The Table Below Shows the Data from Samples of Size $n=5$

Essay

The table below shows the data from samples of size $n=5$ randomly chosen from the outputs of a process on 20 different days. Assume the specification limits are USL $=2.1$ and $\mathrm{LSL}=5.7$ .


$\begin{array}{cccccc}\hline \text { Sample } & & {\text { Data }} \\\hline 1 & 4.5 & 2.1 & 5.4 & 2.7 & 4.5 \\2 & 3.6 & 3.5 & 6.1 & 4.9 & 4.2 \\3 & 5.1 & 6.2 & 2.4 & 3.7 & 5.1 \\4 & 4.9 & 5.4 & 3.5 & 5.4 & 3.7 \\5 & 4.1 & 3.8 & 3.8 & 4.6 & 4.9 \\6 & 3.7 & 4.6 & 4.8 & 4.2 & 5.2 \\7 & 5.6 & 4.7 & 4.1 & 5.1 & 3.1 \\8 & 4.8 & 5.1 & 4.3 & 4.6 & 2.7 \\9 & 6.1 & 4.6 & 4.7 & 3.8 & 4.2 \\10 & 2.4 & 4.8 & 5.6 & 4.1 & 4.8 \\11 & 3.7 & 5.3 & 2.9 & 4.7 & 6.3 \\12 & 4.5 & 3.4 & 3.4 & 5.2 & 4.5 \\13 & 5.2 & 2.7 & 5.1 & 6.2 & 2.9 \\14 & 3.4 & 5.5 & 4.6 & 2.4 & 3.4 \\15 & 4.8 & 3.6 & 4.8 & 4.4 & 4.6 \\16 & 4.1 & 4.6 & 4.9 & 4.9 & 4.3 \\17 & 4.6 & 3.7 & 3.5 & 3.7 & 5.2 \\18 & 5.1 & 4.2 & 5.6 & 4.1 & 5.7 \\19 & 3.7 & 4.8 & 4.9 & 2.3 & 4.5 \\20 & 5.4 & 3.9 & 4.2 & 5.4 & 4.3 \\\hline\end{array}$
a. Assuming the process is under control, construct a capability analysis diagram for the process.
b. Find the percentage of data items that fall outside the specification limits.
c. Is the process capable? Support your answer with a numerical measure of capability.