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23 August, 00:01

Suppose ACT Reading scores are normally distributed with a mean of 21 and a standard deviation of 6.1. A university plans to award scholarships to students whose scores are in the top 9%. What is the minimum score required for the scholarship?

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  1. 23 August, 00:20
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    Answer: the minimum score required for the scholarship is 29.24

    Step-by-step explanation:

    Since the scores are normally distributed, it follows the central limit theorem. The formula for determining the z score is

    z = (x - µ) / σ

    Where

    x = sample mean

    µ = population mean

    σ = population standard deviation

    Since the university plans to award scholarships to students whose scores are in the top 9%, the scores that would be qualified are scores which are at least 91% (100 - 9 = 91).

    Looking at the normal distribution table, the z score corresponding to the probability value of 0.91 (91/100) is 1.35

    From the information given,

    µ = 21

    σ = 6.1

    Therefore,

    1.35 = (x - 21) / 6.1

    6.1 * 1.35 = x - 21

    8.235 = x - 21

    x = 8.235 + 21 = 29.24
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