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Determine Whether the Given Conditions Justify Using the Margin of Error

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Determine whether the given conditions justify using the margin of error E=zα/2σ/n\mathrm { E } = \mathrm { z } _ { \alpha / 2 } \sigma / \sqrt { \mathrm { n } } when finding a confidence interval estimate of the population mean μ\mu .
-The sample size is n n=5,σ=12.7\mathrm { n } = 5 , \sigma = 12.7 and the original population is normally distributed.

Comprehend the use and construction of p-charts for monitoring proportion defective in samples.
Recognize the importance of reducing variation within process control for quality improvement.
Understand how the standard error of the sample proportion affects the calculation of control limits.
Understand the concept and calculation of standard error in the context of sampling distributions.

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