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):
0.83
0.88
0.88
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), i.e., the proportion of all thickness values less than 1.5 [Hint: if you know the values of and , 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)?
