Scores on the GRE are normally distributed with a mean of 514 and a standard deviation of 92. Use the 68-95-99.7 rule to find the percentage

Question

Scores on the GRE are normally distributed with a mean of 514 and a standard deviation of 92. Use the 68-95-99.7 rule to find the percentage of people taking the test who score above 698.
The percentage of people taking the test who are above 698 is ___%

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Philomena 6 months 2021-08-05T00:55:39+00:00 1 Answers 12 views 0

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    2021-08-05T00:57:27+00:00

    Answer:

    2.5%

    Step-by-step explanation:

    The percentage of people taking the test who are above 698 is ___%

    Empirical rule formula states:

    95% of data falls within 2 standard deviations from the mean – between μ – 2σ and μ + 2σ .

    99.7% of data falls within 3 standard deviations from the mean – between μ – 3σ and μ + 3σ

    From the question, we have:

    Mean of 514 and a Standard deviation of 92

    Hence:

    μ ± xσ

    514 ± 92x = 698

    514 + 92x = 698

    92x = 698 – 514

    92x = 184

    x = 184/92

    x = 2

    Hence, the data is correct and it is 2 standard deviation from the mean. Therefore, 95% of data falls within 2 standard deviations from the mean – between μ – 2σ and μ + 2σ .

    The question is asking us to find the percentage of people taking the test who are above 698 is calculated as:

    100 – 95% /2

    = 5/2

    = 2.5%

    The percentage of people taking the test who are above 698 is 2.5%

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