$11.$ A capability study was conducted on a fin forming process for a height dimension. The engineering tolerance is $\mathrm{.}248-\mathrm{.}254$ for this Key Characteristic. The histogram for this process is shown below:

What is the Cp & Cpk given $\backslash$sigma $=\mathrm{.}0006?$ Show all work and formulae.

ANSWER: Cp $=\_\_\_\_\_\_\_$ Cpk $=\_\_\_\_\_\_\_$

From Problem $11$ above, what would the value of sigma$-$hat have to be in order to achieve a Cp $=1\mathrm{.}67$ for a $\mathrm{.}002$ total engineering tolerance band rather than the current $\mathrm{.}006$ total engineering tolerance band? $($This would result in eliminating several expensive operations if we could achieve holding this tighter tolerance band$).$ Round your answer to four decimal places.

ANSWER: $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$