Studies on a machine that molds plastic water pipe indicate that when it is injecting $1-$inch$-$diameter pipe, the process standard deviation is $0\mathrm{.}05$ inches. The $1-$inch pipe has a specification of $1$ inch plus or minus $0\mathrm{.}10$ inch. What is the process capability index $($Cpk$)$ if the long$-$run process mean is $1$ inch?

Multiple Choice

$2\mathrm{.}20$

$0\mathrm{.}67$

$0\mathrm{.}50$

$1\mathrm{.}00$

$2\mathrm{.}00$