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 one$-$inch pipe has a specification of $1-$inch plus or minus $0\mathrm{.}10$ inch. What is the process capability index $($Cp$)?$ Assume the process mean is centered?

a$.1\mathrm{.}33$

b$.1$

c$.0\mathrm{.}5$

d$.2$

e$.0\mathrm{.}67$