A set of quiz scores has a mean of 78 and a standard deviation of 9. Using a common grading scale where 60 and above is a passing score, wha

Question

A set of quiz scores has a mean of 78 and a standard deviation of 9. Using a common grading scale where 60 and above is a passing score, what percentage of the
students passed this test?
Explain your answer in terms of the 68-95-99.7 rule.

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Ngọc Diệp 5 years 2021-07-22T10:22:38+00:00 1 Answers 107 views 0

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  1. Eirian
    0
    2021-07-22T10:24:06+00:00
    Reply

    Answer:

    97.5% of the students passed this test.

    Step-by-step explanation:

    The Empirical Rule states that, for a normally distributed random variable:

    Approximately 68% of the measures are within 1 standard deviation of the mean.

    Approximately 95% of the measures are within 2 standard deviations of the mean.

    Approximately 99.7% of the measures are within 3 standard deviations of the mean.

    In this problem, we have that:

    Mean of 78, standard deviation of 9.

    What percentage of the  students passed this test?

    Above 60.

    60 = 78 – 2*9

    So 60 is two standard deviations below the mean.

    The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.

    Of the 50% above, all passed.

    Of the 50% below, 95%(within 2 standard deviations of the mean) passed.

    So

    p = 0.5 + 0.5*0.95 = 0.975

    97.5% of the students passed this test.

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