Suppose ACT Reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9. A university plans to award scholar

Question

Suppose ACT Reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 9%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.

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Mia 2 hours 2021-10-13T01:16:54+00:00 1 Answer 0

Answers ( )

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    2021-10-13T01:18:20+00:00

    Answer:

    29.2

    Step-by-step explanation:

    Mean = 21.4

    Standard deviation = 5.9%

    The minimum score required for the scholarship which is the scores of the top 9% is calculated using the Z – Score Formula.

    The Z- score formula is given as:

    z = x – μ /σ

    Z score ( z) is determined by checking the z score percentile of the normal distribution

    In the question we are told that it is the students who scores are in the top 9%

    The top 9% is determined by finding the z score of the 91st percentile on the normal distribution

    z score of the 91st percentile = 1.341

    Using the formula

    z = x – μ /σ

    Where

    z = z score of the 91st percentile = 1.341

    μ = mean = 21.4

    σ = Standard deviation = 5.9

    1.341= x – 21.4 / 5.9

    Cross multiply

    1.341 × 5.9 = x – 21.4

    7.7526 = x -21.4

    x = 7.7526 + 21.4

    x = 29.1526

    The 91st percentile is at the score of 29.1526.

    We were asked in the question to round up to the nearest tenth.

    Approximately, = 29.2

    The minimum score required for the scholarship to the nearest tenth is 29.2 .

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45:7+7-4:2-5:5*4+35:2 =? ( )