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Statistics 5.1 – 5.3 Review Name: ___________________ 1. Find the area under the standard normal curve between z = -0.8 and z = 2.3. 2. Find the area under the standard normal curve to the right of z = -1.5. 3. Find the area under the standard normal curve to the left of z = 0.7. Find the area of the indicated region under the standard normal curve. 4. 5. 6. 7. Use the standard normal curve to find P(0 < z < 2.25) 8. Use the standard normal curve to find P(z > -1.83) IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. 9. An individual’s IQ score is found to be 110. Find the z-score corresponding to this value. 10. An individual’s IQ score is found to be 80. Find the z-score corresponding to this value. The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. 11. Find the probability of a pregnancy lasting more than 300 days. 12. Find the probability of a pregnancy lasting less than 250 days. 13. An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with 15.5 and 3.6 . What is the probability that during a given week the airline will lose less than 20 suitcases? 14. Assume that blood pressure readings are normally distributed with a mean of 120 and a standard deviation of 8. A blood pressure reading of 145 or more may require medical attention. What percent of people have a blood pressure reading greater than 145? 15. Assume that the heights of American men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find the percent of men meeting these requirements. 16. Find the z-score associated with an area of 0.2810 under the standard normal curve. 17. Find the z-score for which 90% of the distribution’s area lies between –z and z. 18. Find the z-score that has 84.85% of its distribution’s area to its right. 19. Use a standard normal table to find the z-score that corresponds to the 78th percentile. 20. The scores of a history test have a mean of 65 and a standard deviation of 5. Find the test score that corresponds to the z-score of -1.28. 21. Assume that blood pressure is readings are normally distributed with 124 and 9 . A researcher wishes to select people for a study but wants to exclude the top and bottom 10%. What would be the upper and lower readings to qualify people to participate in this study? 22. The times for completing one circuit of a bicycle course are normally distributed with a mean of 82.1 minutes and a standard deviation of 4.8 minutes. An association wants to sponsor a race, but will cut the bottom 25% of riders. In a trial run, what should be the cutoff time?