A new machine has just been installed to cut and rough$-$shape large slugs. The slugs are then transferred to a precision grinder. One of the critical measurements is the outside diameter. The quality control inspector randomly selected five slugs each half$-$hour, measured the outside diameter, and recorded the results. The sample standard deviation is $\mathrm{.}557.$ The measurements $($in millimeters$)$ for the period $8$:$00$ A$.$M$.$ to $10$:$30$ A$.$M are:

Slug Outside Diameter $($millimeters$)$

Time $12345$

$8$:$0087\mathrm{.}187\mathrm{.}387\mathrm{.}987\mathrm{.}087\mathrm{.}0$

$8$:$3086\mathrm{.}988\mathrm{.}587\mathrm{.}687\mathrm{.}587\mathrm{.}4$

$9$:$0087\mathrm{.}588\mathrm{.}486\mathrm{.}987\mathrm{.}688\mathrm{.}2$

$9$:$3086\mathrm{.}088\mathrm{.}087\mathrm{.}287\mathrm{.}687\mathrm{.}1$

$10$:$0087\mathrm{.}187\mathrm{.}187\mathrm{.}187\mathrm{.}187\mathrm{.}1$

$10$:$3088\mathrm{.}086\mathrm{.}287\mathrm{.}487\mathrm{.}387\mathrm{.}8$

$1.$ Calculate the Mean and Range control chart UCL and LCL$.$

$2.$ Develop the Mean and Range charts and indicate whether each show a process in control or not in control.