A detergent company periodically tests its products for variations in the fill weight. To do this, the company uses -charts. Eight samples, each containing six detergent boxes, were selected from different batches. Historical data for fill weight (in ounces) of the eight samples is presented below.
$\begin{array} { | l | l | l | }
\hline \text { Sample } & \text { Sample Mean } & \text { Sample Range } \
\hline 1 & 15.80 & 0.42 \
\hline 2 & 16.10 & 0.38 \
\hline 3 & 16.02 & 0.08 \
\hline 4 & 15.95 & 0.15 \
\hline 5 & 16.12 & 0.42 \
\hline 6 & 16.18 & 0.23 \
\hline 7 & 15.87 & 0.36 \
\hline 8 & 16.20 & 0.40 \
\hline
\end{array}$
If A2for the
-chart is 0.483, the upper control limit for the
-chart (UCL) will be:
A) less than or equal to 14.
B) more than 14 but less than or equal to 16.
C) more than 16 but less than or equal to 18.
D) more than 18.

Question

A detergent company periodically tests its products for variations in the fill weight. To do this, the company uses -charts. Eight samples, each containing six detergent boxes, were selected from different batches. Historical data for fill weight (in ounces) of the eight samples is presented below.
$\begin{array} { | l | l | l | } 
\hline \text { Sample } & \text { Sample Mean } & \text { Sample Range } \
\hline 1 & 15.80 & 0.42 \
\hline 2 & 16.10 & 0.38 \
\hline 3 & 16.02 & 0.08 \
\hline 4 & 15.95 & 0.15 \
\hline 5 & 16.12 & 0.42 \
\hline 6 & 16.18 & 0.23 \
\hline 7 & 15.87 & 0.36 \
\hline 8 & 16.20 & 0.40 \
\hline
\end{array}$
If A2>for the
-chart is 0.483, the upper control limit for the
-chart (UCL) will be:
A) less than or equal to 14.
B) more than 14 but less than or equal to 16.
C) more than 16 but less than or equal to 18.
D) more than 18.

Quizplus · Accepted Answer

To find the upper control limit (UCL) for the -chart, we need to use the formula:

UCL = Sample Mean + A2 x Sample Range

We are given A2=0.483, and we can find the maximum sample range from the given data as 0.42. So, the UCL will be:

UCL = 16.02 + 0.483 x 0.42
UCL ≈ 16.22

Since the UCL is calculated as 16.22, which is more than 16 but less than or equal to 18, the best choice is C.

A Detergent Company Periodically Tests Its Products for Variations in the Fill