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 + Z * sqrt[(p̄(1-p̄))/n], where p̄ is the average proportion of defects, Z is the Z-value from the standard normal distribution (commonly 3 for control charts), and n is the sample size. First, calculate the average proportion of defects (p̄): Total defects = 113, Total observations = 20 weeks * 100 customers/week = 2000, p̄ = 113/2000 = 0.0565. Using Z = 3, n = 100, UCL = 0.0565 + 3*sqrt[(0.0565*(1-0.0565))/100] ≈ 0.0565 + 0.0367 = 0.0932. Since none of the provided options exactly match this calculation, the closest provided option is 0.0622, indicating a possible miscalculation in the question or answer choices. However, based on the standard approach to calculating UCL for a p-chart, the methodology described is correct for finding the UCL, but the exact answer provided in the options does not match the expected result from the calculation.