Use the information below to answer questions $14$ to $19.$

The thickness, in mm$,$ of metal washers is measured on samples of size $5.$ The following table

presents the means, ranges and standard deviations for $20$ consecutive samples.

$5$

$14.$ Compute the LCL limits for the R$-$chart.

$15.$ Compute the UCL limits for the R$-$chart.

$16.$ Is the process in control $($R$-$chart$)?$ If it is not, when is it first detected to be out of control?

a$.$ The process is in control

b$.$ The process is out of control for the first time on sample $8$

c$.$ The process is out of control for the first time on sample $7$

d$.$ The process is out of control in samples $17$ and $20$ respectively

$17.$ Compute the LCL limits for the X$-$bar chart.

$18.$ Compute the UCL limits for the X$-$bar chart.

$19.$ Is the process in control $($X$-$bar chart$)?$ If it is not, when is it first detected to be out of control?

a$.$ The process is in control

b$.$ The process is out of control for the first time on sample $8$

c$.$ The process is out of control for the first time on sample $7$

d$.$ The process is out of control in samples $17$ and $20$ respectively

The means are $\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})=2\mathrm{.}505\frac{,}{b}ar(R)=0\mathrm{.}1395,$ and $\frac{?}{\text{b}\text{a}\text{r}}(s)=0\mathrm{.}057.$