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$)$

$1$

$156\mathrm{.}9$

$4\mathrm{.}4$

$2$

$151\mathrm{.}2$

$4\mathrm{.}6$

$3$

$151\mathrm{.}6$

$4\mathrm{.}3$

$4$

$153\mathrm{.}5$

$4\mathrm{.}8$

$5$

$158\mathrm{.}6$

$4\mathrm{.}5$

Part $2$

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

x double overbarequals

$$

enter your response here mm $($round your response to two