Part 2- Free Response 202.org



AP StatisticsNAME ___________________________Ch. 2 ReviewHOUR _____35428351676091. For the density curve shown to the right, which statement is true?A.The density curve is symmetric.B.The density curve is skewed right.C.The area under the curve between 0 and 1 is 1.D.The density curve is normal.E.None of the above is correct.2. For the density curve shown in question 1, which statement is true?A.The mean and median are equal.B.The mean is greater than the median.C. The mean is less than the median.D. The mean could be either greater than or less than the median. E. None is the above is correct.3. Which of the following are true statements?I. The area under a normal curve is always 1, regardless of the mean and standard deviation. II. The mean is always equal to the median for any normal distribution. III. The interquartile range for any normal curve extends from ?–1s to ?+1s.A. I and IIB. I and IIIC. II and IIID. I, II, and IIIE. None of the above gives the correct set of true responses.4. A normal density curve has which of the following properties?A. It is symmetric.B. It has a peak centered above its mean.C. The spread of the curve is proportional to it standard deviation.D. All of the properties, (a) to (c), are correct.E. None of the properties, (a) to (c), is correct.5. 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 120. What standard deviation is he assuming for this statement to make sense. (Assume life expectancy is normal.)21.724.425.235.0111.1 Pop1 and Pop2 are normal density curves with means and standard deviations ?1, σ1 and ?2, σ2, respectively. Suppose that ?1 = ?2 and σ1 = 2(σ2). Consider these statements:I. Pop1 has twice as many observations within one standard deviation as Pop2.II. The density curve for Pop1 is taller than that of Pop2.III. The density curves are centered around different numbers.Which of these statements are correct?A. I onlyB. II onlyC. III onlyD. I and II onlyE. None of the above gives the correct set of true responses.6. Which of these variables is least likely to have a Normal distribution?A. Annual income for all 150 employees at a local high schoolB. Lengths of 50 newly hatched pythonsC. Heights of 100 white pine trees in a forestD. Amount of soda in 60 cups filled by an automated machine at a fast-food restaurantE. Weights of 200 of the same candy bar in a shipment to a local supermarketThe distribution of heart disease death rates, per 100,000 people, in 19 developed Western countries is close to this Normal distribution.7.The mean heart disease death rate per 100,000 people takes approximately what value?A. 100B. 150C. 190D. 250E. 3008.The standard deviation of the heart disease rate per 100,000 people is approximately what value?A. 10B. 25C. 60D. 100E. 2504361180-736609. The following graph is a Normal probability plot for the amount of rainfall (in acre-feet) obtained from 26 randomly selected clouds that were seeded with silver oxide. Which of the following statements about the shape of the rainfall distribution is true?A. The distribution is Normal.B. The distribution is approximately Normal.C. The distribution is roughly symmetric.D. The distribution has no potential outliers.E. The distribution is skewed. Part 2- Free Response11.) The individual times of a runner for similar races are approximately normally distributed with the mean of 4.5 and standard deviation of 0.14. The runner thinks he can run his race in 4.2 in the next race. Is that likely to happen? Explain.12.) 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. Assuming that the distribution of weights is normal, sketch the density curve of the weight distribution, with the horizontal axis marked in kilograms.a) What percent of the runners weigh over 58.3 kg.? _____b) What interval would include middle 95% of the data? _____________13.) 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. a) Find the standardized scores for both students.b) Assuming that both tests measure the same kind of ability, who has the higher score, and why?14.) 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.A.Z < –1.5B. –1.5 < Z < 0.8When Tiger Woods is on the driving range, the distance that golf balls travel when he hits them with a driver follows a Normal distribution with mean 310 yards and standard deviation 8 yards.(a) Sketch the distribution of Tiger Woods’s drive distances. Label the points one, two, and three standard deviations from the mean.(b) What proportion of Tiger’s drives travel between 300 and 325 yards? Shade the appropriate area under the curve you drew in (a). Then show your work.(c) Find the 33rd percentile of Tiger’s drive distance distribution. Show your method. ................
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