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?

---

Definitions:

Relaxation

Techniques or activities designed to reduce tension or stress, promoting a state of calm and easing psychological or physical strain.

Exercise

A physical activity intended to improve health and fitness.

Biofeedback

is a treatment technique that teaches individuals to control physiological processes, such as heart rate or muscle tension, through real-time feedback from monitoring devices.

Problem Solving

A cognitive process aimed at resolving a challenge or finding a solution to a complex situation through analytical thinking and decision-making strategies.