The thickness (in millimeters) of the coating applied to disk drives is one 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 5 mm and a standard deviation of 0.03 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determining x, the mean coating thickness for the sample.

When no unusual circumstances are present, we expect x to be within 2_x of5mm,the desired value. An x value farther from5than 2_xis interpreted as an indication of a problem that needs attention.

Compute 52_x.

52_x = __mm

5+2_x= __mm

(c)Referring to part (b), what is the probability that a sample mean will be outside 52_x

just by chance (that is, when there are no unusual circumstances)? (Round your answer to four decimal places.)

(d)Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of5.03mm.What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if x>5+2_x or x<52_x when=5.03.Round your answer to four decimal places.)