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

Sampling $4$ pieces of$$ precision$-$cut wire$($to be used in computer$$ assembly$)$ every hour for the past $24$ hours has produced the following$$ results:

$$

Hour

Bold x overbar

R

Hour

Bold x overbar

R

Hour

Bold x overbar

R

Hour

Bold x overbar

R

$1$

$3\mathrm{.}25"$

$0\mathrm{.}71"$

$7$

$3\mathrm{.}05"$

$0\mathrm{.}53"$

$13$

$3\mathrm{.}11"$

$0\mathrm{.}85"$

$19$

$3\mathrm{.}41"$

$1\mathrm{.}61"$

$2$

$3\mathrm{.}10$

$1\mathrm{.}18$

$8$

$2\mathrm{.}65$

$1\mathrm{.}13$

$14$

$2\mathrm{.}83$

$1\mathrm{.}31$

$20$

$2\mathrm{.}89$

$1\mathrm{.}09$

$3$

$3\mathrm{.}22$

$1\mathrm{.}43$

$9$

$3\mathrm{.}02$

$0\mathrm{.}71$

$15$

$3\mathrm{.}12$

$1\mathrm{.}06$

$21$

$2\mathrm{.}65$

$1\mathrm{.}08$

$4$

$3\mathrm{.}39$

$1\mathrm{.}26$

$10$

$2\mathrm{.}85$

$1\mathrm{.}33$

$16$

$2\mathrm{.}84$

$0\mathrm{.}50$

$22$

$3\mathrm{.}28$

$0\mathrm{.}46$

$5$

$3\mathrm{.}07$

$1\mathrm{.}17$

$11$

$2\mathrm{.}83$

$1\mathrm{.}17$

$17$

$2\mathrm{.}86$

$1\mathrm{.}43$

$23$

$2\mathrm{.}94$

$1\mathrm{.}58$

$6$

$2\mathrm{.}86$

$0\mathrm{.}32$

$12$

$2\mathrm{.}97$

$0\mathrm{.}40$

$18$

$2\mathrm{.}74$

$1\mathrm{.}29$

$24$

$2\mathrm{.}64$

$0\mathrm{.}97$

Based on the sampling$$ done, the control limits for $3-$sigma x overbar chart are $($round all intermediate calculations to three decimal places before proceeding with further $$calculations$)$:

Part $2$

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

$$

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