A tube$-$bending operation produces parts with an included angle $=44\mathrm{.}2\backslash$deg $.$ The process is in

statistical control and the values of included angle are normally distributed with a standard

deviation $=0\mathrm{.}35\backslash$deg $.$ The design specification on the angle $=45\mathrm{.}0\backslash$deg $\backslash$pm $2\mathrm{.}0\backslash$deg $.$

Determine

$($a$)$ the process capability and the upper and lower limits of the process capability range $(3$ points$)$

$($b$)$ the process capability index if the process is adjusted so that its mean $=45\mathrm{.}0\backslash$deg $.(2$ points$)$