Problem pts$]$

Three samples, each consisting of five units, have been measured. The results are recorded in the

following table:

$($a$)$ The table for finding the coefficient A$2$ is given below. Compute the upper control limit $($UCL$)$ and

the lower control limit $($LCL$)$ for the x $-$bar chart. Plot the x $-$bar chart. Is the process in control? $[10$ pts $]$

$($b$)$ The quality manager feels that the measure of item $1$ in Sample $3,$ which is recorded as $15,$ is a little

unusual. He plots this measure of $15$ on the x$-$bar chart constructed in $($a$),$ and observes that this

measure is indeed out of the upper control limit$.$ The manager then reports that the process is out of

control. Do you agree with his conclusion? Explain your reasoning concisely in one or two sentences. $[10$

pts$]$