Probability Analysis for Quality Measurements A manufacturer of home and industrial lawn and garden equipment collects a variety of data from special studies, many of which are related to quality control. The company routinely collects data about functional test performance of its mowers after assembly; results from the past 30 days are given in the worksheet Mower Test in the Excel file Quality Measurements. In addition, many in‐process measurements are taken to ensure that manufacturing processes remain in control and can produce according to design specifications. The worksheet Process Capability provides the results of 200 samples of blade weights taken from the manufacturing process that produces mower blades. You have been asked you to evaluate these data. Specifically, 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 these 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? 2. What fraction of mowers fails the functional performance test using all the data in the worksheet Mower Test? Using this result, what is the probability of having x failures in the next 100 mowers tested, for x from 0 to 20? 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 percentage 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? Summarize all your findings to these questions in a well‐ written report.