Refer to the table Factors for Computing Control Chart Limits $(3$ sigma$)$

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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 size

equals

$=$

$4$

$4.$

$$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

$20\mathrm{.}2$

$20\mathrm{.}2$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}8$

$19\mathrm{.}8$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}8$

$19\mathrm{.}8$

$19\mathrm{.}6$

$19\mathrm{.}6$

$20\mathrm{.}2$

$20\mathrm{.}2$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}0$

$20\mathrm{.}0$

$19\mathrm{.}9$

$19\mathrm{.}9$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}9$

$19\mathrm{.}9$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}8$

$19\mathrm{.}8$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}9$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}8$

$19\mathrm{.}8$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}3$

$20\mathrm{.}3$

$19\mathrm{.}8$

$19\mathrm{.}8$

$19\mathrm{.}7$

$19\mathrm{.}7$

$20\mathrm{.}0$

$20\mathrm{.}0$

$20\mathrm{.}3$

$20\mathrm{.}3$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}7$

$19\mathrm{.}7$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}8$

$19\mathrm{.}8$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}0$

$20\mathrm{.}0$

$19\mathrm{.}7$

$19\mathrm{.}7$

$19\mathrm{.}9$

$19\mathrm{.}9$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$20\mathrm{.}1$

$19\mathrm{.}8$

$19\mathrm{.}8$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}6$

$19\mathrm{.}6$

$19\mathrm{.}9$

$19\mathrm{.}9$

$19\mathrm{.}7$

$19\mathrm{.}7$

$19\mathrm{.}8$

$19\mathrm{.}8$

$19\mathrm{.}4$

$19\mathrm{.}4$

$19\mathrm{.}9$

$19\mathrm{.}9$

$20\mathrm{.}2$

$20\mathrm{.}2$

Part $2$

$$a$)$ What are the control limits for the mean$$ chart?

UCL Subscript x overbar

UCLx

equals

$=$

enter your response here

ounces $($round your response to two decimal$$ places$).$