For $50$ consecutive days, a process engineer has measured the weight of a component after it has been coated with special paint. Each day, she takes a sample of $10$ components. The average across all $500$ components is $45\mathrm{.}343019$ grams. The average range across all parts is $0\mathrm{.}0076382$ grams. When constructing an X$-$bar chart, what would be the centerline, and what would be the upper and lower control limits$?$

$2.$ Process capability

A machined part has a specification of $0\mathrm{.}575\backslash$pm $0\mathrm{.}007$ inches. $25$ parts were measured as seen below. What is its process capability $($Cp$,$ Cpk$)?($Hint: $\backslash$sigma and x$-$bar is the standard deviation and mean calculated from the sample, use five decimal points$)$