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| Math Central | Quandaries & Queries |
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Scores on a college exam are known to be normally distributed with a standard deviation of 20. If the top 3% have scores in excess of 200, what is the mean score? |
(1) At how many standard deviations above the mean does the "top 3%" start? (Use a table or calculator)
(2) How many points is that?
(3) So where's the mean?
[Mandatory real-world warning: Low-level stats texts are full of examples where the standard deviation is "known to be" something and the mean is unknown. In the real world, the chances are if you don't know the mean you don't know the SD either.]
Good Hunting!
RD
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Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.