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Propagation of uncertainty

  1. May 26, 2009 #1
    1. The problem statement, all variables and given/known data

    The area of a flat, rectangular parcel of land is computed from the measurement of the length of two
    adjacent sides, X and Y. Measurements are made using a scaled chain accurate to within 0.5% over its
    indicated length. The two sides are measured several times with the following results:

    X = 556 m
    Stdev =5.3 m
    n = 8

    Y = 222 m
    stdev = 2.1 m
    n = 7


    Estimate the area of the land and state the confidence interval of that measurement at 95%.

    2. Relevant equations

    propagation of uncertainty formula


    [tex]
    \delta z = \sqrt {\left( {\frac{{\partial z}}{{\partial x}}dx} \right)^2 + \left( {\frac{{\partial z}}{{\partial y}}dy} \right)^2 }
    [/tex]



    3. The attempt at a solution

    My issue here is how to account for the accuracy of the chain in the problem statement. I can easily find the values of X&Y at 95% confidence using the mean value and stdev and plug them into the uncertainty formula. What do I do with the 0.5%?
     
  2. jcsd
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