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Math Help - percentage of interval

  1. #1
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    percentage of interval

    For X~N (105,16), then what percent of the data are contained in the interval 97-105?

    I need help getting started on this question...up to the point where I have to calculate the z-scores and I'll take it from there.
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  2. #2
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    Oct 2008
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    Thumbs up Angel (Best Solution)

    X~N (105, 16)
    Compare the given form with general form,
    So,
    X~N (105, 16) Compare to X~N (, σ2 )
    After comparing we get,
    =105
    σ=4
    We have to find the interval from X=97 to X=105.
    When X=97 then
    Z= (97-105)/4
    Z=-2
    When X=105 then Z will be 0 because this is mean.
    So we have to find interval between Z=-2 to Z=0
    P (between Z=-2 to Z=0)=0.4772 required answer
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