Consider the following sample of observations on coating thickness for low-visco

Question

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): .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. d. Estimate P(X

Explanation / Answer

(A) Point estimate of the mean of given data is 1.2856

(B) Median = 1.385

(E) Standard error = s/sqrt(n) = 0.4133/sqrt(16) = 0.1033

(C) For 10% upper, z-value = 1.28
xbar = mean + z*SE
xbar = 1.2856 + 1.28*0.1033
xbar = 1.4178

(D) P(X<1.5) = P(z<(1.5-1.2856)/0.1033) = P(z<2.0755) = 0.9810

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