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# Probability Analysis for Quality Measurements

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A company that crafts home and garden features has collected some data from routine quality control studies on its mowers. The last 30 days' findings are attached as an Excel document to this post containing 200 sample weights of mower blades. They do their best to implement in-process quality checks to remain in control and manufacturing according to the specifications of their designs.

You, a professional statistician have been contracted to analyse their findings.

1. What fraction of mowers fails for each of the 30 samples in the worksheet Mower Test? What distribution might be appropriate to model the failure of an individual mower? Using this data, estimate the sampling distribution of the mean, the overall fraction of failures, and the standard error of the mean. Is a normal distribution an appropriate assumption for the sampling distribution of the mean?

3. Do the data in the worksheet Process Capability appear to be normally distributed? (Construct a frequency distribution and histogram and use these to draw a conclusion.) If not, based on the histogram, what distribution might better represent the data?

4. Estimate the mean and standard deviation for the data in the worksheet Process Capability. Using these values, and assuming that the process capability data are normal, find the probability that blade weights from this process will exceed 5.20. What is the probability that weights will be less than 4.80? What is the actual percent of weights that exceed 5.20 or are less than 4.80 from the data in the worksheet? How do the normal probability calculations compare? What do you conclude?

5.Summarize all findings.