$8\mathrm{.}7.$ A process is in control with $\stackrel{}{x}=100\frac{,}{b}ar(s)=1\mathrm{.}05,$ and $n=5.$ The process specifications are at $95+-10.$ The quality characteristic has a normal distribution.

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

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

$($c$)$ How much could the fallout in the process be reduced if the process were corrected to operate at the nominal specification?