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

Question 10

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


 Sample  Data 14.52.15.42.74.523.63.56.14.94.235.16.22.43.75.144.95.43.55.43.754.13.83.84.64.963.74.64.84.25.275.64.74.15.13.184.85.14.34.62.796.14.64.73.84.2102.44.85.64.14.8113.75.32.94.76.3124.53.43.45.24.5135.22.75.16.22.9143.45.54.62.43.4154.83.64.84.44.6164.14.64.94.94.3174.63.73.53.75.2185.14.25.64.15.7193.74.84.92.34.5205.43.94.25.44.3\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.

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