Problem $1.$ The Lowell MFG Co$.$ has a policy of $C_p=0\mathrm{.}90$ for all new products. All sheet metal specifications are designed with a tolerance of $+-0\mathrm{.}8$ mils. Assume a manufacturing process average of $105$ mils.

$1$a$.$ What is the reject rate for new parts?

$1$b$.$ If the sheet metal punch press average was shifted by $0\mathrm{.}2$ mil, what will the new Reject Rate be in PPM$?$ What will the new $C_{pk}$ be$?$

$1$c$.$ If only the $C_p$ was changed to $1\mathrm{.}10($everything else remains the same as in $1$ a $),$ what will the new reject rate in $\%?($ What normal distribution table is used here? Can you send a screen shoot of the table as well?$)$