Consider the following sample of observations on coatingthickness for lowviscosity paint

Chapter 6, Problem 3

(choose chapter or problem)

Consider the following sample of observations on coating thickness for low viscosity paint (Achieving aTarget Value for a Manufacturing Process: A CaseStudy, J. of Quality Technology, 1992: 2226):.

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 we used. [Hint: Express what you are trying to estimate in terms of \(\mu\) and \(\sigma\).]

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 \(\mu\) and \(\sigma\), 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)?