  2.05
        c.  1.99
        d.  0.48
        e.  0.05

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147-1

    Q:  Assume that the test scores of 600 students are normally distri-
        buted with a mean of 76 and a standard deviation of 8.  The number
        of students scoring between 70 and 82 is:

        a.  328
        b.  164
        c.  260
        d.  136
        e.  272

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149-1

    Q:  Pr(-.25 < Z) is

        a.  greater than .5000
        b.  less than .5000
        c.  equal to .5000
        d.  not possible to determine without more information.

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149-2

    Q:  Given that a distribution has a mean of 32 and a standard deviation of
        4, what score will be associated with a standard Z score of 1.5?

        a)  26
        b)  32
        c)  38
        d)  40

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150-1

    Q:  Pr(Z <= 1.65 or Z > 3.0) is

        1)  0.0508
        2)  0.9518
        3)  0.9482
        4)  0.0482
        5)  None of the above

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150-2

    Q:  Pr(Z > +1.96 or Z < -1.65) is

        1)  0.025
        2)  0.05
        3)  0.0745
        4)  0.0495
        5)  None of the above

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155-2

    Q:  The height of male college freshmen has a normal distribution with
        mean 71 inches and standard deviation 3 inches.  If X is the height
        of a male college freshman selected at random, then P(69.5 <= X <=
        75) =

        a.  .5997
        b.  .6915
        c.  .2167
        d.  .9082
        e.  none of these

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166-1

    Q:  What percent of cases are likely to be between 86 and 93 in a normal
        distribution with mean 87 and variance 4?

             a.  30.85%                     d.  69.02%
             b.  30.72%                     e.  none of these
             c.  49.87%

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166-2

    Q:  In a normal distribution with mean 30 and variance 25, at what
        percentile rank does a score of 42 fall?

        a.    .82%
        b.  49.18%
        c.  50.82%
        d.  99.18%
        e.  none of these

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167-1

    Q:  Suppose a set of data has a normal distribution with mean 43 and
        variance 9. What score has a percentile rank of 33%?

             a.  44.32                 d.  41.68
             b.  39.04                 e.  none of these
             c.  41.47

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167-2

    Q:  In a normal distribution with mean 3 and variance 49, what are the
        upper and lower limit scores for the middle 50% of the data?

        a.  -29.83 and 35.83
        b.   -1.31 and  7.69
        c.   -1.69 and  7.69
        d.    3.00 and 24.00
        e.  none of these

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168-1

    Q:  Consider a normal distribution with a mean of 86 and a standard
        deviation of 16.  What percentage of the scores are above 78?

        a.  69.15%
        b.   2.28%
        c.  97.72%
        d.  77.34%
 e.  none of these

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168-2

    Q:  The 67th percentile of a normal distribution with mean 6 and variance
        9 has an X value equal to:

        a.  12.66          d.  8.22
        b.   6.75          e.  none of these
        c.   8.24

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169-2

    Q:  In a frequency distribution with a median of 50 and a standard
        deviation of 4, what score corresponds to a standard score of 1.0?

        a.  12.5      d.  cannot be determined without additional information
        b.  54        e.  none of the above is true
        c.  46

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170-1

    Q:  A normal distribution has mean 10 and variance 100.  What is the number
        such that 21% of the observations lie below it?

        a.  11.9            d.  9.193
        b.   1.9            e.  none of these
        c.   4.4

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171-1

    Q:  If certain scores are distributed normally with mean 500 and variance
        625, what is the percentage of scores likely to fall below 550?

        (1)  97.72%        (4)  65.54%
        (2)  84.13%        (5)  none of these
        (3)  47.72%

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172-2

    Q:  What proportion of cases in a normal distribution with mean -7
        and variance 4 will fall between -9 and -4?

             a.  .9759                 d.  .7745
             b.  .4649                 e.  none of these
             c.  .5919

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173-1

    Q:  A normally distributed variable has a mean of 10 and a standard devia-
        tion of 2.  The probability that a value between 7 and 9 is obtained is:

        a.  .6247                d.  .0668
        b.  .3085                e.  none of these
        c.  .2417

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176-1

    Q:  The standard normal score Z is:

        a)  Normally distributed with a mean of zero and with a
            standard deviation of one.
        b)  Calculated by the formula Z = [X - MU]/[SIGMA].
        c)  Used to find the probabilities associated with any
            normal distribution.
        d)  All of the above are correct.
        e)  None of the above are correct.

