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 0.06 mm. Suppose that the process will be monitored by selecting a random sample of 13 drives from each shift's production and determining x, the mean coating thickness for the sample.
A) Describe the smapling distribution of m. B) When no unusual circumstances are present, we expect m to be within 3*o(x) of 3 mm, the desired coating thickness value. A value of m farther from 3 than 3*o(x) is interpreted as an indication of a problem that needs attention. Compute 3 + 3*o(x) and 3 - 3*o(x).C) Referring to part (b), what is the probability that m will be outside 3 + 3*o(x) and 3 - 3*o(x) just by chance?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 smapel is taken?