Section 7.4 The Central Limit Theorem for Proportions 323 c. Find the probability that more than 67% of the sampled adults drink coffee daily. 0.951 d. Find the probability that the proportion of the sampled adults who drink coffee daily is between 0.6 and 0.7. 0.8255 Tech: 0.8261 e. Find the probability that less than 62% of the sampled adults drink coffee daily. 0.3707 Tech: 0.3716 f. Would it be unusual if less than 57% of the sampled adults drink coffee daily? Yes 16. Smartphones: A Pew Research report indicated that 37% of teenagers aged 12–17 own smartphones. A random sample of 150 teenagers is drawn. a. Find the mean ��̂p. 0.37 b. Find the standard deviation ��̂p. 0.0394 c. Find the probability that more than 35% of the sampled teenagers own a smartphone. 0.6950 Tech: 0.6940 d. Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.38 and 0.45. 0.3801 Tech: 0.3787 e. Find the probability that less than 40% of the sampled teenagers own smartphones. 0.7764 Tech: 0.7767 f. Would it be unusual if less than 31% of the sampled teenagers owned smartphones? No 17. Student loans: The Institute for College Access and Success reported that 67% of college students in a recent year graduated with student loan debt. A random sample of 85 graduates is drawn. a. Find the mean ��̂p. 0.67 b. Find the standard deviation ��̂p. 0.05100 c. Find the probability that less than 60% of the people in the sample were in debt. 0.0853 Tech: 0.0850 d. Find the probability that between 65% and 80% of the people in the sample were in debt. 0.6463 Tech: 0.6471 e. Find the probability that more than 75% of the people in the sample were in debt. 0.0582 Tech: 0.0584 f. Would it be unusual if less than 65% of the people in the sample were in debt? No 18. High school graduates: The National Center for Educational Statistics reported that 75% of freshmen entering public high schools in the United States in 2007 graduated with their class in 2011. A random sample of 135 freshmen is chosen. a. Find the mean ��̂p. 0.75 b. Find the standard deviation ��̂p. 0.0373 c. Find the probability that less than 80% of freshmen in the sample graduated. 0.9099 Tech: 0.9101 d. Find the probability that the sample proportion of students who graduated is between 0.65 and 0.80. e. Find the probability that more than 65% of freshmen in the sample graduated. 0.9963 Tech: 0.9964 f. Would it be unusual if the sample proportion of students who graduated was more than 0.85? Yes 19. Government workers: The Bureau of Labor Statistics reported in 2013 that 16% of U.S. nonfarm workers are government employees. A random sample of 50 workers is drawn. a. Is it appropriate to use the normal approximation to find the probability that less than 20% of the individuals in the sample are government employees? If so, find the probability. If not, explain why not. No b. A new sample of 90 workers is chosen. Find the probability that more than 20% of workers in this sample are government employees. 0.1492 Tech: 0.1503 c. Find the probability that the proportion of workers in the sample of 90 who are government employees is between 0.15 and 0.18. 0.3011 Tech: 0.2997 d. Find the probability that less than 25% of workers in the sample of 90 are government employees. 0.9901 e. Would it be unusual if the proportion of government employees in the sample of 90 was greater than 0.25? Yes 20. Working two jobs: The Bureau of Labor Statistics reported in a recent year that 5% of employed adults in the United States held multiple jobs. A random sample of 75 employed adults is chosen. a. Is it appropriate to use the normal approximation to find the probability that less than 6.5% of the individuals in the sample hold multiple jobs? If so, find the probability. If not, explain why not. No b. A new sample of 350 employed adults is chosen. Find the probability that less than 6.5% of the individuals in this sample hold multiple jobs. 0.9015 Tech: 0.9011 c. Find the probability that more than 6% of the individuals in the sample of 350 hold multiple jobs. 0.1949 Tech: 0.1953 d. Find the probability that the proportion of individuals in the sample of 350 who hold multiple jobs is between 0.05 and 0.10. 0.4999 Tech: 0.5000 e. Would it be unusual if less than 4% of the individuals in the sample of 350 held multiple jobs? No 21. Future scientists: Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. The Alliance for Science and Technology Research in America reported in 2013 that 28% of freshmen entering college planned to major in a STEM discipline. A random sample of 85 freshmen is selected. a. Is it appropriate to use the normal approximation to find the probability that less than 30% of the freshmen in the sample are planning to major in a STEM discipline? If so, find the probability. If not, explain why not. Yes b. A new sample of 150 freshmen is selected. Find the probability that less than 30% of the freshmen in this sample are planning to major in a STEM discipline. 0.7088 Tech: 0.7073 c. Find the probability that the proportion of freshmen in the sample of 150 who plan to major in a STEM discipline is between 0.30 and 0.35. 0.2631 Tech: 0.2646 d. Find the probability that more than 32% of the freshmen in the sample of 150 are planning to major in a STEM discipline. 0.1379 Tech: 0.1376 e. Would it be unusual if less than 25% of the freshmen in the sample of 150 were planning to major in a STEM discipline? No 22. Blood pressure: High blood pressure has been identified as a risk factor for heart attacks and strokes. The National Health and Nutrition Examination Survey reported that the proportion of U.S. adults with high blood pressure is 0.3. A sample of 38 U.S. adults is chosen. a. Is it appropriate to use the normal approximation to find the probability that more than 40% of the people in the sample have high blood pressure? If so, find the probability. If not, explain why not. Yes
navidi_monk_elementary_statistics_2e_ch7-9
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