SECTION 5.1 Introduction to Normal Distributions and the Standard Normal Distribution 243 Using and Interpreting Concepts Finding Area In Exercises 17–22, find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area. 17. z 0 0.6 18. z 0 −1.5 19. 2 z 0 20. −0.9 0 z 21. −2.25 0 z 22. −0.7 1.2 z 0 Finding Area In Exercises 23–36, find the indicated area under the standard normal curve. If convenient, use technology to find the area. 23. To the left of z = 0.33 24. To the left of z = -3.16 25. To the left of z = -1.675 26. To the left of z = 1.365 27. To the right of z = -0.65 28. To the right of z = 3.25 29. To the right of z = -0.355 30. To the right of z = 2.215 31. Between z = 0 and z = 2.86 32. Between z = -1.53 and z = 0 33. Between z = -1.55 and z = 1.55 34. Between z = -2.33 and z = 2.33 35. To the left of z = -1.28 and to the right of z = 1.28 36. To the left of z = -1.44 and to the right of z = 2.21 37. Manufacturer Claims You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally distributed, with a mean of 40,000 miles and a standard deviation of 4000 miles. You test 16 tires and record the life spans shown below. 48,778 41,046 29,083 36,394 32,302 42,787 41,972 37,229 25,314 31,920 38,030 38,445 30,750 38,886 36,770 46,049 (a) Draw a frequency histogram to display these data. Use five classes. Do the life spans appear to be normally distributed? Explain. (b) Find the mean and standard deviation of your sample. (c) Compare the mean and standard deviation of your sample with those in the manufacturer’s claim. Discuss the differences.
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