$($Q$1)$: Use the following data set:

Sample $1$: $5\mathrm{.}0,5\mathrm{.}3,5\mathrm{.}0$

Sample $2$: $5\mathrm{.}0,5\mathrm{.}3,5\mathrm{.}0$

Sample $3$:$5\mathrm{.}2,5\mathrm{.}2,5\mathrm{.}2$

Sample $4$:$5\mathrm{.}2,5\mathrm{.}2,5\mathrm{.}2$

Sample $5$:$5\mathrm{.}0,5\mathrm{.}3,5\mathrm{.}0$

Sample $6$:$5\mathrm{.}2,5\mathrm{.}2,5\mathrm{.}2$

$($a$)$ Draw an X$-$bar chart. Where is the center line? Assume A$2=0\mathrm{.}483.$ Report the UCL and LCL$.$

$($b$)$ Draw an $R$ chart. Assume D$3=0\mathrm{.}1,D4=2.$ Where are the center line and the UCL and LCL for this R chart?

$($c$)$ Is the process mean under control $?$ Explain your answer.

$($d$)$ Is the process variation under control $?$ Explain your answer.