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Math Help - So confused... Central Areas

  1. #1
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    Sep 2010
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    So confused... Central Areas

    Hey

    I'm having major issues trying to figure this out...

    In America, there are 2 primary standardized tests used by colleges to decide on admissions: SAT & ACT. In 2001, SAT scores had a mean of 500 & a standard deviation of 100, while ACT scores had a mean of 21.0 & a standard deviation of 4.7. In each case, the higher the mark the better the result & the greater the chance of being accepted for admission. Assume that the scores for students in general are Normally Distributed with means & standard deviations as stated above.

    Question: Between what 2 scores do the central 80% of students score in the SAT tests?

    Now this is what I have:

    For the central 80% of SAT student test scores: pr(xL < X < xU) = 0.80
    pr(xL < X < xU) = 0.80 = pr(X < xL) = 0.10 = xL =
    pr(xL < X < xU) = 0.80 = pr(X < xU) = 0.90 = xU =
    The central 80% of SAT test scores fall between


    So I know thats the working formula, I just have no idea how to get the answer... I know we use our calculators to get the figures, but I cant remember how. Its driving me nuts, I've listened to my lectures about 6 times and gone over all my notes and this is making me draw a huge blank and I'm really confused.

    Any help would be greatly appreciated!!
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  2. #2
    Senior Member
    Joined
    Oct 2009
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    I don't know how they do it in your class but I would do:

    pr(X>\frac{x-500}{100})=0.9

    Then find the z-value for the the 90th percentile on a z-table (1.28)

    So then we have:

    pr(X>\frac{x-500}{100}=1.28)

    x=628)

    So the upper limit for the central 80% is 628

    Then

    pr(X<\frac{x-500}{100})=0.1

    Then find the z-value for the the 10th percentile on a z-table (-1.28)

    pr(X>\frac{x-500}{100}=-1.28)

    x=372

    So the upper limit for the central 80% is 372

    The scores for the central 80% are between 372 and 628.
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