uppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5 and a standa

Question

uppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5 and a standard deviation of 0.37. Using the empirical rule, what percentage of the students have grade point averages that are no more than 3.24

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Mộc Miên 3 years 2021-08-26T13:10:19+00:00 1 Answers 4 views 0

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  1. Amity
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    2021-08-26T13:12:08+00:00
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    Answer:

    P(x \le 3.24) = 0.97725

    Step-by-step explanation:

    Given

    \bar x = 2.5

    \sigma = 0.37

    Required

    Percentage that is not more than 3.24

    The above implies that:

    x = 3.24

    Calculate z score

    z = \frac{x - \bar x}{\sigma}

    z = \frac{3.24 - 2.5}{0.37}

    z = \frac{0.74}{0.37}

    z = 2

    So, the probability is represented s:

    P(x \le 3.24) = P(z \le 2)

    From z probability

    P(z \le 2) = 0.97725

    Hence:

    P(x \le 3.24) = 0.97725

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