308 CHAPTER 6 Normal Probability Distributions Cooperative Group Activities 1.In-class activity Each student states the last four digits of their Social Security number. For privacy concerns, those four digits can be given in any order. Construct a dotplot of the digits. What is the distribution of those digits? What value is the approximate center of the distribution? Then, each student calculates the mean of their four digits. Construct another dotplot for these means. What is the distribution of the means? What value is the approximate center of the distribution? Compare the variation in the original dotplot to the variation in the dotplot representing the sample means. What conclusions follow? 2.Out-of-class activity Use the Internet to find “Pick 4” lottery results for 50 different drawings. Find the 50 different means. Graph a histogram of the original 200 digits that were selected, and graph a histogram of the 50 sample means. What important principle do you observe? 3.In-class activity Divide into groups of three or four students and address these issues affecting the design of manhole covers. • Which of the following is most relevant for determining whether a manhole cover diameter of 24 in. is large enough: weights of men, weights of women, heights of men, heights of women, hip widths of men, hip widths of women, shoulder widths of men, shoulder widths of women? • Why are manhole covers usually round? (This was once a popular interview question asked of applicants at IBM, and there are at least three good answers. One good answer is sufficient here.) 4.Out-of-class activity Divide into groups of three or four students. In each group, develop an original procedure to illustrate the central limit theorem. The main objective is to show that when you randomly select samples from a population, the means of those samples tend to be normally distributed, regardless of the nature of the population distribution. For this illustration, begin with some population of values that does not have a normal distribution. FROM DATA TO DECISION Critical Thinking: Designing a campus dormitory elevator An Ohio college student died when he tried to escape from a dormitory elevator that was overloaded with 24 passengers. The elevator was rated for a maximum weight of 2500 pounds. Let’s consider this elevator with an allowable weight of 2500 pounds. Let’s also consider parameters for weights of adults, as shown in the accompanying table (based on Data Set 1 “Body Data” in Appendix B). Weights of Adults Males Females M 189 lb 171 lb S 39 lb 46 lb Distribution Normal Normal We could consider design features such as the type of music that could be played on the elevator. We could select songs such as “Imagine,” or “Daydream Believer.” Instead, we will focus on the critical design feature of weight. a. First, elevators commonly have a 25% margin of error, so they can safely carry a load that is 25% greater than the stated load. What amount is 25% greater than 2500 pounds? Let’s refer to this amount as “the maximum safe load” while the 2500 pound limit is the “placard maximum load.” b. Now we need to determine the maximum number of passengers that should be allowed. Should we base our calculations on the maximum safe load or the 2500 pound placard maximum load? c. The weights given in the accompanying table are weights of adults not including clothing or textbooks. Add another 10 pounds for each student’s clothing and textbooks. What is the maximum number of elevator passengers that should be allowed? d. Do you think that weights of college students are different from weights of adults from the general population? If so, how? How would that affect the elevator design?
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