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Thread: normal distribution help

  1. #1
    Super Member
    Sep 2008

    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.

    a) $\displaystyle 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 $\displaystyle 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 $\displaystyle \frac{100-108}{\sigma} = -1.88 $

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

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