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Math Help - Quick z-score question

  1. #1
    I just need to pass
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    Quick z-score question

    Lil' HW help please. Here is the question as it is written. "Compute and show the range of scores for each test that fall within one standard deviation from the mean. Last, using z-scores, which student did best on all four examinations collectively? Bear in mind that this is not asking for the highest scoring student on each exam; that is self-evident. Which student performed poorest on all four exams collectively?"



    Students 1-8 exams a-d
    ----a b c d
    1 64 64 69 47
    2 79 69 34 58
    3 74 64 49 49
    4 69 69 56 49
    5 64 54 44 54
    6 79 49 54 42
    7 74 44 49 62
    8 79 61 74 56
    Now, I've done the 1st part of the problem and found the standard deviation of the each exam: a=6, b=8.7, c=12.1, d=6.

    I know how to figure a z-score, but I know how to answer his question. Wouldn't be the student how averaged the best? what do z-scores have to do with it?
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Z-scores only matter when you look at more than one sample like we have in this case. You want to not just look at how much better than the average a person did, but we want to compare this for all four exams. To keep them on the same basis, find a mean and standard deviation for each exam. Figure out z-scores for each exam a person takes. Add up their z-scores... highest z-score is the best performer of all the exams collectively.
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