At a college, the mean GPA of the current body is 2.76 with a standard deviation of .64.?

Please help me compute (two decimal places) the GPA of a student with a z-score of 0.3 and another student with a z-score of -1.4.

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  • Anonymous
    1 decade ago
    Favorite Answer

    z = (sample value - mean)/std dev

    0.3 = (sample value - 2.76)/.0.64

    z = 2.76 + 0.64*(0.3)

    z = 2.952 = rounded to 2.95

    z = -1.4 = (sample value - 2.76)/0.64

    sample vaue = 2.76 +(-1.4)*0.64 = 1.864 round to 1.86

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  • 1 decade ago

    The z-score associated with an observation x_i of a random variable X is given by

    z = (x_i - mean) / standard deviation

    Plug in z=0.3, mean = 2.76 and std dev = 0.64, and get

    0.3 = (x_i - 2.76) / 0.64

    => 0.3*0.64 = x_i - 2.76

    => x_i = 2.76 + 0.3*0.64

    => x_i = 2.952

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