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Math Help - z-score question

  1. #1
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    z-score question

    A university aacepts only applicats scoring in the top 16% on an entrance exam. Each year the test scores are normaly distributed with a standard deviation of 30. What is the highest value that the mean can have for Fred to be accepted with a score of 520?

    I was able to figure out the answer to this question but now I can't seem to figure out how I got the z-score number of -0.99????

    z=-0.99
    x=520
    o=30

    mean= x+ (z+o)
    = 520+(-0.99 x 30)
    =490.3

    ahh, help.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by perron View Post
    A university aacepts only applicats scoring in the top 16% on an entrance exam. Each year the test scores are normaly distributed with a standard deviation of 30. What is the highest value that the mean can have for Fred to be accepted with a score of 520?

    I was able to figure out the answer to this question but now I can't seem to figure out how I got the z-score number of -0.99????

    z=-0.99
    x=520
    o=30

    mean= x+ (z+o)
    = 520+(-0.99 x 30)
    =490.3

    ahh, help.
    Note that he needs to be in the top 16% or the 84th percentile.

    Thus, it can be seen in tables, that the z-score that corresponds to the 84th percentile would be .994. (If you have a TI-83, you can find this z value by inputting invNorm(.84))

    Since x=520 and \sigma = 30, we see that \frac{520-\mu}{30}=.994, which leads to something close to your result. I end up with \mu=490.18

    Does this clarify things?
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