Given the following process control data for a normally distributed quality variable (three samples of size four each): $$\begin{array} { r}
{ \text { Measurements } } \
\begin{array} { l l l l l }
\text { Machine } &\
\hline \# 1 & 15 & 14 & 15 & 12 \
\# 2 & 18 & 16 & 20 & 16 \
\# 3 & 16 & 17 & 16 & 17
\end{array}\end{array}$$ If the process is known to have a mean of 15 and a standard deviation of 3, using three-sigma control limits, do any of the sample means indicate an out-of-control process mean?

Question

Given the following process control data for a normally distributed quality variable (three samples of size four each): $$\begin{array} { r} 
 { \text { Measurements } } \
\begin{array} { l l l l l } 
\text { Machine } &\
\hline \# 1 & 15 & 14 & 15 & 12 \
\# 2 & 18 & 16 & 20 & 16 \
\# 3 & 16 & 17 & 16 & 17
\end{array}\end{array}$$ If the process is known to have a mean of 15 and a standard deviation of 3, using three-sigma control limits, do any of the sample means indicate an out-of-control process mean?

Quizplus · Accepted Answer

The Answer of Given the following process control data for a normally distributed quality variable (three samples of size four each): $$\begin{array} { r} 
 { \text { Measurements } } \
\begin{array} { l l l l l } 
\text { Machine } &\
\hline \# 1 & 15 & 14 & 15 & 12 \
\# 2 & 18 & 16 & 20 & 16 \
\# 3 & 16 & 17 & 16 & 17
\end{array}\end{array}$$ If the process is known to have a mean of 15 and a standard deviation of 3, using three-sigma control limits, do any of the sample means indicate an out-of-control process mean?

Given the Following Process Control Data for a Normally Distributed