Project #7640 - Statistics

In a textile company, it is important that the acidity of the solution used to dye fabric be within certain acceptable values. Data values are gathered for a control chart by randomly taking four observations from the solution and determining the average pH value and range. After 25 such samples, the following summary information is obtained. Σ of x-bar is 195 and the Σ of R is 10. The specifications for the pH value are 7.5 ± 0.5.
a. Find the control limits.
b. Find the 1σ and 2σ x-bar chart limits.
c. Assuming a normal distribution of pH values, what fraction of the output is nonconforming?

2. A building contractor subcontracts job involving hanging wallpaper to a local merchant. To have an idea of the quality level of the merchant’s work, the contractor randomly selects 300ft2 and counts the number of blemishes. The total number of blemishes of 30 samples is 80. Construct the centerline and control limits for an appropriate chart. Is it reasonable for the contractor to set a goal on an average of 0.5 blemishes per 100ft2?

3. The weight of plastic pellets for an injection molding process is a characteristic of interest. A random sample of 15 pellets is selected and gives the following weights in grams:
20 19 22 20 21 17 22 21 18 20 17 19 18 20 21
Assuming the distribution of the weight of pellets to be normal, find a two-sided 95% statistical tolerance interval such that at least 90% of the population is contained within it. Find the value of a one-sided 95% upper statistical tolerance limit that is greater that at least 90% of the population. Interpret the difference between the two answers.

4. In question #3 concerning the weight of plastic pellets, suppose the distribution of the weights is unknown. For two-sided nonparametric statistical tolerance limits, find the required sample size. Assume that we want to contain 95% of the population with a probability of .90.

5. You are asked to make a presentation to senior management outlining the demand for a product. Describe the data you would collect and the tools you would use to organize your presentation.

Subject Business
Due By (Pacific Time) 06/10/2013 08:00 pm
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