a. Find the upper control limit

b. Find the lower control limit

\begin{tabular}{cccc} Sample & Mean Factor, & Upper Range, & Lower Range, \\ Size, n & A2 & D4 & D3 \\ \hline 2 & 1.880 & 3.268 & 0 \\ 3 & 1.023 & 2.574 & 0 \\ 4 & 0.729 & 2.282 & 0 \\ 5 & 0.577 & 2.115 & 0 \\ 6 & 0.483 & 2.004 & 0 \\ 7 & 0.419 & 1.924 & 0.076 \\ 8 & 0.373 & 1.864 & 0.136 \\ 9 & 0.337 & 1.816 & 0.184 \\ 10 & 0.308 & 1.777 & 0.223 \\ 12 & 0.266 & 1.716 & 0.284 \\ \hline \end{tabular} 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: \begin{tabular}{ccc|ccc|ccc|ccc} \hline Hour & x & R & Hour & x & R & Hour & x & R & Hour & x & R \\ \hline 1 & 3.15" & 0.71" & 7 & 2.95" & 0.58" & 13 & 3.01" & 0.80" & 19 & 3.31" & 1.56" \\ 2 & 3.20 & 1.13 & 8 & 2.55 & 1.13 & 14 & 2.83 & 1.31 & 20 & 2.89 & 1.14 \\ 3 & 3.32 & 1.48 & 9 & 2.92 & 0.76 & 15 & 3.12 & 1.01 & 21 & 2.75 & 1.13 \\ 4 & 3.39 & 1.21 & 10 & 2.75 & 1.28 & 16 & 2.94 & 0.55 & 22 & 3.38 & 0.46 \\ 5 & 2.97 & 1.22 & 11 & 2.73 & 1.17 & 17 & 2.96 & 1.43 & 23 & 2.84 & 1.53 \\ 6 & 2.86 & 0.42 & 12 & 3.07 & 0.45 & 18 & 2.74 & 1.29 & 24 & 2.64 & 1.02 \\ \hline \end{tabular} Based on the sampling done, the control limits for 3-sigma x chart are (round all intermediate calculations to three decimal places before proceeding with further calculations)