The combined math and verbal scores for students taking a national standardized examination for college admission, is Normally distributed w

Question

The combined math and verbal scores for students taking a national standardized examination for college admission, is Normally distributed with a mean of and a standard deviation of . If a college requires a minimum score of for admission, what percentage of students do not satisfy that requirement?

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Katherine 2 weeks 2021-10-03T16:09:00+00:00 1 Answer 0

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    2021-10-03T16:10:11+00:00

    Answer:

    96.1%

    Step-by-step explanation:

    This is a normal distribution problem

    μ = mean = 500

    σ = standard deviation = 170

    To solve this question, we require the normalized/standard/z-score value of 800.

    The standardized score for any value is the value minus the mean then divided by the standard deviation.

    z = (x – μ)/σ = (800 – 500)/170 = 1.765

    To determine the percentage of student do not satisfy that requirement, this refers to students that do not score up to the minimum requirement of 800.

    P(x < 800) = P(z < 800)

    We’ll use data from the normal probability table for these probabilities

    P(x < 800) = P(z < 1.765) = 1 – P(z ≥ 1.765) = 1 – P(z ≤ -1.765) = 1 – 0.039 = 0.961.

    This points to the fact that 96.1% of the candidates do not normally reach the minimum requirement.

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