The mass (in \(\mathrm{kg}\) ) of a soil specimen is measured to be \(X=1.18 \pm 0.02\). After the sample is dried in an oven, the mass of the dried soil is measured to be \(Y=0.85 \pm 0.02\). Assume that \(X\) and \(Y\) come from normal populations and are unbiased. The water content of the soil is measured to be

a. From what distributions is it appropriate to simulate values \(X^{*}\) and \(Y^{*}\) ?

b. Generate simulated samples of values \(X^{*}, Y^{*}\), and \(W^{*}\).

c. Use the simulated sample to estimate the standard deviation of \(W\).

d. Construct a normal probability plot for the values \(W^{*}\). Is it reasonable to assume that \(W\) is approximately normally distributed?

e. If appropriate, use the normal curve to find a 95\% confidence interval for the water content.

Transcribed Image Text:

W = X - Y X