An injection molding process has been designed to produce a target tolerance of $1\mathrm{.}000+0\mathrm{.}010.$ After running a sample of $50$ parts, it is found that the parts have a mean dimension of $0\mathrm{.}996$ with a sample standard deviation of $0\mathrm{.}0025.$

a$)$ What is the Cp and Cpk for this process?

b$)$ Is the process capable? Why or Why not?

c$)$ Is the process centered? Why or Why not?