Consider the following sample of observations on coating thickness for low-viscosity paint (“Achieving a Target Value for a Manufacturing Process: A Case Study,” *J. of Quality Technology, *1992: 22–26):

Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption).

a.** **Calculate a point estimate of the mean value of coating thickness, and state which estimator you used.

b.** **Calculate a point estimate of the median of the coating thickness distribution, and state which estimator you used.

c.** **Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the

remaining 90%, and state which estimator you used. [*Hint*: Express what you are trying to estimate in terms of m and s.]

d.** **Estimate *P*(*X *< 1.5), i.e., the proportion of all thickness values less than 1.5. [*Hint*: If you knew the values of μ and σ, you could calculate this probability. These values are not available, but they can be estimated.]

e.** **What is the estimated standard error of the estimator that you used in part (b)?