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AP Statistics Chapter 2 Worksheet Name: _____________________________________ Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20 to 34 age group are approximately Normally distributed with µ = 110 and σ = 25. 1. What score would represent the 50th percentile? Explain. 2. Approximately what percent of the scores fall in the range from 70 to 130? 3. A score in what range would represent the top 16% of the scores? 4. At what percentile is an IQ score of 150? 5. What percent of people aged 20 to 34 have IQs between 125 and 150? 6. MENSA is an elite organization that admits as members people who score in the top 2% on IQ tests. What score on the Wechsler Adult Intelligence Scale would an individual have to earn to qualify for MENSA membership? The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. 7. At what percentile is a pregnancy that lasts 240 days (that’s about 8 months)? 8. What percent of pregnancies last between 240 and 270 days (roughly between 8 months and 9 months)? 9. How long do the longest 20% of pregnancies last? Runner’s World reports that the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. 10. Find the proportion of runners who take more than 70 minutes to finish. 11. Find the proportion of runners who finish in less than 43 minutes. Jill scores 680 on the mathematics part of the SAT. The distribution of SAT scores in a reference population is normally distributed with mean 500 and standard deviation 100. Jack takes the ACT mathematics test and scores 27. ACT scores are normally distributed with mean 18 and standard deviation 6. 12. Find the standardized scores for both students. 13. Assuming that both tests measure the same kind of ability, who has the higher score, and why? Using your calculator, find the proportion of observations from a standard normal distribution that satisfies each of the following statements. In each case, sketch the normal curve and shade the area under the curve that is the answer to the question. 14. z < –1.5 15. –0.84 < z < 1.26 16. The 10th percentile. 17. 34% of all observations are greater than z. 18. The 63rd percentile. 19. 75% of all observations are greater than z. 20. The Graduate Record Examinations are widely used to help predict the performance of applicants to graduate schools. The range of possible scores on a GRE is 200 to 900. The psychology department finds that the scores of its applicants on the quantitative GRE are approximately normal with mean 544 and standard deviation 103. What minimum score would a student need in order to score in the top 10% of those taking the test?