A process is in control with $x-$doublebar $=100$ and $s-$bar $=1\mathrm{.}05,$ and $n=5.$ The process specifications are at $95+-10.$ The quality characteristic has a normal distribution.

a$)$ Estimate the process capability ratio $(Cp=2\mathrm{.}98).$

b$)$ Estimate the process capability index $($long term; Cpk$=1\mathrm{.}49).$

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