Day Mean Xbar $($mm$)$ Range R $($mm$)$

$1154\mathrm{.}94\mathrm{.}0$

$2151\mathrm{.}24\mathrm{.}4$

$3151\mathrm{.}63\mathrm{.}9$

$4157\mathrm{.}55\mathrm{.}0$

$5158\mathrm{.}64\mathrm{.}7$

Question content area

Part $1$

Refer to Table S$6\mathrm{.}1-$ Factors for Computing Control Chart Limits $(3$ sigma$)$LOADING$...$ for this problem.

Auto pistons at Wenming$$ Chung's plant in Shanghai are produced in a forging$$ process, and the diameter is a critical factor that must be controlled. From sample sizes of $10$ pistons produced each$$ day, the mean and the range of this diameter have been as$$ follows:

$$

Day

Mean Bold x overbar

$($mm$)$

Range R

$($mm$)$

$1$

$154\mathrm{.}9$

$4\mathrm{.}0$

$2$

$151\mathrm{.}2$

$4\mathrm{.}4$

$3$

$151\mathrm{.}6$

$3\mathrm{.}9$

$4$

$157\mathrm{.}5$

$5\mathrm{.}0$

$5$

$158\mathrm{.}6$

$4\mathrm{.}7$

Part $2$

$$a$)$ What is the value of x double overbar$?$

x double overbarequals

select: $154\mathrm{.}76$

$154\mathrm{.}76$ mm $($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ What is the value of Upper R overbar$?$

Upper R overbarequals

$$

$4\mathrm{.}4$ mm $($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ What are the UCL Subscript x overbar and LCL Subscript x overbar using $3-$sigma$?$

Upper Control Limit $($UCL Subscript x overbar$)=$

select mm $($round y