A Quality Analyst Wants to Construct a Sample Mean Chart

question 6

Essay

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that when the process is operating as intended, packaging weight is normally distributed with a mean of twenty ounces, and a process standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below.
$$\begin{array} { | l | l | l | l | l | } \hline& { \text { Weight } } \\\hline \text { Day } & \text { Package 1 } & \text { Package 2 } & \text { Package 3 } & \text { Package 4 } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\hline \text { Tuesday } & 23 & 21 & 19 & 21 \\\hline \text { Wednesday } & 20 & 19 & 20 & 21 \\\hline \text { Thursday } & 18 & 19 & 20 & 19 \\\hline \text { Friday } & 18 & 20 & 22 & 20 \\\hline\end{array}$$
(a) If he sets an upper control limit of 21 and a lower control limit of 19 around the target value of twenty ounces, what is the probability of concluding that this process is out of control when it is actually in control?
(b) With the UCL and LCL of part a, what do you conclude about this process-is it in control?

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Definitions:

Global Basis

A perspective or action at the worldwide level, considering global impact rather than local or national alone.

Least Amount

The minimal quantity or degree of something required or present.

Canada

Canada is a country in North America, known for its vast landscapes, multicultural cities, and as a member of the Commonwealth, with a parliamentary democracy and a constitutional monarchy.

Water

A transparent, tasteless, odorless, and nearly colorless chemical substance, essential for all known forms of life, and the most widely used solvent.