Review Exercises 287 In Exercises 21–26, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. 21. P1z 6 1.282 22. P1z 7 -0.742 23. P1-2.15 6 z 6 1.552 24. P10.42 6 z 6 3.152 25. P1z 6 -2.50 or z 7 2.502 26. P1z 6 0 or z 7 1.682 Section 5.2 In Exercises 27–32, the random variable x is normally distributed with mean m = 74 and standard deviation s = 8. Find the indicated probability. 27. P1x 6 842 28. P1x 6 552 29. P1x 7 802 30. P1x 7 71.62 31. P160 6 x 6 702 32. P172 6 x 6 822 In Exercises 33 and 34, find the indicated probabilities. If convenient, use technology to find the probabilities. 33. Yearly amounts of greenhouse gases from U.S. energy sources since 1990 are normally distributed, with a mean of 5774 million metric tons carbon dioxide equivalent (MMT CO2 eq.) and a standard deviation of 333 MMT CO2 eq. Find the probability that the amount of greenhouse gases from energy sources for a randomly selected year is (a) less than 5500 MMT CO2 eq. (b) between 6000 and 6500 MMT CO2 eq. (c) greater than 5900 MMT CO2 eq. (Source: Environmental Protection Agency) 34. The daily surface concentration of carbonyl sulfide on the Indian Ocean is normally distributed, with a mean of 9.1 picomoles per liter and a standard deviation of 3.5 picomoles per liter. Find the probability that on a randomly selected day, the surface concentration of carbonyl sulfide on the Indian Ocean is (a) between 5.1 and 15.7 picomoles per liter. (b) between 10.5 and 12.3 picomoles per liter. (c) more than 11.1 picomoles per liter. (Source: Atmospheric Chemistry and Physics) 35. Determine whether any of the events in Exercise 33 are unusual. Explain your reasoning. 36. Determine whether any of the events in Exercise 34 are unusual. Explain your reasoning. Section 5.3 In Exercises 37– 42, use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile. 37. 0.4721 38. 0.1 39. 0.993 40. P2 41. P85 42. P46 43. Find the z@score that has 30.5% of the distribution’s area to its right. 44. Find the positive z@score for which 94% of the distribution’s area lies between -z and z.
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