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176-2

    Q:  A physical education instructor told his class that they  could  earn
        an A for the triple-jump if they could jump further than 24 feet.  If
        the distances jumped by students are normally distributed with a mean
        of 22 feet and a standard deviation of 3 feet, what percentage of his
        students will earn an A?

        a)  0.0228      b)  0.2486      c)  0.2514      d)  0.4772
        e)  None of the above are correct.

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177-1

    Q:  Rods produced by G&R Company are normally distributed with a mean of 66
        cm. and a standard deviation of 2 cm.  Rods are too long  to be useable
        if they are longer than 68.5 cm.  What percentage of these rods are too
        long?

        a)  0.1056      b)  0.1151      c)  0.3849      d)  0.3944
        e)  None of the above are correct.

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177-2

    Q:  Rods produced by G&R Company are normally distributed with a mean  of
        66  cm.  and a standard deviation of 2 cm.  If the shortest 4 percent
        are too short, what is the cut off length  between  "too  short"  and
        "acceptable length"?

        a)  62.5      b)  63.36      c)  64.25      d)  65.96
        e)  None of the above are correct.

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185-1

    Q:  The average time students need to finish a particular test is 70 minutes
        with a standard deviation of 12 minutes.  (Assume that these times are
        normally distributed.)  If we want 90% of the students to have suffi-
        cient time to finish the test, how much time should we give them?
        a.  54.64 minutes
        b.  85.36 minutes
        c.  136.48 minutes
        d.  254.32 minutes

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189-1

    Q:  If the times recorded for a group of 150 high school students measured
        on the 600 yard run-walk represent a normal distribution, how would you
        answer the following:

        Given:  XBAR = 2 minutes      SIGMA = 12 seconds      n = 150

        a.  time for the best student?
        b.  time for the worst student?
        c.  number of students worse than 2 minutes, 15 seconds?
        d.  number of students better than 1 minute, 42 seconds?
        e.  what is the mode?
        f.  what is the median?

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190-1

    Q:  Assuming  that the monthly food expenditures of families of a certain
        size in one economic group  are  approximately  normally  distributed
        with a mean of $130 and a standard deviation of $20:

        a.  What proportion of the expenditures are less than $90?

        b.  What percentage of the expenditures are between $100 and $120?

        c.  What percentage of the expenditures are either less than $120
            or more than $150?

        d.  Above what value does the top 14 percent of the expenditures
            lie?

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193-2

    Q:  Suppose the length of life of certain kinds of batteries is normally
        distributed with MU = 36 months, SIGMA = 4 months.  The company guar-
        antees the battery to last 30 months.  What proportion of the batter-
        ies will they have to make an adjustment on?

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200-1

    Q:  The U.S. Department of Commerce has just completed a sample survey of
        weekly food expenditures.  A simple random sample of 100 families was
        taken.  The average weekly food expenditure was $70.00 per week, with
        a standard deviation of $8.00.  You may assume expenditures in the
        population to be normally distributed.

        a.  What proportion of the families spent $85.00 or more per week
            on food?  Be sure to diagram your problem solution]

        b.  Using the information above, find the expenditure value above
            which 80% of the families lie.

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202-1

    Q:  Suppose a floor manager of a large department store is
        studying buying habits of their customers.

        a)  If he is willing to assume that monthly income of these customers
            is distributed normally, what proportion of the income should he
            expect to fall in the interval determined by MU +/- 1.2(SIGMA)?

        b)  What proportion of the income should he expect to be greater
            than MU + SIGMA?

        c)  Still assuming normality, what is the probability that a
            customer selected at random will have an income exceeding the
            population mean by 3*SIGMA?

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206-2

    Q:  Suppose a floor manager of a large department store is studying
        the buying habits of the store's customers.

        a)  If he is willing to assume that monthly income of these
            customers is distributed normally and SIGMA = $500, find
            the proportion of customers exceeding the population mean
            by $375.

        b)  Find the proportion of customers within $125 of the
            population mean.

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207-1

    Q:  A floor manager of a large department store is studying the buying
        habits of the store's customers.  Suppose the manager has  someone
        tell him that monthly income of these customers is distributed nor-
        mally with a population mean of $600 and standard deviation of $500.

        a)  What proportion of the customers should he expect to have
            incomes less than $600?

        b)  What proportion should he expect to have incomes less
            than $725?

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213-1

    Q:  Assume that commuting time via bicycle to the campus is a normal
        random variable with mean MU = 8 minutes and standard deviation
        SIGMA = 2 minutes.

        If 91% of the bike-commuters take longer to reach campus than you
        do, then your commuting time is approximately:

        (a)  5.32            (d)  10.68
        (b)  5.71            (e)  4.88
        (c)  7.54

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213-2

    Q:  If X is a random variable from a normal distribution with mean = 2.0
        and variance = 4.0 then P(-1 < X < 5) = _______________.

