Process Capability Index $(Cpk)$

Bearcats Engineering has a new catalyst injection system for your

countertop production line. Your process engineering department

has conducted experiments and determined that the mean $is8\mathrm{.}01$

grams with a standard deviation $of0\mathrm{.}03.$ Your specifications are: $=$

$8\mathrm{.}0$ and $=0\mathrm{.}04$ which means $an$ upper specification $limitof8\mathrm{.}12$

$=8\mathrm{.}0+3(0\mathrm{.}04)$ and a lower specification $limitof-$

$3(0\mathrm{.}04).$

What $is$ the $Cpk$ performance $of$ the injection system?