In an electronics company that produces transistors,1000 transistors are inspected at regular intervals.The proportion of nonconforming transistors produced by the process,estimated from data collected in a 1-month period,is = 0.0026.What would be the value of the lower control limit for a p chart of future samples of size 10,000?

A) 0
B) 0.0011
C) 0.0021
D) This cannot be determined because the data involve samples of size 1000.

Question

In an electronics company that produces transistors,1000 transistors are inspected at regular intervals.The proportion of nonconforming transistors produced by the process,estimated from data collected in a 1-month period,is

= 0.0026.What would be the value of the lower control limit for a p chart of future samples of size 10,000?

A) 0
B) 0.0011
C) 0.0021
D) This cannot be determined because the data involve samples of size 1000.

Coraima Perez · Accepted Answer

Final Answer : B, Explanation :   The formula for the lower control limit for a p chart is given by   L C L = p ^ − 3 p ^ ( 1 − p ^ ) n LCL=\hat{p}-3\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} L C L = p ^ ​ − 3 n p ^ ​ ( 1 − p ^ ​ ) ​ ​   where $\hat{p}$ is the estimated proportion of nonconforming items in the current process, and $n$ is the sample size. Here, $\hat{p}=0.0026$ and $n=10,000$, so   L C L = 0.0026 − 3 0.0026 ( 1 − 0.0026 ) 10000 ≈ 0.0011 LCL=0.0026-3\sqrt{\frac{0.0026(1-0.0026)}{10000}}\approx0.0011 L C L = 0.0026 − 3 10000 0.0026 ( 1 − 0.0026 ) ​ ​ ≈ 0.0011   Therefore, the answer is B.

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