Suppose ACT Reading scores are normally distributed with a mean of 21.3 and a standard deviation of 6. A university plans to award scholarships to students whose scores are in the top 5%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.

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Asked Dec 6, 2019
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Suppose ACT Reading scores are normally distributed with a mean of 21.3 and a standard deviation of 6. A university plans to award scholarships to students whose scores are in the top 5%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.

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Expert Answer

Step 1

Given Data

Mean = 21.3

Standard Deviation = 6

Top 5 % is given by Finding the Z-value corresponding to p = 0.95

...

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X — и Х—21.3 X – 21.3 1.645 6. X = 6 x 1.645 + 21.3 = 31. 17 - 31.2

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