You want to determine the lower control line for a "p" chart for quality control purposes.You take several samples of a size of 50 items in your production process.From the samples you determine the fraction defective is 0.006 and the standard deviation is 0.001.If the desired confidence level is 99.7 percent,which of the following is the resulting LCL value for the line?
A)0.0
B)0.002
C)0.003
D)0.004
E)None of the above

Question

Quizplus · Accepted Answer

To calculate the lower control line (LCL) for a "p" chart, we need the following formula:

LCL = p̂ - 3√(p̂(1-p̂)/n)

Where p̂ is the average fraction defective, n is the sample size and √ represents the square root.

Here, p̂ = 0.006 and n = 50, so we have:

LCL = 0.006 - 3√(0.006(1-0.006)/50) = 0.003

Since we want a confidence level of 99.7%, we need to use a z-score of 3 (which corresponds to the 99.7% level). If we use this value, we get the LCL of 0.003.

Therefore, the correct choice is C.

You Want to Determine the Lower Control Line for a "P