PROBLEM 3. [3Upts) The target value of the diameter of a ball bearing is 12 nm1. Each morning machines are set at the target value, but at some time during the day they move off target. A sample of 109 bearings produced by a particular machine is randomly selected to decide whether they have been produced when the machine worked properly. The sample average diameter of bearings was found to be 12.2 mm. Assume that the population standard deviation is known to be 0.36 mm. (a) [lUpts) Compute a 99% condence interval for the true mean diameter of bearings. (b) [10pts) Judging by the condence interval computed in part {a}, can it be concluded that the machine moved off target? Explain. (c) l[lllpts) TWhat is the minimum required sample size1 if we wish the 90% confidence interval to be within 9.99 mm from the true mean value? Use the standard deviation of 9.36 mm. PROBLEM 4. [20pts) Two processes are employed to produce bearings used in an aircraft wing assembly. Of 290 bearings selected from process 1, 5% do not conform to the strength specications, while of 399 bearings selected from process '2, 7% are nonconforming. (a) [lUpts) Construct a 99% CI for the true difference in fraction of noncon- forming bearings between the two processes. Can it be concluded that the two processes produce the same proportion of defectives?l Give a clear ex- planation. (b) [10pts) Explain in words what we mean when we say \"a 99% condence interval\". Will a 93% condence interval be wider or narrower? Explain