Solve problem $8\mathrm{.}10$ on p$.405$ of your textbook. Note that the process fallout in part $c$ refers to the proportion of non$-$conforming items, and the nominal dimension is the target value. $(20$ points$)$

$8\mathrm{.}10.$ A process is in control with $\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})=75$ and $\frac{?}{\text{b}\text{a}\text{r}}(s)=2.$ The process specifications are at $80+-8.$ The sample size $n=5$

$($a$)$ Estimate the potential capability.

$($b$)$ Estimate the actual capability.

$($c$)$ How much could process fallout be reduced by shifting the mean to the nominal dimension? Assume that the quality characteristic is normally distributed.