A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is in control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each: $$\begin{array} { l l c c l }
\text { Day } && { \text { Weight (ounces) } } \
\hline \text { Monday } & 23 & 22 & 23 & 24 \
\text { Tuesday } & 23 & 21 & 19 & 21 \
\text { Wednesday } & 20 & 19 & 20 & 21 \
\text { Thursday } & 18 & 19 & 20 & 19 \
\text { Friday } & 18 & 20 & 22 & 20
\end{array}$$
What is the mean of the sampling distribution of sample means when this process is in control?
A) 18 ounces
B) 19 ounces
C) 20 ounces
D) 21 ounces
E) 22 ounces

Question

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is in control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each: $$\begin{array} { l l c c l } 
\text { Day } && { \text { Weight (ounces) } } \
\hline \text { Monday } & 23 & 22 & 23 & 24 \
\text { Tuesday } & 23 & 21 & 19 & 21 \
\text { Wednesday } & 20 & 19 & 20 & 21 \
\text { Thursday } & 18 & 19 & 20 & 19 \
\text { Friday } & 18 & 20 & 22 & 20
\end{array}$$
What is the mean of the sampling distribution of sample means when this process is in control?
A) 18 ounces
B) 19 ounces
C) 20 ounces
D) 21 ounces
E) 22 ounces

Quizplus · Accepted Answer

When the process is in control, the package weight is normally distributed with a mean of 20 ounces and a standard deviation of 2 ounces. The sample size is 4.

The mean of the sampling distribution of sample means can be calculated using the formula: 
$\mu_{\bar{x}} = \mu = 20$

Therefore, the answer is C, 20 ounces.

A Quality Analyst Wants to Construct a Sample Mean Chart