HW$-7-$Part$-2-$CH $10(8$ pts$)$ The diameter of a shaft used to connect two sections of the shell of a microcomputer is designed to be $50$ millimeters. Twenty$-$five samples, each of which has $4$ separate measures, were taken directly from the process of producing the shafts. $($Please calculate four decimal places$)\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}\backslash$hline Sample Number & Observation $1$ & Observation $2$ & Observation $3$ & Observation $4\backslash \backslash \backslash$hline $1$ & $49$ & $47$ & $52$ & $48\backslash \backslash \backslash$hline $2$ & $48$ & $48$ & $54$ & $49\backslash \backslash \backslash$hline $3$ & $49$ & $49$ & $51$ & $47\backslash \backslash \backslash$hline $4$ & $47$ & $47$ & $50$ & $51\backslash \backslash \backslash$hline $5$ & $51$ & $51$ & $57$ & $52\backslash \backslash \backslash$hline $6$ & $52$ & $54$ & $54$ & $54\backslash \backslash \backslash$hline $7$ & $54$ & $57$ & $45$ & $57\backslash \backslash \backslash$hline $8$ & $51$ & $52$ & $49$ & $53\backslash \backslash \backslash$hline $9$ & $52$ & $51$ & $42$ & $54\backslash \backslash \backslash$hline $10$ & $54$ & $52$ & $41$ & $51\backslash \backslash \backslash$hline $11$ & $49$ & $45$ & $48$ & $52\backslash \backslash \backslash$hline $12$ & $48$ & $47$ & $45$ & $50\backslash \backslash \backslash$hline $13$ & $47$ & $49$ & $51$ & $54\backslash \backslash \backslash$hline $14$ & $52$ & $51$ & $54$ & $49\backslash \backslash \backslash$hline $15$ & $54$ & $50$ & $43$ & $48\backslash \backslash \backslash$hline $16$ & $55$ & $47$ & $42$ & $49\backslash \backslash \backslash$hline $17$ & $54$ & $46$ & $48$ & $46\backslash \backslash \backslash$hline $18$ & $51$ & $44$ & $46$ & $47\backslash \backslash \backslash$hline $19$ & $52$ & $41$ & $51$ & $51\backslash \backslash \backslash$hline $20$ & $49$ & $49$ & $50$ & $52\backslash \backslash \backslash$hline $21$ & $48$ & $48$ & $54$ & $46\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}\backslash$hline $22$ & $47$ & $52$ & $55$ & $52\backslash \backslash \backslash$hline $23$ & $51$ & $57$ & $52$ & $50\backslash \backslash \backslash$hline $24$ & $50$ & $52$ & $52$ & $51\backslash \backslash \backslash$hline $25$ & $51$ & $50$ & $49$ & $51\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}$ Suppose the standard deviation of the shaft diameter used to connect two sections of a microcomputer case is $2\mathrm{.}65$ millimeters. $1.$ Determine the Upper Control Limit $($UCL$)(1\mathrm{.}5$ pts $)2.$ Determine the Lower Control Limit $($LCL$)(1\mathrm{.}5$ pts $)3.$ Calculate the sample mean $(\backslash (\backslash$hat$\{$h$\})\backslash )?(1$ pts$)4.$ Draw the control chart and determine if the production process is in control or out of control. $(4$ pts$)$