[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Bridies' Bearing Works manufactures bearing shafts whose

diameters are normally distributed with parameters [math]\mu = 1[/math], [math]\sigma = .002[/math]. The buyer's specifications require these diameters to be [math]1.000 \pm .003[/math] cm. What fraction of the manufacturer's shafts are likely to be rejected? If the manufacturer improves her quality control, she can reduce the value of [math]\sigma[/math]. What value of [math]\sigma[/math] will ensure that no more than 1 percent of her shafts are likely to be rejected?