Final answer:
The LCL for the p-chart is calculated using the sample proportion of defects, the z-value for the desired confidence level, and the sample size. However, if the LCL calculation returns a negative value, it should be set to zero. The correct answer choice wasn't calculated in this explanation, as we don't set the z-value without further context.
Step-by-step explanation:
The question pertains to the computation of a Lower Control Limit (LCL) for a p-chart, which is used in statistical quality control to monitor the proportion of defectives in a manufacturing process. The LCL can be calculated using the formula:
LCL = p - z*sqrt((p(1-p))/n)
Where:
- p is the sample proportion of defectives,
- z is the z-value corresponding to the desired confidence level,
- n is the sample size,
- The square root term represents the standard error of the proportion.
In this case:
- Total samples (k) = 100
- Sample size (n) = 50
- Total number of defects = 75
- p = 75 / (100*50)
Assuming a commonly used 95% confidence level, the z-value would be approximately 1.96. As such, the LCL may be calculated as follows:
LCL = (75 / 5000) - 1.96*sqrt(((75 / 5000)*(1 - (75 / 5000)))/50)
If the computation results in a negative value, it is conventional to set the LCL to zero, since a negative proportion of defects doesn't make practical sense. One of the answer choices provided might assume a z-value that is relevant to the specific context or confidence level being used for the p-chart.