CHAPTER 12 Test 841 46. Construct a histogram of the frequency distribution. * 47. Construct a frequency polygon of the frequency distribution. * 48. Does this distribution appear to be normal? Explain. No, it is skewed to the right. 49. Do you think the number of children per family in the United States is a normal distribution? Explain. Answers will vary. 50. Do you think this set of data is representative of the U.S. population? Explain. Answers will vary. Test CHAPTER 12 In Exercises 1– 6, for the set of data 22 38 38 40 47 , , , , , determine the 1. mean. 37 2. median. 38 3. mode. 38 4. midrange. 34.5 5. range. 25 6. standard deviation. 84 9.17 ≈ In Exercises 7–9, use the set of data 26 28 35 46 49 56 26 30 36 46 49 58 26 32 40 47 50 58 26 32 44 47 52 62 27 35 46 47 54 66 to construct the following. 7. a frequency distribution; let the first class be 25–30 * 8. a histogram of the frequency distribution * 9. a frequency polygon of the frequency distribution on the same set of axes as the histogram * Statistics on Salaries In Exercises 10–15, use the following data on weekly salaries at Donovan’s Construction Company. Mean $820 First quartile $770 Median $790 Third quartile $825 Mode $815 79th percentile $832 Standard deviation $40 10. What is the most common salary? $815 11. What salary did half the employees exceed? $790 12. About what percent of employees’ salaries exceeded $770? 75% 13. About what percent of employees’ salaries was less than $832? 79% 14. If the company has 100 employees, what is the total weekly salary of all employees? $82,000 $ $ $ $ $ 15. What salary represents one standard deviation above the mean? $860 Anthropology In Exercises 16–19, assume that anthropologists have determined that the akidolestes, a small primitive mammal believed to have lived with the dinosaurs, had a head circumference that was normally distributed with a mean of 42 cm and a standard deviation of 5 cm. 16. What percent of head circumferences were between 36 and 53 cm? 87.10% 17. What percent of head circumferences were greater than 35.75 cm? 89.44% 18. What percent of head circumferences were greater than 48.25 cm? 10.56% 19. What percent of head circumferences were less than 50 cm? 94.52% 20. Time Spent Studying Six students provided the length of time they studied for a sociology exam and the grade they received. Time studied (minutes) 20 40 50 60 80 100 Grade received (percent) 40 45 70 76 92 95 a) Construct a scatter diagram placing the time studied on the horizontal axis. * b) Use the scatter diagram in part (a) to determine whether you believe a correlation exists between the time studied and the grade received. Yes c) Determine the correlation coefficient between the time studied and the grade received. 0.950 d) Determine whether a correlation exists at 0.01. α= Yes e) Determine the equation of the line of best fit, y mx b, = + between the time studied and the grade received. Round both m and b to the nearest hundredth. y x 0.77 24.86 = + f) Use the equation in part (e) to estimate the grade received for a student who studied for 75 minutes. 83 ≈ *See Instructor Answer Appendix $
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