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 $1010$ pistons produced each$$ day, the mean and the range of this diameter have been as$$ follows:

$$

Day

Mean Bold x overbarx

$($mm$)$

Range R

$($mm$)$

$1$

$158\mathrm{.}9158\mathrm{.}9$

$4\mathrm{.}04\mathrm{.}0$

$2$

$151\mathrm{.}2151\mathrm{.}2$

$4\mathrm{.}64\mathrm{.}6$

$3$

$151\mathrm{.}6151\mathrm{.}6$

$4\mathrm{.}34\mathrm{.}3$

$4$

$155\mathrm{.}5155\mathrm{.}5$

$5\mathrm{.}05\mathrm{.}0$

$5$

$156\mathrm{.}6156\mathrm{.}6$

$4\mathrm{.}74\mathrm{.}7$

Part $2$

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

x double overbarxequals$=$enter your response here mm $($round your response to two decimal$$ places$).$