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$=44.$

$$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

$20\mathrm{.}220\mathrm{.}2$

$19\mathrm{.}919\mathrm{.}9$

$19\mathrm{.}819\mathrm{.}8$

$20\mathrm{.}120\mathrm{.}1$

$19\mathrm{.}819\mathrm{.}8$

$20\mathrm{.}220\mathrm{.}2$

$20\mathrm{.}220\mathrm{.}2$

$20\mathrm{.}120\mathrm{.}1$

$20\mathrm{.}020\mathrm{.}0$

$19\mathrm{.}919\mathrm{.}9$

$20\mathrm{.}120\mathrm{.}1$

$19\mathrm{.}919\mathrm{.}9$

$20\mathrm{.}120\mathrm{.}1$

$20\mathrm{.}320\mathrm{.}3$

$19\mathrm{.}919\mathrm{.}9$

$19\mathrm{.}919\mathrm{.}9$

$20\mathrm{.}120\mathrm{.}1$

$20\mathrm{.}120\mathrm{.}1$

$20\mathrm{.}120\mathrm{.}1$

$20\mathrm{.}120\mathrm{.}1$

$19\mathrm{.}919\mathrm{.}9$

$19\mathrm{.}819\mathrm{.}8$

$20\mathrm{.}120\mathrm{.}1$

$20\mathrm{.}320\mathrm{.}3$

$19\mathrm{.}819\mathrm{.}8$

$19\mathrm{.}719\mathrm{.}7$

$20\mathrm{.}020\mathrm{.}0$

$19\mathrm{.}419\mathrm{.}4$

$20\mathrm{.}120\mathrm{.}1$

$19\mathrm{.}719\mathrm{.}7$

$19\mathrm{.}919\mathrm{.}9$

$19\mathrm{.}219\mathrm{.}2$

$20\mathrm{.}120\mathrm{.}1$

$20\mathrm{.}120\mathrm{.}1$

$19\mathrm{.}719\mathrm{.}7$

$19\mathrm{.}719\mathrm{.}7$

$19\mathrm{.}919\mathrm{.}9$

$20\mathrm{.}120\mathrm{.}1$

$20\mathrm{.}120\mathrm{.}1$

$19\mathrm{.}819\mathrm{.}8$

$19\mathrm{.}919\mathrm{.}9$

$19\mathrm{.}519\mathrm{.}5$

$19\mathrm{.}919\mathrm{.}9$

$19\mathrm{.}719\mathrm{.}7$

$19\mathrm{.}819\mathrm{.}8$

$19\mathrm{.}519\mathrm{.}5$

$19\mathrm{.}919\mathrm{.}9$

$20\mathrm{.}220\mathrm{.}2$

Part $2$

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

UCL Subscript x overbarUCLxequals$=20\mathrm{.}320\mathrm{.}3$ ounces $($round your response to two decimal$$ places$).$

Part $3$

LCL Subscript x overbarLCLxequals$=19\mathrm{.}5619\mathrm{.}56$ ounces $($round your response to two decimal$$ places$).$

Part $4$

Choose the correct graph of the sample data for the x overbarx$-$chart.

A$.$

$0$

$5$

$10$

$15$

$19\mathrm{.}00$

$19\mathrm{.}50$

$20\mathrm{.}00$

$20\mathrm{.}50$

$21\mathrm{.}00$

Sample

Adjustable weight in ounces

A coordinate system, with the horizontal axis, labeled Sample, ranges from $0$ to $15$ and has ticks for every $5$ units. The vertical axis, labeled Adjustable weight in ounces, ranges from $19\mathrm{.}00$ to $21\mathrm{.}00$ with ticks in increments of $00\mathrm{.}50.$ Two dashed horizontal lines and $12$ points are plotted on the graph. One of the horizontal line cuts the vertical axis at $20\mathrm{.}71$ and other horizontal line cuts the vertical axis at $19\mathrm{.}18.$ The points are plotted at $(1,19\mathrm{.}950),(2,20\mathrm{.}025),(3,19\mathrm{.}825),(4,19\mathrm{.}950),(5,19\mathrm{.}775),(6,20\mathrm{.}025),(7,19\mathrm{.}975),(8,19\mathrm{.}875),(9,19\mathrm{.}800),(10,19\mathrm{.}950),(11,20\mathrm{.}000),$ and $(12,20\mathrm{.}000).$

B$.$

$0$

$5$

$10$

$15$

$19\mathrm{.}00$

$19\mathrm{.}50$

$20\mathrm{.}00$

$20\mathrm{.}50$

$21\mathrm{.}00$

Sample

Adjustable weight in ounces

A coordinate system, with the horizontal axis, labeled Sample, ranges from $0$ to $15$ and has ticks for every $5$ units. The vertical axis, labeled Adjustable weight in ounces, ranges from $19\mathrm{.}00$ to $21\mathrm{.}00$ with ticks in increments of $00\mathrm{.}50.$ Two dashed horizontal lines and $12$ points are plotted on the graph. One of the horizontal line cuts the vertical axis at $20\mathrm{.}30$ and other horizontal line cuts the vertical axis at $19\mathrm{.}56.$ The points are plotted at $(1,20\mathrm{.}000),(2,20\mathrm{.}000),(3,19\mathrm{.}950),(4,19\mathrm{.}800),(5,19\mathrm{.}975),(6,19\mathrm{.}875),(7,20\mathrm{.}025),(8,19\mathrm{.}775),(9,19\mathrm{.}950),(10,19\mathrm{.}825),(11,19\mathrm{.}950),$ and $(12,20\mathrm{.}025).$

Your answer is correct.C$.$

$0$

$5$

$10$

$15$

$19\mathrm{.}00$

$19\mathrm{.}50$

$20\mathrm{.}00$

$20\mathrm{.}50$

$21\mathrm{.}00$

Sample

Adjustable weight in ounces

A coordinate system, with the horizontal axis, labeled Sample, ranges from $0$ to $15$ and has ticks for every $5$ units. The vertical axis, labeled Adjustable weight in ounces, ranges from $19\mathrm{.}00$ to $21\mathrm{.}00$ with ticks in increments of $00\mathrm{.}50.$ Two dashed horizontal lines and $12$ points are plotted on the graph. One of the horizontal line cuts the vertical axis at $20\mathrm{.}50$ and other horizontal line cuts the vertical axis at $19\mathrm{.}37.$ The points are plotted at $(1,20\mathrm{.}000),(2,20\mathrm{.}20),(3,20\mathrm{.}35),(4,19\mathrm{.}60),(5,20\mathrm{.}27),(6,19\mathrm{.}78),(7,20\mathrm{.}43),(8,19\mathrm{.}97),(9,20\mathrm{.}17),(10,20\mathrm{.}15),(11,20\mathrm{.}02),$ and $(12,20\mathrm{.}025).$

Part $5$

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

UCL Subscript Upper RUCLRequals$=$enter your response here ounces $($round your response to two decimal$$ places$).$