The following data represents sample data of $6$ oz$.$ bottles of after$-$shave. Develop the X$-$bar and R control charts for the following sample. A process that is considered to be in control measures an ingredient in ounces. Below are the samples taken from the process. Assuming the population standard deviation $\backslash$sigma $=3.$

Sample $123456$ X$-$bar R

$16\mathrm{.}005\mathrm{.}906\mathrm{.}005\mathrm{.}906\mathrm{.}005\mathrm{.}90$

$26\mathrm{.}006\mathrm{.}006\mathrm{.}306\mathrm{.}046\mathrm{.}026\mathrm{.}00$

$35\mathrm{.}906\mathrm{.}006\mathrm{.}065\mathrm{.}906\mathrm{.}005\mathrm{.}90$

$46\mathrm{.}106\mathrm{.}005\mathrm{.}966\mathrm{.}006\mathrm{.}106\mathrm{.}02$

Average

a$)$ Fill in the above table.

b$)$ If Z $=2,$ what are the control limits for the mean chart?

c$)$ What are the control limits for the range chart?

d$)$ Is the process in control? Show your explanation.