120 CHAPTER 3 Describing, Exploring, and Comparing Data 39. Age of President at First Inauguration (years) Frequency 40–44 2 45–49 7 50–54 10 55–59 10 60–64 6 65–69 3 70–74 1 40. Duration of Old Faithful Eruptions (sec) Frequency 125–149 1 150–174 0 175–199 0 200–224 3 225–249 34 250–274 12 41.The Empirical Rule Based on Data Set 1 “Body Data” in Appendix B, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells>mL.) Using the empirical rule, what is the approximate percentage of women with platelet counts a. within 2 standard deviations of the mean, or between 124.3 and 385.9? b. between 189.7 and 320.5? 42.The Empirical Rule Based on Data Set 5 “Body Temperatures” in Appendix B, body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20°F and a standard deviation of 0.62°F. Using the empirical rule, what is the approximate percentage of healthy adults with body temperatures a. within 1 standard deviation of the mean, or between 97.58°F and 98.82°F? b. between 96.34°F and 100.06°F? 43. Chebyshev’s Theorem Based on Data Set 1 “Body Data” in Appendix B, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000cells>mL.) Using Chebyshev’s theorem, what do we know about the percentage of women with platelet counts that are within 3 standard deviations of the mean? What are the minimum and maximum platelet counts that are within 3 standard deviations of the mean? 44. Chebyshev’s Theorem Based on Data Set 5 “Body Temperatures” in Appendix B, body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20°F and a standard deviation of 0.62°F (using the data from 12 AM on day 2). Using Chebyshev’s theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean? What are the minimum and maximum body temperatures that are within 2 standard deviations of the mean? 3-2 Beyond the Basics 45.Why Divide by n − 1? Let a population consist of the values 9 cigarettes, 10 cigarettes, and 20 cigarettes smoked in a day (based on data from the California Health Interview Survey). Assume that samples of two values are randomly selected with replacement from this population. (That is, a selected value is replaced before the second selection is made.) a. Find the variance s 2 of the population {9 cigarettes, 10 cigarettes, 20 cigarettes}. b. After listing the nine different possible samples of two values selected with replacement, find the sample variance s2 (which includes division by n - 1) for each of them; then find the mean of the nine sample variances s2. c. For each of the nine different possible samples of two values selected with replacement, find the variance by treating each sample as if it is a population (using the formula for population variance, which includes division by n); then find the mean of those nine population variances.
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