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10 December, 02:29

A mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. if the top 3% of students receive $500, find the minimum score you would need to receive this award.

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  1. 10 December, 02:30
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    To solve for the minimum score required, we find for the z score value at P = 0.97 (top 3%). The z score is:

    z = 1.88

    Then we use the formula to find for X:

    z = (X - u) / s

    1.88 = (X - 400) / 100

    X = 588

    You have to score at least 588.
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