Factors for Calculating Three$-$Sigma Limits for the Chart and R$-$Chart. Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Calculate control limits for a chart that will monitor performance to target. The correct control limits as $($LCL$,$UCL$)$ are: chart attached $\backslash$table$[[\backslash$table$[[$Size of$],[$Sample$],[($n$)]],\backslash$table$[[$Factor for UCL$],[$and LCL for$],[$x$-$bar$-$Charts$],[$A$\_(2)]],\backslash$table$[[$Factor for$],[$LCL for$],[$R$-$Charts$],[$D$\_(3)]],\backslash$table$[[$Factor for$],[$UCL for$],[$R$-$Charts$],[$D$\_(4)]]],[2,1\mathrm{.}880,0,3\mathrm{.}267],[3,1\mathrm{.}023,0,2\mathrm{.}575],[4,0\mathrm{.}729,0,2\mathrm{.}282],[5,0\mathrm{.}577,0,2\mathrm{.}115],[6,0\mathrm{.}483,0,2\mathrm{.}004],[7,0\mathrm{.}419,0\mathrm{.}076,1\mathrm{.}924],[8,0\mathrm{.}373,0\mathrm{.}136,1\mathrm{.}864],[9,0\mathrm{.}337,0\mathrm{.}184,1\mathrm{.}816],[10,0\mathrm{.}308,0\mathrm{.}223,1\mathrm{.}777]]$

Question $1$ options:

A$)(69\mathrm{.}84,73\mathrm{.}14)$

B$)(65\mathrm{.}94,74\mathrm{.}83)$

C$)(62\mathrm{.}28,73\mathrm{.}31)$

D$)(68\mathrm{.}94,74\mathrm{.}89)$

E$)(66\mathrm{.}80,74\mathrm{.}05)$