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Thread: Standard Normal Variable Z ... I do not understand

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    Standard Normal Variable Z ... I do not understand






    Hi,

    This is not a homework question as I have the answer, just trying to figure out the method;

    I have a "Normal Distribution Table" infront of me.

    Sample mean = 76.8
    Standard Deviation = 12.43
    n = 40, m = 8 intervals

    And below are the defined intervals of the standard normal variable (z).
    What I do not understand is how the values 1.15, 0.675, 0.32, 0.00 have been produced. Could someone kindly inform me / show me,


    Prob (z < -1.15) = 0.125
    Prob (-1.15 < -0.675) = 0.125
    Prob (-0.675 < -0.32) = 0.125
    Prob (-0.32 < -0.00) = 0.125
    Prob ( 0.00 < +0.32) = 0.125
    Prob ( 0.32 < +0.675) = 0.125
    Prob ( 0.675 < +1.15) = 0.125
    Prob ( z > +1.15) = 0.125

    Thanks

  2. #2
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    z represents the number of standard deviations away from the mean a particular value is:

    z = (x - mu)/s

    Your table is a smaller version of a normal table that shows the proportion (roughly) of z scores that should fall within particular ranges if the variable follows a normal distribution.

  3. #3
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    Thank you for such a quick response.

    z = (x - mu)/s

    I googled those terms, but still can't seem to fathem it.

    would X be 76.8, and S = 12.43.

    How would I get the value mu.

    Could you run through the first line or two, I would be extremly grateful (i.e. obtaining value -1.15 and -0.675).

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