A process that is considered to be in control measures an ingredient in grams. Below are the last $10$ samples$($each of size nequals$5)$ taken. The population standard deviation is $1\mathrm{.}36.$

$$

Samples

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$10$

$11$

$13$

$10$

$11$

$9$

$9$

$13$

$8$

$9$

$10$

$9$

$9$

$10$

$10$

$10$

$11$

$15$

$7$

$11$

$9$

$12$

$9$

$10$

$10$

$8$

$10$

$7$

$11$

$9$

$9$

$11$

$9$

$9$

$10$

$13$

$9$

$11$

$12$

$8$

$11$

$10$

$10$

$11$

$11$

$9$

$10$

$7$

$10$

$13$

LOADING... Click the icon to view the table of control chart constants Upper A $2,$ Upper D $4,$ Upper D $3.$

Part $2$

$$a$)$ What is the process standard deviation sigma$?$ What is sigma Subscript x overbar$?$

The process standard deviation is

$$

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

Part $3$

Standard deviation of the sampling meansequals

$$

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

Part $4$

$$b$)$ With zequals$3,$ the control limits for the mean chart$$ are:

UCL Subscript x overbarequals

$$

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

Part $5$

LCL Subscript x overbarequals

$$

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

Part $6$

$$c$)$ The control limits for the$$ R$-$chart are:

UCL Subscript Upper Requals

$$

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

Part $7$

LCL Subscript Upper Requals

$$

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

Part $8$

$$d$)$ Based on the x overbar$-$chart, the process is

$$

OUT OF CONTROL

IN CONTROL

$.$

Part $9$

Based on the$$ R$-$chart, the process is

$$

OUT OF CONTROL

IN CONTROL

$.$

Part $10$

Based on both the x overbar$-$chart and the$$ R$-$chart, the process is

$$

OUT OF CONTROL

IN CONTROL

$.$