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12 June, 20:24

A psychology professor assigns letter grades on a test according to the following scheme. A: Top 11% of scores B: Scores below the top 11% and above the bottom 61% C: Scores below the top 39% and above the bottom 16% D: Scores below the top 84% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 81.8 and a standard deviation of 7.8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

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  1. 12 June, 22:41
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    Answer: the minimum score required for an A grade is 91

    Step-by-step explanation:

    Since the scores on the test are normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = scores on the test.

    µ = mean score

    σ = standard deviation

    From the information given,

    µ = 81.8

    σ = 7.8

    The probability value for the scores in the top 11% would be (1 - 11/100) = (1 - 0.11) = 0.89

    Looking at the normal distribution table, the z score corresponding to the probability value is 1.23

    Therefore,

    1.23 = (x - 81.8) / 7.8

    Cross multiplying by 114, it becomes

    1.23 * 7.8 = x - 81.8

    9.594 = x - 81.8

    x = 9.594 + 81.8

    x = 91 rounded to the nearest whole number.
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