5.3 EXERCISES SECTION 5.3 Normal Distributions: Finding Values 257 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary Finding a z-Score In Exercises 1–16, use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile. 1. 0.2090 2. 0.4364 3. 0.6736 4. 0.7995 5. 0.05 6. 0.94 7. 0.85 8. 0.0093 9. P33 10. P67 11. P97.5 12. P1.5 13. P25 14. P40 15. P91 16. P75 Graphical Analysis In Exercises 17–22, find the indicated z-score(s) shown in the graph. 17. z = ? 0 z Area = 0.3520 18. z Area = 0.5987 z 0 = ? 19. z Area = 0.0233 z = ? 0 20. z Area = 0.7190 z = ? 0 21. Area = 0.05 Area = 0.05 z z = ? z = ? 0 22. z Area = 0.475 Area = 0.475 z = ? z = ? 0 Finding a z-Score Given an Area In Exercises 23–30, find the indicated z-score. 23. Find the z@score that has 11.9% of the distribution’s area to its left. 24. Find the z@score that has 78.5% of the distribution’s area to its left. 25. Find the z@score that has 63.7% of the distribution’s area to its right. 26. Find the z@score that has 20.9% of the distribution’s area to its right. 27. Find the z@score that has 2.275% of the distribution’s area to its left. 28. Find the z@score that has 84.1345% of the distribution’s area to its right. 29. Find the positive z@score for which 80% of the distribution’s area lies between -z and z. 30. Find the positive z@score for which 12% of the distribution’s area lies between -z and z.
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