5 Review Exercises 286 CHAPTER 5 Normal Probability Distributions Section 5.1 In Exercises 1 and 2, use the normal curve to estimate the mean and standard deviation. 1. 5 10 15 20 25 x 2. 40 45 50 55 60 65 70 75 x In Exercises 3 and 4, use the normal curves shown at the left. 3. Which normal curve has the greatest mean? Explain your reasoning. 4. Which normal curve has the greatest standard deviation? Explain your reasoning. In Exercises 5 and 6, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area. 5. 0.46 z 0 6. −0.8 −2.35 z 0 In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area. 7. To the left of z = 0.33 8. To the left of z = -1.95 9. To the right of z = -0.57 10. To the right of z = 3.22 11. To the left of z = -2.825 12. To the right of z = 0.015 13. Between z = -1.64 and z = 0 14. Between z = -1.55 and z = 1.04 15. Between z = 0.05 and z = 1.71 16. Between z = -2.68 and z = 2.68 17. To the left of z = -1.5 and to the right of z = 1.5 18. To the left of z = 0.64 and to the right of z = 3.415 The scores for the reading portion of the ACT test are normally distributed. In a recent year, the mean test score was 21.2 and the standard deviation was 6.9. The test scores of four students selected at random are 17, 29, 8, and 23. Use this information in Exercises 19 and 20. (Source: ACT, Inc.) 19. Find the z@score that corresponds to each value. 20. Determine whether any of the values are unusual. C A B 80 90 100 110 120 130 140 x FIGURE FOR EXERCISES 3 AND 4
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