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

$1$

$3\mathrm{.}25"$

$0\mathrm{.}71"$

$7$

$3\mathrm{.}05"$

$0\mathrm{.}48"$

$13$

$3\mathrm{.}01"$

$0\mathrm{.}85"$

$19$

$4\mathrm{.}51"$

$1\mathrm{.}61"$

$2$

$3\mathrm{.}20$

$1\mathrm{.}23$

$8$

$2\mathrm{.}65$

$1\mathrm{.}08$

$14$

$2\mathrm{.}73$

$1\mathrm{.}36$

$20$

$2\mathrm{.}99$

$1\mathrm{.}14$

$3$

$3\mathrm{.}22$

$1\mathrm{.}38$

$9$

$3\mathrm{.}12$

$0\mathrm{.}66$

$15$

$3\mathrm{.}02$

$1\mathrm{.}06$

$21$

$2\mathrm{.}65$

$1\mathrm{.}08$

$4$

$3\mathrm{.}49$

$1\mathrm{.}21$

$10$

$2\mathrm{.}85$

$1\mathrm{.}33$

$16$

$2\mathrm{.}94$

$0\mathrm{.}45$

$22$

$3\mathrm{.}18$

$0\mathrm{.}41$

$5$

$3\mathrm{.}07$

$1\mathrm{.}12$

$11$

$2\mathrm{.}83$

$1\mathrm{.}12$

$17$

$2\mathrm{.}76$

$1\mathrm{.}38$

$23$

$2\mathrm{.}84$

$1\mathrm{.}63$

$6$

$2\mathrm{.}96$

$0\mathrm{.}42$

$12$

$3\mathrm{.}07$

$0\mathrm{.}40$

$18$

$2\mathrm{.}74$

$1\mathrm{.}24$

$24$

$2\mathrm{.}54$

$0\mathrm{.}97$

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$).$