At a motorcycle the painted car bodies have to be heat treated in an oven. Too much time in the oven, will cause the paint to flake, and too little time in oven will cause unacceptable paint finish. The specification on baking time in the oven are 8 + 0.2 minutes. Random samples of 4 are chosen and the times they spent in the oven are noted down. The sample means and standard deviations for each sample are calculated. Information on such 30 samples yields the following information:

Mean of 30 sample means = 7.9 and mean of 30 sample standard deviations = 0.07

(a)Calculate the center line, upper control and lower control for Mean X- and s- charts.

(b)Estimate the process mean and standard deviation assuming process is under control.

(c)What proportion of the output is nonconforming?

(d)If the process mean changes to 8.2 minutes, what is the probability of dedecting this change on the first sample taken after the shift, assuming that the process standard deviation has not changed?