Use the given process data to construct a control chart for p. A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below. $$\begin{array} { l l l l l l l l l l l l l l l l l l l l }
4 & 4 & 5 & 5 & 5 & 5 & 5 & 6 & 6 & 6 & 6 & 12 & 6 & 6 & 6 & 7 & 6 & 7 & 8 & 7
\end{array}$$ What is the value of the upper control limit?
A) 1
B) 0.0783
C) 0.0622
D) 6.2

Question

Use the given process data to construct a control chart for p. A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below. $$\begin{array} { l l l l l l l l l l l l l l l l l l l l } 
4 & 4 & 5 & 5 & 5 & 5 & 5 & 6 & 6 & 6 & 6 & 12 & 6 & 6 & 6 & 7 & 6 & 7 & 8 & 7
\end{array}$$ What is the value of the upper control limit?
A) 1
B) 0.0783
C) 0.0622
D) 6.2

Quizplus · Accepted Answer

The upper control limit (UCL) for a p-chart is calculated using the formula: UCL = p̄ + Zσp, where p̄ is the average proportion of defects, Z is the Z-value from the standard normal distribution (commonly 3 for control charts), and σp is the standard deviation of the proportion of defects. First, calculate the average proportion of defects (p̄) and then the standard deviation of the proportion (σp). Finally, use these to calculate the UCL. Given the data, the correct calculation leads to the UCL value represented by option C.