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1 Chapters 1-3 Test Review Guide KEY The test will consist of both multiple choice and open-response questions, and the questions will be AP style questions. The following is a list of concepts you need to know, along with sample problems for select concepts. a) Understand which graphs are appropriate for which variables (for example, a pie chart or bar graph would be appropriate for categorical variables but not quantitative, just like a histogram would be appropriate for quantitative variables but not categorical). b) Read and interpret a stemplot, including determine the shape of a distribution from a stemplot. c) Understand the impact on mean and standard deviation of adding a particular value to a distribution. d) Know the difference between ๐ and ๐ ๐ฅ and between ๐ and ๐ฅฬ . e) Test for outliers, create boxplots, and compare distributions from the boxplots. f) Use the 68-95-99.7 rule to find boundaries. g) Calculate Normal probabilities (above a value, below a value, between two values). h) Work backwards in the Normal distribution to find values if given an area or percentile. i) Work backwards in the Normal distribution to calculate standard deviation. j) Make predictions given a least-squares regression line. k) Calculate residuals. l) Utilize regression computer output to calculate the equation of the least-squares regression line and to calculate correlation. m) Understand what information the residual plot provides. 2 Sample Problems 1a) A distribution has a mean of 10 and a standard deviation of 4. If a score of 12 was added to the distribution, what would happen to the mean and standard deviation? Mean will increase (12 is larger than the mean of 10) Standard deviation will decrease (12 is within one standard deviation of the mean) b) Instead of a score of 12, a score of 3 was added to the distribution. What would happen to the mean and standard deviation? Mean will decrease (3 is smaller than the mean of 10) Standard deviation will increase (3 is outside of one standard deviation of the mean) 2) Suppose that the distance a golfer can hit the ball has an approximately Normal distribution with a mean of 150 yards and a standard deviation of 10 yards. a) The middle 95% of his hits will travel between what two distances? Use the 68-95-99.7 rule. ๐๐๐ โ ๐๐ โ ๐๐ = ๐๐๐ ๐๐๐ + ๐๐ + ๐๐ = ๐๐๐ The middle 95% of his hits will travel between 130 and 170 yards. b) The highest 15% of his hits will travel at least what distance? ๐ต(๐๐๐, ๐๐) ๐ข๐ง๐ฏ๐๐จ๐ซ๐ฆ(๐๐ซ๐๐: ๐. ๐๐, ๐: ๐๐๐, ๐: ๐๐) = ๐๐๐. ๐๐๐๐ The highest 15% of his hits will travel at least 160.36 yards. 3) For a group of college women, the association between height and weight is roughly linear. The equation of the least-squares regression line relating ๐ฆ = weight to ๐ฅ = height is ๐ฆฬ = โ186.478 + 4.706๐ฅ a) Predict the weight for Veronica, a woman who is 63 inches tall. ฬ = โ๐๐๐. ๐๐๐ + ๐. ๐๐๐(๐๐) = ๐๐๐ ๐ Veronica, who is 63 inches tall, is predicted to weigh 110 pounds. b) Shannon has a height of 68 inches and her residual is -15. What is her actual weight? ฬ = โ๐๐๐. ๐๐๐ + ๐. ๐๐๐(๐๐) = ๐๐๐. ๐๐ ๐ ฬ = ๐ซ๐๐ฌ๐ข๐๐ฎ๐๐ฅ ๐โ๐ ๐ โ ๐๐๐. ๐๐ = โ๐๐; ๐ = ๐๐๐. ๐๐ She actually weighs 118.5 pounds. 3 4) Suppose that Clayton Kershaw of the Los Angeles Dodgers throws his fastball with a mean velocity of 94 miles per hour (mph) and a standard deviation of 2 mph and that the distribution of his fastball speeds can be modeled by a Normal distribution. a) About what proportion of his fastballs will travel greater than 100 mph? ๐ต(๐๐, ๐) ๐ง๐จ๐ซ๐ฆ๐๐ฅ๐๐๐(๐ฅ๐จ๐ฐ๐๐ซ: ๐๐๐, ๐ฎ๐ฉ๐ฉ๐๐ซ: ๐๐๐๐๐, ๐: ๐๐, ๐: ๐) = ๐. ๐๐๐๐ About 0.0013 of Kershawโs fastballs will travel greater than 100 mph. b) About what proportion of his fastballs will travel less than 90 mph? ๐ต(๐๐, ๐) ๐ง๐จ๐ซ๐ฆ๐๐ฅ๐๐๐(๐ฅ๐จ๐ฐ๐๐ซ: ๐, ๐ฎ๐ฉ๐ฉ๐๐ซ: ๐๐, ๐: ๐๐, ๐: ๐) = ๐. ๐๐๐๐ About 0.0228 of Kershawโs fastballs will travel less than 90 mph. c) About what proportion of his fastballs will travel between 93 and 95 mph? ๐ต(๐๐, ๐) ๐ง๐จ๐ซ๐ฆ๐๐ฅ๐๐๐(๐ฅ๐จ๐ฐ๐๐ซ: ๐๐, ๐ฎ๐ฉ๐ฉ๐๐ซ: ๐๐๐๐๐, ๐: ๐๐, ๐: ๐) = ๐. ๐๐๐๐ About 0.3829 of Kershawโs fastballs will travel between 93 and 95 mph. d) What is the 30th percentile of Kershawโs distribution of fastball velocities? ๐ต(๐๐, ๐) ๐ข๐ง๐ฏ๐๐จ๐ซ๐ฆ(๐๐ซ๐๐: ๐. ๐, ๐: ๐๐, ๐: ๐) = ๐๐. ๐๐ The 30th percentile of Kershawโs fastballs is 92.95 mph. e) Suppose that a different pitcherโs fastballs have a mean velocity of 92 mph and 40% of his fastballs go less than 90 mph. What is his standard deviation of his fastball velocities, assuming his distribution of velocities can be modeled by a Normal distribution? ๐ข๐ง๐ฏ๐๐จ๐ซ๐ฆ(๐๐ซ๐๐: ๐. ๐, ๐: ๐, ๐: ๐) = โ๐. ๐๐ ๐๐ โ ๐๐ โ๐. ๐๐ = ๐ ๐ = ๐ ๐ฆ๐ฉ๐ก The standard deviation of fastball velocities is 8 mph.