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529-2

    Q:  Which of the following random variables are continuous and which
        are discrete?

                a.  IQ
                b.  number of kittens in a litter
                c.  number of responses made by a rat in a bar-pressing
                        situation
                d.  the rate of bar pressing (responses/time)

        1.  a, b  continuous;  c, d  discrete
        2.  a, c, d  continuous;  b  discrete
        3.  d  continuous;  a, b, c  discrete
       4.  a  continuous;  b, c, d  discrete
        5.  none of these.

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530-3

    Q:  What is the principal distinction between a discrete and continuous
        random variable?  Give an example of each.

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531-2

    Q:  True or False?  If False, correct it.

        The number of individuals in a family is a continuous variable.

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531-3

    Q:  Variables in which measurement is always approximate because they
        permit an unlimited number of intermediate values are:

             a.  nominal.
             b.  discrete.
             c.  ordinal.
             d.  continuous.
             e.  interval.

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532-2

    Q:  A continuous variable:

        a)  may take on only integer values (e.g. 0, 1, 2, ...).
        b)  may take on only a finite number of different values.
        c)  may take on an infinite number of values.
        d)  must be any nonnegative real number.

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743-1

    Q:  True or False?  If False, correct it.

        The breaking strength of a cable is a discrete variable.

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1776-4

    Q:  Consider a normal distribution with MU = 67 and SIGMA**2 = 144.
        If each score is raised by 7 points, what percentage of the new
        scores is less than 74?

        a.  72%
        b.  88%
        c.  50%
        d.  52%
        e.  none of these

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1859-3

    Q:  True or False?

        If the mean depth of a river is 2 feet, it would be safe for a non-
        swimmer to wade across.

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1860-1

    Q:  True or False?

        The mean number of children per family in LA is quoted as 2.2.
        Since very few families have 2/10 of a child, this figure must
        be wrong.

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2035-1

    Q:  What percent of the area of a distribution lies between the first and
        third quartiles?

        a.  25
        b.  50
        c.  68
        d.  75
        e.  The question can't be answered without knowledge of the specific
            distribution.

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2054-1

    Q:  True or False?  If False, correct it.

        The 70th percentile of the distribution of a random variable X is an
        x-value which is exceeded by 70% of the population of X.

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2054-2

    Q:  True or False?  If False, correct it.

        Not more than 10% of a set of measurements can be above the 95th
        percentile.

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Answers:

31-2

    A:  c)  Assigns probabilities to the various values of x.

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31-3

    A:  b)  characteristic which takes on different values

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38-3

    A:  Definition:  A characteristic or measurement that only takes one
                     unchanging value.
        Example:     Suppose that we accurately record the amount of change
                     carried by each person attending a class on a particular
                     day.  The mean for that population is a constant, say,
                     53 cents.  It has one value which will not change.  (On the
                     other hand, if we consider drawing a random sample of 5
                     from the class and calculating a sample mean, we are
                     dealing with a random variable.  If we draw one sample
                     it will have one mean, say, 82 cents.  If we draw another
                     sample, it almost always will have another mean, say,
                     45 cents, etc.)

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45-1

    A:  b.  Because here the sum of the probabilities is greater than 1.

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56-1

    A:  a.  P(T <= 0) = .5

        b.  P(T >= 0 and T < 2) = P(T = 0 or T = 1)
                                = P(T = 0) + P(T = 1)
                                = .5 + .3
                                = .8

        c.  E(T) = SUM(t * P(T = t))
                 = (0*.5) + (1*.3) + (2*.2)
                 = 0.7

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63-1

    A:  This question can have many correct answers.  One of them follows.
	
                          ---------------------
                   |      |   |       ||      |
        REL.       |      |   |       ||      |
        FREQ.      |      |   |       ||      |
                   |      |   |       ||      |
                   ---------------------------------
                          0   .2     .6 .65   1   VALUES OF RANDOM NUMBER

        If the random number is between

        0 and .2       print Hooray]
        .2+ and .6     print Yep.
        .6+ and .65    print Bullseye]
        .65+ and 1     print Fantastic]

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119-2

    A:  2.  7

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120-1

    A:  c.  mean equal 0 and variance equal 1.

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121-2

    A:  (a)  .0228

                      Z = (4800 - 4200)/300 = 2.00
             Area for Z = 2.00 is .4772.

             Therefore, the desired area is .5000 - .4772 = .0228.

        (b)  .7011

             Z(1) = (3700 - 4200)/300 = -1.67
             Z(2) = (4400 - 4200)/300 = 0.67

             Prob(-1.67 < Z <= 0) = 0.4525
             Prob(0 < Z < 0.67) = 0.2486

             Therefore, the desired area is 0.4525 + 0.2486 = .7011.

