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    Statistics : Distributions, Probability, Means, Medians, Quartiles and Five-Number Summary (13 Problems)

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    1. The array below shows the number of days required for approval for
    a random selection of small business loan applications:

    56 21 38 17 15 67 45 48 60 56 22 53 37 17

    50 92 39 16 59 73 17 31 28 51 74 42 31

    What is the arithmetic mean for these observations? (Round the
    calculation to two decimal places.)
    a. 42.00
    b. 42.78
    c. 41.25
    d. None of the above

    2. Using the array in #1 above, calculate the median of the
    distribution, rounding to two decimal places.
    a. 42.00
    b. 42.78
    c. 41.25
    d. None of the above

    3. Using the array in question 1 above, calculate the arithmetic mean
    with the single most extreme outlier removed. Round the
    calculation to two decimal places.
    a. 40.50
    b. 40.89
    c. 41.92
    d. 43.85

    4. The following is a five-number summary calculated from
    observations of the percentage of calories that come from fat in 23
    items advertised as "reduced" fat from a sample of fast food chain
    restaurants. Form the box-and-whisker plot, select the phrase
    below which bests describes the shape of the distribution.
    | 15 | 20 | 22 | 26 | 30 |
    |____ |______ |______ |_______|_______|

    a. Skewed slightly to the left
    b. Skewed slightly to the right
    c. Symmetrical distribution
    d. There is not enough information given to determine the shape

    5. The following data represents the processing times required to pack
    20 randomly selected computer hardware orders for mailing:

    5.62 16.25 11.46 8.45 5.41 11.62 7.5 4.42 7.58 7.54

    5.29 10.92 21.62 8.58 11.42 7.29 7.96 10.5 9.29 8.92

    What is the third quartile?
    a. 10.92
    b. 11.05
    c. 11.42
    d. 11.46

    6. What is the standard deviation of the distribution of the
    observations in the array shown in question 11 above?
    a. 0.894
    b. 3.998
    c. 4.199
    d. 15.981

    7. What is the coefficient of variation for the observations in the array
    shown in question 11 above?
    a. 39.97 %
    b. 44.15%
    c. 42.61%
    d. 46.94 %

    8. The employees of a company were surveyed on questions regarding
    their educational background and marital status. Of the 600
    employees, 400 had college degrees, 100 were single, and 60 were
    single college graduates. The probability that an employee of the
    company is married and has a college degree is:
    a. 40/600
    b. 340/600
    c. 400/600
    d. 500/600

    9. An advertising executive is studying TV viewing habits of married
    men and women during prime time hours. On the basis of past
    viewing records, the executive has determined that during prime
    time, husbands are watching TV 60% of the time that their wives
    are also watching TV. When the husband is not watching TV, 30%
    of the time his wife is watching TV. What is the probability that, if
    the wife is watching TV, her husband is also watching TV?
    a. 0.12
    b. 0.24
    c. 0.36
    d. 0.67

    10. Mothers Against Drunk Driving is a very visible group whose main
    focus is to educate the public about the harm caused by drunk
    drivers. A study was recently done that emphasized the problem we
    all face with drinking and driving. Four hundred accidents that
    occurred on a Saturday night were analyzed. Two items noted were
    the number of vehicles involved and whether alcohol played a role in
    the accident. The numbers are shown below:

    Number of vehicles Involved
    Did alcohol play a role? 1 2 3 Totals
    Yes 50 100 20 170
    No 25 175 30 230 1
    Totals 75 275 50 400

    Referring to the table above, what proportion of accidents involved
    more than one vehicle?
    a. 50/400
    b. 75/400
    c. 275/400
    d. 325/400

    11. Referring to the table in question 20 above, what proportion of the
    non-alcohol related accidents were multiple vehicle accidents?
    a. 50/170
    b. 120/170
    c. 205/230
    d. 25/230

    12. A company has 2 machines that produce widgets. An older machine
    produces 23% defective widgets, while the new machine produces
    only 8% defective widgets. In addition, the new machine produces 3
    times as many widgets as the older machine does. What is the
    probability that a randomly chosen widget produced by the company
    is defective?
    a. .055
    b. .0775
    c. .1175
    d. .256

    13. A survey is taken among customers of a fast-food restaurant to
    determine preference for hamburger or chicken. Of 200 respondents
    selected, 75 were children and 125 were adults. 120 preferred
    hamburger and 80 preferred chicken. 55 of the children preferred
    hamburger. What is the probability that a randomly selected
    individual is an adult?
    a. 0.50
    b. 0.625
    c. 0.75
    d. None of the above

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    Solution Summary

    Thirteen Statistics problems involving Distributions, Probability, Means, Quartiles and Five Number Summary are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.