Suppose the engineering specifications on the shelf depth of a certain slug to be turned on a CNC lathe are from .0275 in. to .0278 in. and that values of this dimension produced on the lathe can be described using a normal distribution with mean LaTeX: \mu μ and standard deviation LaTeX: \sigma σ . (a) If LaTeX: \mu μ = .0276 and LaTeX: \sigma σ = .0001, about what fraction of shelf depths are in specifications? (b) What machine precision (as measured by LaTeX: \sigma σ ) would be required in order to produce about 98% of shelf depths within engineering specifications (assuming that LaTeX: \mu μ is at the midpoint of the specifications)?