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131-2

    A:  a.  239

            (K - 200)/20 = 1.96
            Therefore, K = 239

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135-1

    A:  B.  .006

        MU (deck) = 52 * .01 = .52
        Var(deck) = 52 * .000052 = .002704

        Z = (.65 - .52)/SQRT(.002704) = .13/.052
          = 2.5

        P(Z > 2.5) = .0062

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136-3

    A:  e.  0.7422

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137-1

    A:  c.  .0124

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137-2

    A:  (c)  74.86

                      Z = (11 - 9)/3 = .67
             P(Z < .67) = (.2486) + (.5000)
                        = .7486
                        = 74.86%

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138-1

    A:  (d)  .6480

             From the table of cumulative normal distribution, the area under
             the curve to the right of Z = -0.38 is .6480.

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138-2

    A:  (a)  .001350

             P(XBAR > 15) = P(Z > (15 - 10)/(5/3)) = P(Z > 3)
                          = .001350

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139-1

    A:  e.  none of these
               P(z<=?) = .33
                     z = -.44
                  -.44 = (x-1000)/(100)
                   x = -44 + 1000
                       = 956

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141-1

    A:  c.  standard score with a mean of zero.

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141-3

    A:  d.  above and below the mean in standard deviation units from
                the mean.

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142-1

    A:  d)  +1.00

            Z = (X - MU)/Standard Deviation
              = (40 - 30)/10 = 1

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142-2

    A:  c)  61.50

               Z = (X - MU)/Standard Deviation
            1.15 = (X - 50)/10
               X = 61.50

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143-1

    A:  e)  97 percent

                            Z = -2
            Area to left of Z = .0228
                   Total area = 1

            Percentage of people above that person = 1 - .0288
                                                   = .9712*100
                                                   = 97.12 percent

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144-1

    A:  d)  84 percent

            Z = (X - MU)/Standard Deviation
            Z = (600 - 500)/100 = 1

            Area between Z and Mean = .3413
                  Area to Left of Z = .5 + .3413 = .8413

            Percentile Rank = 100*.8413 = 84.13

            Therefore, the person has performed better than 84 percent of
            the people.

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144-2

    A:  b.  one.

            Z-score = (X - MU)/SIGMA
             VAR(Z) = 1.0

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145-2

    A:  a.  has a Z-score of 1.60.

            Z-score = (X - MU)/SIGMA
                    = (85 - 45)/25 = 1.60

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146-2

    A:  (e)

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147-1

    A:  a.  328

                     Z = (X - MU)/SIGMA
        Z-Score for 70 = (70-76)/8 = -.75
        Z-Score for 82 = (82-76)/8 = .75

        The area between -.75 and .75 = .2734 + .2734 = .5468

        Number of students = 600*.5468 = 328

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149-1

    A:  a.  greater than .5000.

            Pr(-.25 < Z) = .5000 + .0987 = .5987.

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149-2

    A:  c)  38

              Z = (X - MU)/SIGMA
            1.5 = (X - 32)/4
              X = 32 + 1.5*4 = 32 + 6 = 38

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150-1

    A:  (2)  0.9518

             P(Z <= 1.65 or Z > 3.0) = P(Z <= 1.65) + P(Z > 3.0)
                                     = .9505 + .0013 = .9518

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150-2

    A:  (3)  0.0745
        Pr(Z > +1.96 or Z < -1.65) = P(Z > 1.96) + P(Z < -1.65)
                                   = .0251 + .0494 = .0745

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155-2

    A:  a.  .5997

        Z(1) = (69.5 - 71)/3 = -.5
        Z(2) = (75   - 71)/3 = 1.33

        P(69.5 <= X <= 75) = P(-.5 <= Z <= 1.33)
                           = .1915 + .4082 = .5997

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166-1

    A:  d.  69.02%

        Mean = 87
        Variance = 4
        SIGMA = 2

        Z = (X - MU)/SIGMA
        Z to the left of mean = (86 - 87)/2 = -1/2 = -.5
        Z to the right of mean = (93 - 87)/2 = 6/2 = +3

        Area between Z values of -.5 to +3 = .1915 + .4987 = .6902.
        Percentage of cases between 86 and 93 = 69.02%

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166-2

    A:  d.  99.18%

            Mean = 30      Variance = 25      SIGMA = 5
            Z = (X - MU)/SIGMA = (42 - 30)/5 = 2.4
            Area to the right of Z = 2.4 is .0082.

