Chapter 21.4, Problem 43E

To determine

Calculate the lower control limit and the upper control limit.

Explanation of Solution

The value of centerline $\left(\overline{\text{p}}\right)$ is 0.035. The lower control limit (LCL) can be calculated as follows:

$\begin{array}{c}\text{LCL}=\overline{\text{p}}-\text{3}\sqrt{\frac{\overline{\text{p}}\text{(1}-\overline{\text{p}}\text{)}}{\text{n}}}\\ =0.35-3\sqrt{\frac{(0.035)(1-0.035)}{1,000}}\\ =0.0174\end{array}$

The lower control limit is 0.0174.

The upper control limit (UCL) can be calculated as follows:

$\begin{array}{c}\text{UCL}=\overline{\text{p}}+\text{3}\sqrt{\frac{\overline{\text{p}}\text{(1}-\overline{\text{p}}\text{)}}{\text{n}}}\\ =0.35+3\sqrt{\frac{(0.035)(1-0.035)}{1,000}}\\ =0.0524\end{array}$

The lower control limit is 0.0524.