8. A manufacturer sets a statistical process-control system to measure deviations, X, from a critical dimension (Lot the dimension itself). The company treats these deviations as noise. In order to set the process charts, 20 samples, each of size 4, are collected. These yield the following sample (noise) statistics: X = 0.5 mm and E 21.0 mm. Must Show All Your Work for Full Marks! (a) Determine the 90% condence-level Scontrol limits, assuming sample standard-deviation values are normally distributed. [5 points]