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25 November, 01:50

Amanda and ben are in different statistics classes. amanda scores a 15 on a quiz. her classmates have a mean of 20 and the standard deviation of 5 on the quiz. ben scores a 70 on a quiz. his classmates have a mean of 75 and a standard deviation of 10 on the quiz. who did better relative to their classmates?

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  1. 25 November, 03:16
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    In order to understand who did better relative to the class, you need to find and compare the Z-scores (considering that the grades are normally distributed).

    The Z-score can be found by the formula:

    z = (X - m) / σ

    where:

    X = grade

    m = mean

    σ = standard deviation

    For Amanda:

    z = (15 - 20) / 5

    = - 1.00

    For Ben:

    z = (70 - 75) / 10

    = - 0.50

    Looking at a standard normal table, we find:

    P (z < - 1.00) = 0.15866

    P (z < - 0.50) = 0.30854

    Therefore, the probability to have a grade lower than Anna's in her class is around 16%, while the probability to have a grade lower than Ben's in his class is around 31%.

    Hence, Ben did better relative to his class.
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