$[20$ points$]$ A process is in statistical control with $=41\mathrm{.}8$ and $=2\mathrm{.}4.$ The control

chart uses a sample size of $=2.$ Specifications are at $41\backslash$pm $5.$ The quality

characteristic is normally distributed.

$($a$)[10$ points$]$ Estimate the potential capability of the process $()($Note that your

answer will have four significant figures.$).$

$($b$)[10$ points$]$ Estimate the actual process capability $()($Note that your answer will

have four significant figures.$).$