Discuss each of the following topics in class or review the topics on your own. Then write a brief but complete essay in which you summarize the main points. Please include formulas and graphs as appropriate.
1. If you look up the word normal in a dictionary, you will find that it is synonymous with the words standard or usual. Consider the very wide and general applications of the normal probability distribution. Comment on why good synonyms for normal probability distribution might be standard probability distribution or usual probability distribution. List at least three random variables from everyday life to which you think the normal probability distribution could be applicable.
2. Why are standard z values so important? Is it true that z values have no units of measurement? Why would this be desirable for comparing data sets with different units of measurement? How can we assess differences in quality or performance by simply comparing z values under a standard normal curve? Examine the formula for computing standard z values.
3. If you look up the word empirical in a dictionary, you will find that it means “relying on experiment and observation rather than on theory.” Discuss the empirical rule in this context. The empirical rule certainly applies to the normal distribution, but does it also apply to a wide variety of other distributions that are not exactly (theoretically) normal? Discuss the terms mound-shaped and symmetrical. Draw several sketches of distributions that are mound-shaped and symmetrical. Draw sketches of distributions that are not mound-shaped or symmetrical. To which distributions will the empirical rule apply?
4. Most companies that manufacture a product have a division responsible for quality control or quality assurance. The purpose of the quality-control division is to make reasonably certain that the products manufactured are up to company standards. Write a brief essay in which you describe how the statistics you have learned so far could be applied to an industrial application (such as control charts and the Antlers Lodge example).