A process in being evaluated for stability using X bar R chart. The sample size is $4$ and sampling frequency is $2$ hours. No of subgroups taken for calculation of control limits are $15.$ The Grand Average is $100$ and Average Range is $7.$ What are the control limits for X bar and R chart $?$

A

UCL x$-$bar $=121$ LCL x$-$bar $=79$ UCL R $=21$ LCL R $=0$

B

UCL x$-$bar $=105\mathrm{.}10$ LCL x$-$bar $=94\mathrm{.}89$ UCL R $=15\mathrm{.}97$ LCL R $=0$

C

UCL x$-$bar $=101\mathrm{.}56$ LCL x$-$bar $=98\mathrm{.}439$ UCL R $=11\mathrm{.}57$ LCL R $=2\mathrm{.}43$

D

UCL x$-$bar $=114$ LCL x$-$bar $=86$ UCL R $=14$ LCL R $=3\mathrm{.}5$