EXCEL MINITAB TI-84 PLUS Age Distribution in California TECHNOLOGY Technology 293 Extended solutions are given in the technology manuals that accompany this text. Technical instruction is provided for Minitab, Excel, and the TI-84 Plus. One of the jobs of the U.S. Census Bureau is to keep track of the age distribution in the country and in each of the states. The estimated age distribution in California in 2019 is shown in the table and the histogram. (Adapted from U.S. Census Bureau) Relative frequency Age (in years) 2 7 121722273237424752576267727782879297 1% 2% 3% 4% 5% 6% 7% 8% 9% Age Distribution in California Class Class midpoint Relative frequency 0–4 2 6.0% 5–9 7 6.3% 10–14 12 6.4% 15–19 17 6.4% 20–24 22 6.7% 25–29 27 7.8% 30–34 32 7.5% 35–39 37 7.0% 40–44 42 6.3% 45–49 47 6.4% 50–54 52 6.2% 55–59 57 6.3% 60–64 62 5.8% 65–69 67 4.8% 70–74 72 3.8% 75–79 77 2.6% 80–84 82 1.7% 85–89 87 1.2% 90–94 92 0.6% 95–99 97 0.1% The means of 36 randomly selected samples generated by technology with n = 40 are shown below. 37.03, 35.43, 39.40, 34.55, 34.88, 41.00 35.30, 34.03, 36.80, 41.90, 39.63, 39.20, 43.50, 38.35, 38.38, 41.85, 38.55, 39.03, 30.50, 33.58, 38.85, 40.88, 41.13, 41.68, 37.75, 34.18, 33.88, 36.28, 41.23, 40.88, 39.93, 36.45, 38.58, 36.63, 38.55, 39.35 1. Use technology and the age distribution to estimate the mean age in California. 2. Use technology to find the mean of the set of 36 sample means. How does it compare with the mean age in California found in Exercise 1? Does this agree with the result predicted by the Central Limit Theorem? 3. Are the ages of people in California normally distributed? Explain your reasoning. 4. Sketch a relative frequency histogram for the 36 sample means. Use nine classes, with interval width 3, starting at 30.5. Is the histogram approximately bell-shaped and symmetric? Does this agree with the result predicted by the Central Limit Theorem? 5. Use technology and the age distribution to find the standard deviation of the ages of people in California. 6. Use technology to find the standard deviation of the set of 36 sample means. How does it compare with the standard deviation of the ages found in Exercise 5? Does this agree with the result predicted by the Central Limit Theorem? EXERCISES
RkJQdWJsaXNoZXIy NjM5ODQ=