            Percentile rank = 100 - (.0082*100)
         = 99.18%

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167-1

    A:  d.  41.68

        Z value corresponding to .33 = -.44
        Z = (X - MU)/SIGMA = (X - 43)/3
        (-.44) * 3 = X - 43
        X = 43 - 1.32 = 41.68

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167-2

    A:  c.  -1.69 and 7.69

            Mean = 3,    Variance = 49,    SIGMA = 7

            We want the limits for the middle 50% of the data, i.e. from
            the 25th percentile to the 75th percentile.

            Z value on left of mean corresponding to 25th percentile   = -.67
            Z value on right of mean corresponding to 25th percentile  =  .67

                Z = (X - MU)/SIGMA
             -.67 = (X - 3)/7
            -4.69 = X - 3

            X(lower limit) = -1.69
            Similarly, X(upper limit) =  3 + 4.69 = 7.69

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168-1

    A:  a.  69.15%

            Mean = 86      SIGMA = 16      X = 78

            Z = (X - MU)/SIGMA = (78 - 86)/16 = -8/16 = -.5

            Area to the right of Z value of -.5 = .1915 + .5 = .6915
            Percentage of scores above 78 = 69.15%.

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168-2

    A:  e.  none of these

            Area for 67th percentile = .17 (between Z and mean)
            Z value corresponding to .17 = .44

            Z = (X - MU)/SIGMA = (X - 6)/3
            X = (.44 * 3) + 6 = 7.32

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169-2

    A:  d.  cannot be determined without additional information

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170-1

    A:  b.  1.9

            Z = (X - MU)/SIGMA

            An area corresponding to the 21st percentile is the same as an
            area = .29 between X and the mean.

            Z value corresponding to this area = -.81

            -.81 = (X - MU)/SIGMA
                 = (X - 10)/10
            -8.1 = X - 10
               X = 1.9

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171-1

    A:  (1)  97.72%

                Mean = 500
            Variance = 625
               SIGMA = 25

             Z = (X - MU)/SIGMA = (550 - 500)/25 = 2

             Area beyond Z value of 2 = .0228 or 2.28%
             2.28% of scores fall above 550

             Percentage of scores falling below 550 = 100% - 2.28% = 97.72%

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172-2

    A:  d.  .7745

        Z value for an observation of -9 = (X - MU)/SIGMA
                                         = (-9 - (-7))/2 = -1
        Z value for an observation of -4 = (-4 - (-7))/2 = 1.5

        Area between Z values of -1 to 1.5 = .3413 + .4332 = .7745

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173-1

    A:  c.  .2417

            Z value associated with 9 = (X - MU)/SIGMA
                                      = (9 - 10)/2
                                      = -.5

            Z value associated with 7 = (7 - 10)/2
                                      = -1.5

            Area between Z values of -1.5 and -.5 = .4332-.1915 = .2417

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176-1

    A:  d)  All of the above are correct.

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176-2

    A:  c)  0.2514

            Z = [X - MU]/[SIGMA]
              = [24 - 22]/[3]
              = .666

            Prob.(Z>.666) = .2514

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177-1

    A:  a)  0.1056

            Z = [X - MU]/[SIGMA]
              = [68.5 - 66]/[2]
              = 1.25

            Prob.(Z>1.25) = .1056

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177-2

    A:  a)  62.5

            Prob.(Z= 46) = p(Z >= [46-40]/[8])
                       = p(Z >= .75)
                       = .2266

            Expected frequency E(f) = N * p
                                    = (10,000) * (.2266)
                                    = 2266

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185-1

    A:  b.  85.36 minutes
            The upper 10% of the students (needing the most time) correspond
            to a Z-score in a standard normal distribution of 1.28
            1.28 = [X-70]/[12]  implies X = 85.36

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189-1

    A:  a.  Using the empirical rule, the expected Z score for the fastest
            runner would be near -3, which converts to an approximate time of
            84 seconds.

            ((120 - 3*12) = 120 - 36 = 84)

        b.  Again using the empirical rule, the expected Z score for the
            slowest runner would be near +3, which converts to an approximate
            time of 156 seconds.

