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26 November, 03:59

you score a 65% on your ap statistics exam and a 78% on your economics exam. the AP statistics scores were normally distributed with an average of 60% and a standard deviation of 6%. the economics scires were also normally distributed with an average of 75% and the standard deviation of 2.5%. In which class did you perform better relative to the class average? be sure to justify your answer

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  1. 26 November, 06:59
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    You performed better relative to the class average in your economics class.

    Step-by-step explanation:

    There are two classes.

    AP statistics class and Economic class

    Using the z score formula,

    z = (x-μ) / σ, where

    x is the raw score

    μ is the population mean

    σ is the population standard deviation.

    In the AP statistics class, you scored a percentage of 65%. The class average was 60%

    x is the raw score = 65%

    μ is the population mean = 60%

    σ is the population standard deviation = 6%

    z = (x-μ) / σ

    z = (65 - 60) / 6

    z = 5/6

    z = 0.8333333333

    In the Economics classes, you scored a percentage of 78% with a class average of 75%

    x is the raw score = 78%

    μ is the population mean = 75%

    σ is the population standard deviation = 2.5%

    z = (x-μ) / σ

    z = (78 - 75) / 2.5

    z = 3/2.5

    z = 1.2

    Comparing the z score of both exams taken from different classes, we can see that your z score was higher in the Economics class compared to the A. P statistics class.

    Therefore, you performed better relative to the class average in your economics class.
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