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AP Statistics Coley / P. Myers / Wylder Chapter 2 Review Name __________________________________________________________ Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice. 1. For the density curve illustrated, which of the following is true? I. II. III. (a) (b) (c) (d) (e) The mean is smaller than the median. The proportion of outcomes between 0.1 and 0.7 is equal to 0.3. The proportion of outcomes exceeding 0.5 is equal to 0.75. I only II only I and II II and III I, II and III .5 0 1 2 2. The weights of cockroaches living in a typical college dormitory are approximately 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) (b) (c) (d) (e) 99.7% 95% 68% 55% 34% 3. Scores on the American College Test (ACT) are normally distributed with a mean of 18 and a standard deviation of 6. The interquartile range of the scores is approximately: (a) (b) (c) (d) (e) 8.1 12 6 10.3 7 4. The test grades at at a large school have an approximately normal distribution with a mean of 50. What is the standard deviation of the data so that 80% of the students are within 12 points (above or below) the mean? (a) (b) (c) (d) (e) 5.875 9.375 10.375 14.5 cannot be determined from the given information 5. In the accompanying display, which has the larger mean and which has the larger standard deviation? (a) Larger mean, A; larger standard deviation, A (b) Larger mean, A; larger standard deviation, B (c) Larger mean, B; larger standard deviation, A (d) Larger mean, B; larger standard deviation, B (e) Larger mean, B; same standard deviation 1 6. You have a set of data that you suspect came from a normal distribution. In order to assess normality, you construct a normal probability plot. Which of the following would constitute evidence that the data actually came from a normal distribution? (a) (b) (c) (d) (e) A strongly linear relationship between the data and their standardized values. A bell-shaped (normal) relationship between the data and their standardized values. A random scattering of points when the standardized values are plotted against the data. A strongly non-linear relationship (with no outliers) between the data and their percentiles. A uniform relationship between the percentiles and the standardized values. 7. The average cost per ounce for 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) (b) (c) (d) (e) 0.96 1.31 1.94 2.25 3.00 8. Which of the following are true statements? I. II. III. (a) (b) (c) (d) (e) In all normal distributions, the mean and median are equal. All bell-shaped curves are normal distributions for some choice of and . Virtually all the area under a normal curve is within three standard deviations of the mean, no matter what the particular mean and standard deviation are. I and II I and III II and III I, II, and III None of the above gives the complete set of true responses. 9. Jay Olshansky from the University of Chicago was quoted in Chance News as arguing that for the average life expectancy to reach 100, 18% of people would have to live to age 120. What standard deviation is he assuming for this statement to make sense? (a) (b) (c) (d) (e) 21.7 24.4 25.2 35.0 111.1 10. If a density curve was a semicircle, the radius would be approximately: (a) (b) (c) (d) (e) 0.2 0.4 0.6 0.8 1 2 Part II – Free Response (Questions 11-14) – Show your work and explain your results clearly. 11. The density curve f(x) is displayed at the right. f(x) (a) Show that the density curve is well-defined. 4 2 (b) Determine the median. .1 (c) Find Q1 and Q3. .2 .3 x (d) For the mathematically curious only: Define f(x). 12. The heights of NCAA women basketball players are approximately normally distributed with the following, illustrate with a picture and evaluate. 70 and 2.5 . For each of Height 74) (a) P(Height > 66) __________ (b) P(72 (c) P(Height < 64) __________ (d) The value of X if P(Height > X) = 0.215. __________ __________ 3 13. The following are the scores on an AP Calculus Test on Points of Inflection. Comment on the distribution and discuss the normality of the data. 87 85 82 84 88 78 96 83 88 85 87 88 84 91 82 87 91 84 83 85 96 82 78 82 84 89 83 87 88 91 82 84 86 88 79 90 88 84 85 79 14. The amount of time a Woodward Academy AP Statistics student spends on homework each evening is approximately normally distributed. If 22% of the 75 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. 4