Problem $10-22($Algo$)$

C$-$Spec, Incorporated is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of $2+-0\mathrm{.}08$ inche. After a trial run on this machine, C$-$Spec has determined that the machine has a sample mean of $2\mathrm{.}000$ inches with a standard deviation of $0\mathrm{.}010$ inch.

a$.$ Calculate the $(C_{pk})$ for this machine. Note: Round your answer to $3$ decimal places.

Capability Index

b$.$ Should C$-$Spec use this machine to produce this part?

No

Yes