            ((120 + 12*3) = 156)

        c.  Z = 135 - 120/12 = 1.25
            Area to the right of Z = 1.25 is .1056
            .1056 * 150 = 16 students

        d.  (102 - 120)/12 = -1.5
            Area to the left of Z = -1.5 is .0668
            .0668 * 150 = 10 students

        e.  two minutes

        f.  two minutes

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190-1

    A:  a.           Z = (90 - 130)/20 = -2
            percentage = .5 - .4772 = 2.28 percent

        b.           Z = (100 - 130)/20 = -1.5
                     Z = (120 - 130)/20 = - .5
            percentage = .4332 - .1915  = 24.17 percent

        c.      Z(120) = -.5   percentage = .5 - .1915 = 30.85 percent
                Z(150) = 1.0   percentage = .5 - .3413 = 15.87 percent

            total percentage = 46.72 percent

        d.  .5 - .14 = .36      Z = 1.08

            1.08 = (value - 130)/20    value = $151.60

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193-2

    A:  P(X < 30) = P(Z < (30 - 36)/4)
                  = P(Z < -1.5)
                  = .0668 or 6.68%

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200-1

    A:  If available, consult file of graphs and diagrams that could not be
        computerized.

        a)  Z = (X - MU)/SIGMA
              = (85 - 70)/8
              = 1.875

            Area beyond this Z value is .0301, so 3.01% of the families spent
            85 dollars or more per week.

        b)  A cumulative Z value such that 80% lies above it or 20% lies below
            it is -.84.

               Z = (X - MU)/SIGMA
            -.84 = (X - 70)/8
               X = 63.28

            Therefore, 80% of the families lie above the expenditure value of
            $63.28/week.

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202-1

    A:  a)  P(MU <= X <= 1.2SIGMA) = .3849
            P(X is in interval MU +/- 1.2SIGMA) = 2(.3849) = .7698

        b)  P(X > (MU + SIGMA)) = (.5 - .3413) = .1587

        c)  P(X > MU + (3*SIGMA)) = (.5 - .4987) = .0013

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206-2

    A:  a)  Z = 375/500 = .75
            P(Z > .75) = (0.5 - .2734) = .2266

        b)  Z = 125/500 = .25
            P(-.25 <= Z <= .25) = 2(.0987) = .1974

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207-1

    A:  a)  .5

        b)  Z = (725 - 600)/500 = .25
            P(Z < .25) = .5 + .0987 = .5987

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213-1

    A:  (a)  5.32

             Area beyond Z = .09
                         Z = -1.34

                         Z = (X - MU)/SIGMA
                     -1.34 = (X - 8)/2
                     -2.68 = X - 8
                      5.32 = X

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213-2

    A:  P(-1 < X < 5) = .8664
        P(-1 < X < 5) = P[ -1 - 2 < X - 2 < 5 - 2]
                      = P[(-1 - 2)/2 < (X - 2)/2 < (5 - 2)/2]
                      = P[-1.5 < Z < 1.5]
                      = .8664

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529-2

    A:  5.  none of these

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530-3

    A:  The principal distinction is that a discrete random variable can assume
        a countable number of values, while a continuous random variable can
        assume an uncountably infinite number of values.

        Examples of a discrete random variable:
                a.  The number of heads obtained when a coin is flipped three
                    times.
                b.  The number that turns up when a die is rolled.
                c.  The number of people waiting in line at a movie theater

        Examples of a continuous random variable:
                a.  The height of a human
                b.  The amount of rainfall
                c.  Time required to run a mile

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531-2

    A:  False - The number of individuals in a family is a discrete variable,
        since the values it can assume are only whole numbers.

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531-3

    A:  d.  continuous.

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532-2

    A:  c)  may take on an infinite number of values.

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743-1

    A:  False, the breaking strength of a cable is a continuous variable.

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1776-4

    A:  c.  50%

            Since each score has been raised by 7 points, the mean will also be
            raised by 7 points.  The new mean is 74.  50% of the scores will be
            less than the mean of a normal distribution.

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1859-3

    A:  False.  Actual depth may exceed the mean depth in some places.

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1860-1

    A:  False

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2035-1

    A:  b.  50

            Between the twenty-fifth percentile, and the seventy-fifth percen-
            tile, the percentage of area is

                 75 - 25 = 50%.

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2054-1

    A:  False, the 70th percentile value is exceeded by 30% of the population.

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2054-2

    A:  False, only 5 percent of the measurements are above the 95th per-
        centile.

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Identification:

31-2

Item is still being reviewed
        Multiple Choice
PROBFUNCTION      BASICTERMS/PROB
        PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension
D= 3    General

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31-3

Item is still being reviewed
        Multiple Choice
BASICTERMS/STATS  BASICTERMS/PROB
        STATISTICS        PROBABILITY

T= 2    Comprehension
D= 2    General

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38-3

Based upon item submitted by J. Warren - UNH
        Definition
BASICTERMS/PROB   BASICTERMS/STATS
        I650I             PROBABILITY       STATISTICS

T= 5    Comprehension
D= 3    General

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45-1

Item is still being reviewed
        Multiple Choice
CONCEPT/OTHER     PROBMODELS        GRAPH/PICTOGRAPH
        PROBDISTRIBUTION  PROBABILITY       DESCRSTAT/P
        PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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56-1

