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

Your$$ supervisor, Lisa$$ Lehmann, has asked that you report on the output of a machine on the factory floor. This machine is supposed to be producing optical lenses with a mean weight of $50$ grams and a range of $3\mathrm{.}5$ grams. The following table contains the data for a sample size of n$6$ taken during the past $3$ hours:

$$

Sample

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$55$

$47$

$49$

$50$

$52$

$57$

$55$

$48$

$51$

$56$

R

$3$

$1$

$5$

$3$

$2$

$6$

$3$

$2$

$2$

$3$

Part $2$

Set the control limits for this process for the $-$chart when the machine is working properly.

$$

enter your response here grams $($round your response to two decimal$$ places$).$

Part $3$

$$

enter your response here grams $($round your response to two decimal$$ places$).$

Part $4$

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

A$.$

$0$

$4$

$8$

$12$

$45\mathrm{.}00$

$50\mathrm{.}00$

$55\mathrm{.}00$

$60\mathrm{.}00$

Sample

Adjustable weight in grams

x y graph

B$.$

$0$

$4$

$8$

$12$

$45\mathrm{.}00$

$50\mathrm{.}00$

$55\mathrm{.}00$

$60\mathrm{.}00$

Sample

Adjustable weight in grams

x y graph

C$.$

$0$

$4$

$8$

$12$

$45\mathrm{.}00$

$50\mathrm{.}00$

$55\mathrm{.}00$

$60\mathrm{.}00$

Sample

Adjustable weight in grams

x y graph

Part $5$

Set control limits for this process for the$$ R$-$chart.

$$

enter your response here grams $($round your response to two decimal$$ places$).$

Part $6$

$$

enter your response here grams $($round your response to two decimal$$ places$).$

Part $7$

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

A$.$

$0$

$4$

$8$

$12$

$0\mathrm{.}00$

$2\mathrm{.}00$

$4\mathrm{.}00$

$6\mathrm{.}00$

$8\mathrm{.}00$

Sample

Adjustable weight in grams

x y graph

B$.$

$0$

$4$

$8$

$12$

$0\mathrm{.}00$

$2\mathrm{.}00$

$4\mathrm{.}00$

$6\mathrm{.}00$

$8\mathrm{.}00$

Sample

Adjustable weight in grams

x y graph

C$.$

$0$

$4$

$8$

$12$

$0\mathrm{.}00$

$2\mathrm{.}00$

$4\mathrm{.}00$

$6\mathrm{.}00$

$8\mathrm{.}00$

Sample

Adjustable weight in grams

x y graph

Part $8$

Has the process been in$$ control?

No

Yes