A process for filling liquid laundry detergent bottles monitors the volume in each bottle.The Operations Manager has taken 5 samples with 4 observations (bottles)in each sample to determine if the variation in volume is reasonable.The measurement unit is fluid ounces.Calculate the center line for a process control chart that indicates whether the variation within samples is reasonable (in a state of control). $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Bottle } & \text { Sarnple 1 } & \text { Sarnple 2 } & \text { Sarnple 3 } & \text { Sarnple 4 } & \text { Sarnple 5 } \
\hline 1 & 11.8 & 12.0 & 11.8 & 11.9 & 10.7 \
\hline 2 & 12.1 & 12.0 & 11.8 & 12.0 & 11.2 \
\hline 3 & 12.0 & 11.9 & 11.9 & 11.8 & 11.9 \
\hline 4 & 12.2 & 11.8 & 11.7 & 11.9 & 11.7 \
\hline
\end{array}$$
A)1.0
B)Between 0 and 1.0
C)Less than 0
D)There is not enough information to determine the correct response

Question

A process for filling liquid laundry detergent bottles monitors the volume in each bottle.The Operations Manager has taken 5 samples with 4 observations (bottles)in each sample to determine if the variation in volume is reasonable.The measurement unit is fluid ounces.Calculate the center line for a process control chart that indicates whether the variation within samples is reasonable (in a state of control). $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Bottle } & \text { Sarnple 1 } & \text { Sarnple 2 } & \text { Sarnple 3 } & \text { Sarnple 4 } & \text { Sarnple 5 } \
\hline 1 & 11.8 & 12.0 & 11.8 & 11.9 & 10.7 \
\hline 2 & 12.1 & 12.0 & 11.8 & 12.0 & 11.2 \
\hline 3 & 12.0 & 11.9 & 11.9 & 11.8 & 11.9 \
\hline 4 & 12.2 & 11.8 & 11.7 & 11.9 & 11.7 \
\hline
\end{array}$$
A)>1.0
B)Between 0 and 1.0
C)Less than 0
D)There is not enough information to determine the correct response

Quizplus · Accepted Answer

The center line for a process control chart that indicates whether the variation within samples is reasonable (in a state of control) is calculated as the average of the sample ranges. The sample range is the difference between the largest and smallest observation in each sample. The sample ranges for the given data are:Sample 1: 12.2 - 11.8 = 0.4Sample 2: 12.1 - 11.8 = 0.3Sample 3: 11.9 - 11.7 = 0.2Sample 4: 12.0 - 11.7 = 0.3Sample 5: 11.9 - 10.7 = 1.2The average of the sample ranges is (0.4 + 0.3 + 0.2 + 0.3 + 1.2) / 5 = 0.48. Therefore, the center line for the process control chart is 0.48.

A Process for Filling Liquid Laundry Detergent Bottles Monitors the Volume