The thickness (in millimeters) of the coating applied to disk drives is a characteristic that determines the usefulness of the product. When no...

I need help with the following stat problem. I got the first part wrong and cannot figure out what I did wrong

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 anormal distribution with a mean of 3 mm and a standard deviation of 0.03 mm. Suppose that the process will be monitored by selecting a random sample of 12 drives from each shiit's production anddetermining )7, the mean coating thickness for the sample. (Round all your intermediate calculations to four decimal places. Round the answers to four decimal places.) (a) What are the mean and standard deviation of the )7 sampling distribution? ”)7:a}: (b) When no unusual circumstances are present, we expect } to be within 30; of 3 mm, the desired value. An 2 value farther from 3 than 315 is interpreted as an indication of a problem thatneeds attention. Compute 3 :t 30;. (Enter solutions from smallest to largest. Round your answers to four decimal places.) I(c) Referring to Part (b), what is the probability that a sample mean will be outside 3 t 30'; 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 3.03 mm. What is the probability that a problem will be detected when thenext sample is taken? (Hint: This will occur if)? > 3 + 30; or)? < 3 - 30;, when [1 = 3.03.) I You may need to use the appropriate table in Appendix A to answer this question. Need Help? "' ’i" I SubmitAnswer I I Save Progress I I I Practice AnotherVersion I I