The width of a gold bar is intended to be $0\mathrm{.}42$ cms$.$ Inspection samples contain six bars each. The average range of these samples is $0\mathrm{.}007$ cms$.$ Note: use $3-$sigma limits

a$)$ What is the lower x$-$bar control limit for this process?

b$)$ What is the upper x$-$bar control limit for this process?

c$)$ What is the lower R$-$chart control limit for this process?

d$)$ What is the upper R$-$chart control limit for this process?

NOTE: Answer with $4$ decimal places