Historically, the average proportion of defective bars has been 0.015. Samples will be of 100 bars each. Construct a p-chart using z = 3. What is the value of LCL?
A) less than or equal to 0.01
B) greater than 0.01 but less than or equal to 0.02
C) greater than 0.02 but less than or equal to 0.03
D) greater than 0.03

Question

Quizplus · Accepted Answer

To construct a p-chart using z = 3, we need to find the control limits.
Upper Control Limit (UCL) = p̄ + 3σp̂, where p̄ is the average proportion of defective bars and σp̂ is the standard deviation of the proportion of defective bars.
σp̂ = √(p̄(1-p̄)/n) = √(0.015(1-0.015)/100) = 0.0038
UCL = 0.015 + 3(0.0038) = 0.0254

Lower Control Limit (LCL) = p̄ - 3σp̂
LCL = 0.015 - 3(0.0038) = 0.0046

Since the LCL is less than or equal to 0.01, the answer is A.

Historically, the Average Proportion of Defective Bars Has Been 0