The intended width of a bronze bar is one$-$eight of an inch $(0\mathrm{.}125$ inches$).$ Inspection samples contain $4$ rods each. The average range of the samples is $0\mathrm{.}01$ inches. What are the $3-$sigma upper and lower control limits for the mean of this process?

a$.0\mathrm{.}0354$ and $0\mathrm{.}0004$

b$.0\mathrm{.}3750$ and $0\mathrm{.}0413$

c$.0\mathrm{.}1323$ and $0\mathrm{.}1177$

d$.0\mathrm{.}8954$ and $4\mathrm{.}8759$