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Math Help - normal distribution help

  1. #1
    Super Member
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    Sep 2008
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    normal distribution help

    Jam is sold in jars and the mean weight of the contents is 108 grams. Only 3% of jars have contents weighing less than 100 grams. Assuming that the weight of jam in a jar is normally distributed find
    a the standard deviation of the weight of jam in a jar,
    b the proportion of jars where the contents weigh more than 115 grams.
    J∼N(108,σ2)

    a)  p(J<100) = 0.03

    From here do I not just look up the z value for 0.03 in the 'z tables'? In the book it gives z = -1.88? I dont know how they got this number. Can anyone explain?

    I thought the equation should be  Z = \frac{100-108}{\sigma} = 0.5120

    0.5120 is the value in the 'z'' tables that corresponds to 0.03.

    but the correct equation to solve for the standard deviation is  \frac{100-108}{\sigma} = -1.88

    Thanks.
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  2. #2
    Newbie
    Joined
    Apr 2009
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    you should transform J into standard normal distribution variable before solving the equation for {\sigma}

    which is \frac{J-108}{\sigma}
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