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AP Statistics: Normal Distribution Review Homework Name______________________________________ Date____________________________Period______ 1. The weights of cockroaches living in a typical college dormitory are approximately normally distributed with a mean of 80 grams and a standard deviation of 4 grams. The percentage of cockroaches weighing between 77 grams and 83 grams is about: (a) 99.7% (b) 95% (c) 68% (d) 55% (e) 34% 2. The average cost per ounce for Windex glass cleaner is 7.7 cents with a standard deviation of 2.5 cents. What is the z-score of Windex with a cost of 10.1 cents per ounce? (a) 0.96 (b) 1.31 (c) 1.94 (d) 2.25 (e) 3.00 3. If a density curve was a semicircle, the radius would be approximately: (a) 0.2 (b) 0.4 (c) 0.6 (d) 0.8 (e) 1 __________________________________________________________________________________________________ 4. The amount of time a GMHS AP Statistics student spends on homework each evening is approximately normally distributed. If 22% of the 52 students spend at least 47 minutes doing homework and Erin, who spends 65 minutes has a standardized score of 1.932, determine: (a) the mean and standard deviation of the distribution (b) the approximate number of students who spend less than 15 minutes on homework. _________________________________________________________________________________________________ The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are normally distributed with µ = 100 and σ = 15. 5. What score would represent the 50th percentile? Explain. 6. Approximately what percent of the scores fall in the range from 70 to 130? 7. A score in what range would represent the top 16% of the scores? __________________________________________________________________________________________ In a study of elite distance runners, the mean weight was reported to be 63.1 kilograms (kg), with a standard deviation of 4.8 kg. 8. Assuming that the distribution of weights is normal, sketch the density curve of the weight distribution, with the horizontal axis marked in kilograms. Put percentages from the Empirical Rule. __________________________________________________________________________________________________ 9. 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. Find the standardized scores for both runners. 10. Assuming that both tests measure the same kind of ability, who has the higher score, and why? _________________________________________________________________________________________________ Using Table A (table of standard normal probabilities) or 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. 11. P(Z < –1.5) 12. P(1.5 < Z < 2.8)