A Quality Analyst Wants to Construct a Sample Mean Chart $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Weight }$

question 94

Essay

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is two ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below.
$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Weight }$
$\begin{array}{|l|l|l|l|l|}\hline \text { Day } & \text { Package 1 } & \text { Package 2 } & \text { Package 3 } & \text { Package 4 } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\hline \text { Tuesday } & 23 & 21 & 19 & 21 \\\hline \text { Wednesday } & 20 & 19 & 20 & 21 \\\hline \text { Thursday } & 18 & 19 & 20 & 19 \\\hline \text { Friday } & 18 & 20 & 22 & 20\\\hline\end{array}$
(a) Calculate all sample means and the mean of all sample means.
(b) Calculate upper and lower control limits that allow for natural variations.
(c) Is this process in control?

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Definitions:

Inspiratory Reserve Volume

The additional amount of air that can be inhaled after a normal inhalation.

Expiratory Reserve Volume

The additional amount of air that can be forcibly exhaled after the completion of a normal, controlled exhalation.

Anatomic Dead Space

The portion of the respiratory system that conducts air but does not participate in gas exchange, including the nose, trachea, and bronchi.

Anatomic Dead Space

The portion of the respiratory system where gas exchange does not occur, including the trachea and bronchi.