C$-$Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of $3+-0\mathrm{.}05$ inches. After a trial run on this machine, C$-$Spec has determined that the machine has a sample mean of $3\mathrm{.}001$ inches with a standard deviation of $0\mathrm{.}030$ inch.

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

$0\mathrm{.}567$

$0\mathrm{.}544$

$0\mathrm{.}679$

$0\mathrm{.}468$