14 015 runner 1 runner 2 runner 3 runner 4 a runner 3

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Unformatted text preview: e approximately normally distributed with the following means and standard deviations. Mean 4.9 4.7 4.5 4.8 Standard Deviation 0.15 0.16 0.14 0.15 Runner 1 Runner 2 Runner 3 Runner 4 (a) Runner 3 thinks that he can run a mile in less than 4.2 minutes in the next race. Is this likely to happen? Explain. (b) The distribution of possible team times is approximately normal. What are the mean and standard deviation of this distribution? (c) Suppose the team’s best time to date is 18.4 minutes. What is the probability that the team will beat its own best time in the next race? Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 7 GO ON TO THE NEXT PAGE. 2002 AP® STATISTICS FREE-RESPONSE QUESTIONS 4. Commercial airlines need to know the operating cost per hour of flight for each plane in their fleet. In a study of the relationship between operating cost per hour and number of passenger seats, investigators computed the regression of operating cost per hour on the number of passenger seats. The 12 sample aircraft used in the study included planes with as few as 216 passenger seats and planes with as many as 410 passenger seats. Operating cost per hour ranged between $3,600 and $7,800. Some computer output from a regression analysis of these data is shown below. Predictor Constant Seats S = 845.3 Coef 1136 14.673 R-Sq = 57.0% StDev 1226 4.027 T 0.93 3.64 P 0.376 0.005 R-Sq (adj) = 52.7% (a) What is the equation of the least squares regression line that describes the relationship between operating cost per hour and number of passenger seats in the plane? Define any variables used in this equation. (b) What is the value of the correlation coefficient for operating cost per hour and number of passenger seats in the plane? Interpret this correlation. (c) Suppose that you want to describe the relationship between operating cost per hour and number of passenger seats in the plane for planes only in the range of 250 to 350 seats. Does the line shown in the scatterplot still provide the best description of the relationship for data in this range? Why or why not? Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 8 GO ON TO THE NEXT PAGE. 2002 AP® STATISTICS FREE-RESPONSE QUESTIONS 5. Sleep researchers know that some people are early birds (E), preferring to go to bed by 10 P.M. and arise by 7 A.M., while others are night owls (N), preferring to go to bed after 11 P.M. and arise after 8 A.M. A study was done to compare dream recall for early birds and night owls. One hundred people of each of the two types were selected at random and asked to record their dreams for one week. Some of the results are presented below. Number of Dreams Recalled During the Week Mean Median Standard Deviation 7.26 6.0 6.94 9.55 9.5 5.88 Proportion Who Recalled No 5 or more dreams dreams 0.24 0.55 0...
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