Item is still being reviewed
        Numerical Answer
EVENTS            EXPECTATION       PROBDISTRIBUTION
        PROBABILITY

T= 5    Computation
D= 3    General
                ***Multiple Parts***

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63-1

Based upon item submitted by J. Warren - UNH
        Numerical Answer
UNIFORM
        RANDOMNUMBERS     I650I             PROBDISTRIBUTION
        PROBABILITY       RANDOMVARIABLES

T= 5    Application
D= 3    General

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119-2

Item is still being reviewed
        Multiple Choice
STANDUNITS/NORMA
        PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension
D= 2    Education           General
                ***Statistical Table Necessary***

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120-1

Based upon item submitted by J. Inglis
        Multiple Choice
STANDUNITS/NORMA  MEAN              VARIANCE
        PROBDISTRIBUTION  PROBABILITY       DESCRSTAT/P
        PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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121-2

Item is still being reviewed
        Numerical Answer
ZSCORE            STANDUNITS/NORMA
        PROBDISTRIBUTION  PROBABILITY

T=10    Computation
D= 3    General
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


131-2

Based upon item submitted by A. Bugbee - UNH
        Multiple Choice
OTHER/N           ZSCORE
        NORMAL            PROBDISTRIBUTION  PROBABILITY
        STANDUNITS/NORMA  ASSUMPTCUSTOMARY

T= 2    Computation
D= 2    General

Back to review this question

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135-1

Item is still being reviewed
        Multiple Choice
ZSCORE            STANDERROR/OTHER
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Application
D= 4    Business            General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


136-3

Item is still being reviewed
        Multiple Choice
ZSCORE            NORMAL
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Application
D= 2    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


137-1

Item is still being reviewed
        Multiple Choice
ZSCORE            NORMAL
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 1    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


137-2

Item is still being reviewed
        Multiple Choice
PROPORTION        ZSCORE
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Application
D= 4    Biological Sciences General             Natural Sciences
                ***Statistical Table Necessary***

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Back to this chapter's Contents


138-1

Based upon item submitted by H. B. Christensen - BYU
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


138-2

Item is still being reviewed
        Multiple Choice
ZSCORE
        CENTRALLIMITTHM   STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       CONCEPT           STATISTICS

T= 5    Computation     Comprehension
D= 3    General
                ***Statistical Table Necessary***

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139-1

Based upon item submitted by A. Bugbee - UNH
        Multiple Choice
PERCENTILE        ZSCORE
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Application
D= 4    General             Natural Sciences
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


141-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension
D= 1    General

Back to review this question

Back to this chapter's Contents


141-3

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


142-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        MEAN              STANDARDDEVIATIO  STANDUNITS/NORMA
        PROBDISTRIBUTION  PROBABILITY       DESCRSTAT/P
        PARAMETRIC        STATISTICS

T= 5    Computation
D= 4    General
                ***Calculator Necessary***

Back to review this question

Back to this chapter's Contents


142-2

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
ZSCORE
        MEAN              STANDARDDEVIATIO  STANDUNITS/NORMA
        PROBDISTRIBUTION  PROBABILITY       DESCRSTAT/P
        PARAMETRIC        STATISTICS

T= 5    Computation
D= 4    General
                ***Calculator Necessary***

Back to review this question

Back to this chapter's Contents


143-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
ZSCORE            PERCENTILE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


144-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
ZSCORE            PERCENTILE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T=10    Computation
D= 5    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


144-2

Based upon item submitted by R. Pruzek - SUNY at Albany
        Multiple Choice
STANDARDDEVIATIO  ZSCORE
        POPULATIONMODELS  DESCRSTAT/P       PARAMETRIC
        STATISTICS        STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY

T= 2    Comprehension
D= 2    General

Back to review this question

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145-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 1    General

Back to review this question

Back to this chapter's Contents


146-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
ZSCORE            PERCENTILE
        I650I             STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


147-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
ZSCORE            NORMAL
        APPLICATIONEX     STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       MISCELLANEOUS

T= 5    Computation     Comprehension   Application
D= 2    General             Education
                ***Statistical Table Necessary***

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149-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation     Comprehension
D= 1    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


149-2

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 1    General

Back to review this question

Back to this chapter's Contents


150-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 2    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


150-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 2    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


155-2

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


166-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T=10    Computation
D= 4    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


166-2

Item is still being reviewed
        Multiple Choice
PERCENTILE        ZSCORE
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 4    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


167-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 4    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


