Ch 5 case

45. Apply the chi-square goodness of fit test to the data in the Airport Service Times Excel file to determine if an exponential distribution models the data. Use bins of width 100. Note that for an exponential dis- tribution, the number of degrees of freedom for the CHISQ.INV.RT function should be the number of bins minus 2 as discussed in the chapter. 5 (07551 SR & S 21RO 21\Y A\ [0 SR WA\ N W@ 10T 1o V[ =\ g PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company 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 Per- formance Lawn Equipment Database. In addition, many in-process measurements are taken to ensure that manufac- turing processes remain in control and can produce accord- ing to design specifications. The worksheet Blade Weight shows 350 measurements of blade weights taken from the manufacturing process that produces mower blades dur- ing the most recent shift. Elizabeth Burke has asked you to study these data from an analytics perspective. Draw- ing upon your experience, you have developed a number of questions. 1. For the mower test data, what distribution might be appropriate to model the failure of an individual mower? 2. What fraction of mowers fails the functional perfor- mance test using all the mower test data? 3. What is the probability of having x failures in the next 100 mowers tested, for x from 0 to 20? Chapter 5 Probability Distributions and Data Modeling 217 46. Compute the daily change of the closing price for the data in the Excel file S&P 500. Compute descriptive statistics, a frequency distribution, and histogram for the closing prices (using a bin width of 25). What probability distribution would you propose as a good fit for the data? Verify your choice using the chi- square goodness of fit test. 4. What is the average blade weight and how much variability is occurring in the measurements of blade weights? 5. Assuming that the data are normal, what is the proba- bility that blade weights from this process will exceed 5.20? 6. What is the probability that blade weights will be less than 4.80? What is the actual percent of blade weights that exceed 5.20 or are less than 4.80 from the data in the worksheet? 8. Is the process that makes the blades stable over time? That is, are there any apparent changes in the pattern of the blade weights? 9. Could any of the blade weights be considered outliers, which might indicate a problem with the manufactur- ing process or materials? 10. Is the assumption that blade weights are normally distributed justified? 7 Summarize all your findings to these questions in a well-written report. Scanned with CamScanner