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)?
