3. 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. Qual. Tech., 1992: 22—26):

.83 .88 .88 1.04 1.09 1.12 1.29 1.31 1.48 1.49 1.59 1.62 1.65 1.71 1.76 1.83 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), that is, the proportion of all thickness values less than 1.5. (Hint: If you knew the values of m and s, 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)?