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Math Help - Help with normal distribution/mean question

  1. #1
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    Help with normal distribution/mean question

    I'm having trouble with this seemingly easy question:

    On an exam with normally distributed grades, 32 points put you at the border of the bottom 2.5% of your class, while 97 points puts you right at the top 0.15%.
    a. What is the class average grade?
    b. What is the z-score for a grade of 65?
    c. What percentile is a grade of 58?

    For part a, I know that the bottom 2.5% is 2 standard deviations away from the mean, but I don't understand how you can find the mean with just that information. There's also the 97 points is the top .15%, but .15% isn't a clear-cut SD number like 2.5% is. So 32 points is 2 standard deviations away from the mean, and 97 is the top .15%...I'm not sure where to go from here.

    b and c, I can't do those without the class mean, right?

    Thanks for your help!
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  2. #2
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    Quote Originally Posted by pianopiano View Post
    I'm having trouble with this seemingly easy question:

    On an exam with normally distributed grades, 32 points put you at the border of the bottom 2.5% of your class, while 97 points puts you right at the top 0.15%.
    a. What is the class average grade?
    b. What is the z-score for a grade of 65?
    c. What percentile is a grade of 58?

    For part a, I know that the bottom 2.5% is 2 standard deviations away from the mean, but I don't understand how you can find the mean with just that information. There's also the 97 points is the top .15%, but .15% isn't a clear-cut SD number like 2.5% is. So 32 points is 2 standard deviations away from the mean, and 97 is the top .15%...I'm not sure where to go from here.

    b and c, I can't do those without the class mean, right?

    Thanks for your help!
    Using the well known empirical rule:

    \mu + 3 \sigma = 97 .... (1)

    \mu - 2 \sigma = 32 .... (2)

    Solve equations (1) and (2) simultaneously for \mu and \sigma.
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