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# Quality Control Statistics Discussion

Question 1 is attached.

Question 2: Ferric chloride is used as a flux in some types of extraction metallurgy processes. This material is shippedin containers, and the container weight varies. It is important to obtain an accurate estimate of meancontainer weight. Suppose that from long experience a reliable value for the standard deviation of fluxcontainer weight is determined to be 10 lb. How large a sample would be required to construct a 95%two-sided confidence interval on the mean that has a total width of 1 lb?Question 3: The output voltage of a power supply is assumed to be normally distributed. Ten observationstaken at random on voltage are as follows: 14, 14.8, 13.9, 14.8, 16, 13.9, 16.4, 15.6, 14.5, 16.1.

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a. Construct a 95% two-sided confidence interval on 𝜇.

b. Construct a 95% two-sided confidence interval on 𝜎^ 2. c. Construct a 95% upper confidence interval on 𝜎^ 2.

Question 4: What is the type I error for x-bar control charts with 0.005 probability limit and sample size of 11?

Assume the mean shift is 2𝜎 (𝜎 is the process standard deviation, that is, the standard deviation ofindividual observations), what is the type II error under this mean shift?

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