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25 May, 01:42

Consider a value to be significantly low if its z score less than or equal to minus2 or consider a value to be significantly high if its z score is greater than or equal to 2. A test is used to assess readiness for college. In a recent year, the mean test score was 21.9 and the standard deviation was 4.9. Identify the test scores that are significantly low or significantly high.

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  1. 25 May, 04:02
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    Step-by-step explanation:

    Since we are dealing with z scores, then the distribution is a normal distribution. The formula for determining the z score is expressed as

    z = (x - µ) / σ

    Where

    x = sample mean

    µ = population mean

    σ = standard deviation

    From the information given,

    µ = 21.9

    σ = 4.9

    For significantly low values, z = - 2

    Therefore,

    - 2 = (x - 21.9) / 4.9

    - 2 * 4.9 = x - 21.9

    - 9.8 = x - 21.9

    x = - 9.8 + 21.9

    x = 12.1

    Significantly low test score = 12.1

    For significantly high values, z = 2

    Therefore,

    2 = (x - 21.9) / 4.9

    2 * 4.9 = x - 21.9

    9.8 = x - 21.9

    x = 9.8 + 21.9

    x = 31.7

    Significantly high score = 31.7
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