Calculating Land Area and Confidence Interval with Uncertainty Propagation

[mx6er2587]

Homework Statement

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%.

Homework Equations

propagation of uncertainty formula


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

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%?

 

[mfb]

It's not clear how the distribution for the scale looks like. If it's a Gaussian distribution with a standard deviation of 0.5 you can simply add that in quadrature. If it's a uniform distribution within +-0.5% it's messy.