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

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Samples

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$13$

$13$

$10$

$12$

$10$

$9$

$14$

$9$

$10$

$8$

$11$

$10$

$10$

$9$

$9$

$10$

$9$

$7$

$11$

$9$

$13$

$11$

$12$

$10$

$9$

$11$

$7$

$11$

$9$

$8$

$13$

$10$

$11$

$11$

$12$

$7$

$9$

$11$

$8$

$12$

$12$

$10$

$10$

$9$

$10$

$9$

$9$

$10$

$12$a$)$ Standard deviation of the sampling means$=\_\_\_\_$

$$

$\_\_\_\_$ounces $($round your response to three decimal$$ places$).$

Part $3$

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

UCL Subscript x overbar $=$

$$

$\_\_\_\_\_\_$ounces $($round your response to three decimal$$ places$).$

Part $4$

LCL Subscript x overbar $=$

$$

$\_\_\_\_$ ounces $($round your response to three decimal$$ places$).$

Part $5$

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

UCL Subscript Upper R $=$

$$

$\_\_\_\_$ ounces $($round your response to three decimal$$ places$).$

Part $6$

LCL Subscript Upper R $=$

$$

$\_\_\_$ ounces $($round your response to three decimal$$ places$).$

Part $7$

$$d$)$ Based on the x overbar$-$chart, is one or more samples beyond the control$$ limits$?$

YES or NO

$.$

Part $8$

Based on the$$ R$-$chart, is one or more samples beyond the control$$ limits$?$

YES or NO

$.$