PCDrives has a manufacturing process that is normally distributed and has the sample means and ranges for 15 samples of size 5, found in the worksheet Q4 in the HW3Data.xlsx file. Note that only sample statistics have been given, instead of the raw data from the samples. (1) Estimate the standard deviation of the process; (0.25 points) (2) Suppose specifications are determined to be 70 25. Determine the process capability indices by using the estimated standard deviation in (1). (0.25 points) (3) Under the same specifications given in (2), and under the assumption that the process is normally distributed, what percentage of the process output will be out of specification? (0.25 points) (4) Conduct a SPC analysis, and conclude if the process is in control. What conclusions can you make based on the SPC analysis and process capability study? (0.25 points)

\begin{tabular}{|c|c|c|c|c} \hline & A & B & C & D \\ \hline 1 & PCDrives & & & \\ \hline 2 & & & & \\ \hline 3 & Sample & x-bar & R & \\ \hline 4 & 1 & 77.4 & 18.3 & \\ \hline 5 & 2 & 60.2 & 20.1 & \\ \hline 6 & 3 & 63.5 & 22.6 & \\ \hline 7 & 4 & 64.0 & 27.5 & \\ \hline 8 & 5 & 58.4 & 15.3 & \\ \hline 9 & 6 & 74.4 & 17.9 & \\ \hline 10 & 7 & 70.8 & 26.8 & \\ \hline 11 & 8 & 74.6 & 30.6 & \\ \hline 12 & 9 & 77.3 & 19.2 & \\ \hline 13 & 10 & 65.7 & 14.6 & \\ \hline 14 & 11 & 63.4 & 24.5 & \\ \hline 15 & 12 & 76.6 & 21.7 & \\ \hline 16 & 13 & 71.7 & 25.5 & \\ \hline 17 & 14 & 70.9 & 29.7 & \\ \hline 18 & 15 & 59.6 & 14.5 & \\ \hline 19 & & & & \\ \hline \end{tabular}