Refer to the table Factors for Computing Control Chart Limits $(3$ sigma$)$LOADING$...$ for this problem.

A process at Amit Eynan Bottling Company that is considered in control measures liquid in ounces. Below are the last $12$ samples taken. The sample sizeequals$4.$

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$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

$20\mathrm{.}2$

$19\mathrm{.}9$

$19\mathrm{.}8$

$20\mathrm{.}1$

$19\mathrm{.}8$

$19\mathrm{.}7$

$20\mathrm{.}2$

$20\mathrm{.}1$

$20\mathrm{.}0$

$19\mathrm{.}9$

$20\mathrm{.}1$

$19\mathrm{.}9$

$20\mathrm{.}1$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}9$

$20\mathrm{.}1$

$19\mathrm{.}6$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}9$

$19\mathrm{.}8$

$20\mathrm{.}1$

$19\mathrm{.}4$

$19\mathrm{.}8$

$19\mathrm{.}7$

$20\mathrm{.}0$

$19\mathrm{.}9$

$20\mathrm{.}1$

$19\mathrm{.}7$

$19\mathrm{.}9$

$19\mathrm{.}8$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}8$

$19\mathrm{.}7$

$19\mathrm{.}9$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}8$

$19\mathrm{.}9$

$19\mathrm{.}4$

$19\mathrm{.}9$

$19\mathrm{.}7$

$19\mathrm{.}8$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}8$

Part $2$

$$a$)$ Set control limits for this process for the x overbar$-$chart.