A metal fabricator produces connecting rods with an outer diameter that has a $1\backslash$pm $0\mathrm{.}04$ inch specification.

A machine operator takes several sample measurements over time and determines the sample mean

outer diameter to be $1\mathrm{.}002$ inches with a standard deviation of $0\mathrm{.}009$ inch.

a$.$ Calculate the process capability index for this example. $($Round your answer to $3$ decimal places.$)$

b$.$ Is the process capable of producing the desired quality? Explain