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25 October, 11:08

If the scores of a math test are normally distributed with an average score of 76 and a standard deviation of 5, what percentage of students scored below a 65?

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  1. 25 October, 11:20
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    Step-by-step explanation:

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

    z = (x - µ) / σ

    Where

    x = math test scores.

    µ = mean score

    σ = standard deviation

    From the information given,

    µ = 76

    σ = 5

    The probability that a student scored below 65 is expressed as

    P (x < 65)

    For x = 65

    z = (65 - 76) / 5 = - 2.2

    Looking at the normal distribution table, the probability corresponding to the z score is 0.014

    The percentage of students that scored below 65 is

    0.014 * 100 = 1.4%
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