167-2

Based upon item submitted by J. Inglis
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 4    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


168-1

Based upon item submitted by J. Inglis
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 4    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


168-2

Item is still being reviewed
        Multiple Choice
ZSCORE            PERCENTILE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


169-2

Based upon item submitted by J. Inglis
        Multiple Choice
MEDIAN            ZSCORE
        MEAN              DESCRSTAT/NP      NONPARAMETRIC
        STATISTICS        STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       DESCRSTAT/P       PARAMETRIC

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


170-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T=10    Computation
D= 4    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


171-1

Based upon item submitted by J. Inglis
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


172-2

Item is still being reviewed
        Multiple Choice
ZSCORE            NORMAL
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


173-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


176-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


176-2

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 1    General             Education
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


177-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 1    General             Natural Sciences
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


177-2

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 2    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


185-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 2    Computation
D= 2    General             Education
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


189-1

Based upon item submitted by K. Amsden - UNH
        Numerical Answer
ZSCORE            MODE              MEDIAN
        I650I             STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       DESCRSTAT/NP      NONPARAMETRIC
        STATISTICS

T=10    Computation
D= 3    General             Education           Biological Sciences
                ***Multiple Parts***

Back to review this question

Back to this chapter's Contents


190-1

Item is still being reviewed
        Numerical Answer
ZSCORE
        OTHER/N           STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       NORMAL

T=10    Computation     Application
D= 4    General             Economics
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


193-2

Based upon item submitted by H. B. Christensen - BYU
        Numerical Answer
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 2    General             Business
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


200-1

Item is still being reviewed
        Numerical Answer
NORMAL            ZSCORE
        PROBDISTRIBUTION  PROBABILITY       STANDUNITS/NORMA

T=10    Computation
D= 4    General             Business
                ***Calculator Necessary***
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


202-1

Item is still being reviewed
        Numerical Answer
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 1    Business            General
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


206-2

Based upon item submitted by R. E. Lund - Montana State U.
        Numerical Answer
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 2    Business            General
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


207-1

Based upon item submitted by R. E. Lund - Montana State U.
        Numerical Answer
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 1    Business            General
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


213-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Numerical Answer
NORMAL            ZSCORE
        MEAN              STANDARDDEVIATIO  PROBDISTRIBUTION
        PROBABILITY       STANDUNITS/NORMA  DESCRSTAT/P
        PARAMETRIC        STATISTICS

T=10    Computation
D= 3    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


213-2

Based upon item submitted by S. Selvin - UC Berkeley
        Numerical Answer
OTHER/N           ZSCORE
        NORMAL            PROBDISTRIBUTION  PROBABILITY
        STANDUNITS/NORMA

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


529-2

Based upon item submitted by J. Inglis
        Multiple Choice
DISCRETERANVAR    CONTINUOUSRANVAR
        RANDOMVARIABLES   PROBABILITY

T= 2    Comprehension
D= 2    Psychology          General

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530-3

Based upon item submitted by A. Bugbee - UNH
        Short Answer
DISCRETERANVAR    CONTINUOUSRANVAR
        RANDOMVARIABLES   PROBABILITY

T= 5    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


531-2

Item is still being reviewed
        True/False
DISCRETERANVAR
        RANDOMVARIABLES   PROBABILITY

T= 2    Comprehension
D= 1    General

Back to review this question

Back to this chapter's Contents


531-3

Item is still being reviewed
        Multiple Choice
CONTINUOUSRANVAR
        RANDOMVARIABLES   PROBABILITY

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


532-2

Item is still being reviewed
        Multiple Choice
CONTINUOUSRANVAR
        RANDOMVARIABLES   PROBABILITY

T= 2    Comprehension
D= 1    General

Back to review this question

Back to this chapter's Contents


743-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
BASICTERMS/STATS
        STATISTICS

T= 5    Comprehension
D= 3    General

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1776-4

Item is still being reviewed
        Multiple Choice
MEAN              PROPORTION
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1859-3

Based upon item submitted by J. L. Mickey -UCLA
        True/False
MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

Back to review this question

Back to this chapter's Contents


1860-1

Based upon item submitted by J. L. Mickey -UCLA
        True/False
MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

Back to review this question

Back to this chapter's Contents


2035-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


2054-1

Item is still being reviewed
        True/False
PERCENTILE
        RANDOMVARIABLES   DESCRSTAT/P       PARAMETRIC
        STATISTICS        PROBABILITY

T= 2    Comprehension
D= 5    General

Back to review this question

Back to this chapter's Contents


2054-2

Item is still being reviewed
        True/False
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

Back to review this question

Back to this chapter's Contents


Return to the list of chapters

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