In order to better understand a particular​ metal-stamping process, a manufacturer wishes to estimate the mean length of items produced by the process during the past 24 hours. a. How many parts should be sampled in order to estimate the population mean to within millimeter​ (mm) with ​% ​confidence? Previous studies of this machine have indicated that the standard deviation of lengths produced by the stamping operation is about mm. b. Time permits the use of a sample size no larger than . If a ​% confidence interval for is constructed using ​, will it be wider or narrower than would have been obtained using the sample size determined in part a​? Explain. c. If management requires that be estimated to within mm and that a sample size of no more than be​ used, what is​ (approximately) the maximum confidence level that could be attained for a confidence interval that meets​ management's specifications?