Twenty five samples of size 1000 each were drawn from a manufacturing process and the number of defectives in each sample was counted. The average sample proportion was 0.05. The upper control limit for the p chart is:
A) 0.0475
B) 0.0206
C) 0.0293
D) 0.0707
E) 0.0635

Question

Quizplus · Accepted Answer

The upper control limit (UCL) for a p-chart is calculated using the formula: UCL = $ \bar{p} + Z\sqrt{\frac{\bar{p}(1-\bar{p})}{n}} $, where $ \bar{p} $ is the average proportion of defectives, $ Z $ is the Z-value from the standard normal distribution corresponding to the desired confidence level (commonly 3 for control charts, representing 3 standard deviations from the mean), and $ n $ is the sample size. Given $ \bar{p} = 0.05 $ and $ n = 1000 $, and assuming a Z-value of 3 for control charts, the calculation is: UCL = 0.05 + 3*sqrt((0.05*0.95)/1000) = 0.05 + 0.0207 = 0.0707.

Twenty Five Samples of Size 1000 Each Were Drawn from a Manufacturing