Q$1$: A process is in statistical control with $\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})=199$ and $\frac{?}{\text{b}\text{a}\text{r}}(R)=3\mathrm{.}5.$ The control chart uses a sample size of $n=4.$ Specifications are at $200+-8.$ The quality characteristic is normally distributed.

a$.$ Estimate the potential capability of the process. $Cp=$

$[1]$ Round to the hundredths place.

b$.$ Estimate the actual process capability. Cpk $=[2]$ Round to the hundredths place.

c$.$ How much improvement could be made in process performance $($meaning how much could we improve our fraction nonconforming to specifications$)$ if the mean could be centered at the nominal value? $($This is $P_{\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}^{-}$ Pimprovement