The thickness (in millimeters) of the coating applied to

Chapter 0, Problem 8.22

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The thickness (in millimeters) of the coating applied to disk drives is a characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shifts production and determining , the mean coating thickness for the sample. a. Describe the sampling distribution of (for a sample of size 16). b. When no unusual circumstances are present, we expect to be within of 3 mm, the desired value. An value farther from 3 than is interpreted as an indication of a problem that needs attention. Compute . (A plot over time of values with horizontal lines drawn at the limits is called a process control chart.) c. Referring to Part (b), what is the probability that a sample mean will be outside just by chance (i.e., when there are no unusual circumstances)? d. Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of 3.05 mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if m 3.05.)