A Quality Analyst Wants to Construct a Sample Mean Chart

question 148

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:

Rate of Interest

The percentage of a sum of money charged for its use, often expressed annually.

Compounded Semi-Annually

Interest on an investment or loan calculated twice a year and then added to the principal amount, affecting future interest calculations.

Retirement Plan

A financial strategy designed to help individuals save and invest money to provide for financial security in their retirement years.

Single Investment

A one-time contribution of funds to a particular investment vehicle.