It costs more to produce defective items - since they must be scrapped or reworked - than it does to produce non-defective items. This simple fact suggests that manufacturers should ensure the quality of their products by perfecting their production processes instead of depending on inspection of finished products (Deming, 1986). 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 0.1 millimeter (mm) with 90% confidence?
b. Time permits the use of a sample size no larger than 100. If a 90% confidence interval for the mean is constructed with n = 100, will it be wider or narrower than would have been obtained using the sample size determined in part a?