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Name: _______________________________________________ Per: ____ Date: ______________Chapter 2 Problem Set A.P. StatisticsNinety-eight women and 225 men participated in a five kilometer road race. Below are summary statistics from Minitab on their times in the race. Descriptive Statistics: Women, MenVariable N Mean StDev Minimum Q1 Median Q3 MaximumWomen 98 28.891 6.481 17.717 24.229 26.917 32.525 48.800Men 225 24.758 5.026 15.050 21.117 24.050 27.608 48.417Thiago finished in 51st place among the men, with a time of 20.9 minutes. Keisha finished 33rd among women, with a time of 25.2 minutes. Use percentiles and z-scores to compare Thiago’s and Keisha’s relative standing among men and women, respectively.Suppose the timers of the race discovered that they accidently started the clock 15 seconds before the race actually started, so that each racer’s finish time should be 15 seconds less.Describe the impact this would have on the mean, median, standard deviation, and interquartile range.Below are cumulative frequency graphs for the age distributions of the populations of France and the Philippines.Use the graphs to compare the median and interquartile range of ages in the two countries.0190500One of these distributions is strongly skewed to the right. Which one is it, and how can you tell?Approximate the median, mean, and standard deviation of the Normal distribution graphed below.0317500Median: __________Mean: __________Standard Deviation: __________Approximate the lowest score possible to place in the top 2.5%.The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are approximately Normally distributed with μ = 100 and σ = 15.(a) What score would represent the 50th percentile? Explain.(b) A score in what range would represent the top 1% of the scores?(c) What proportion of the reference population has WISC scores below 110?(d) What proportion of the reference population has WISC scores between 80 and 110?The weights of healthy adult male Labrador Retrievers are approximately Normally distributed with a mean of 77 pounds and a standard deviation of 6 pounds. What is the interquartile range of male Labrador weights?Twenty students were asked to guess the age of a man in a photograph. Here are their guesses:44 43 48 37 44 40 33 42 43 41 50 49 43 46 46 45 43 38 39 41 Are these guesses approximately Normally distributed? Provide evidence to support your answer.Mr. Wilder has a reputation for holding his classes for a few minutes after the bell has rung at the end of the period. In fact, it seems he ends class according to his own “internal clock.” Below is a density curve that describes the distribution of times when Mr. Wilder end his class, where negative values are minutes before the bell rings and positive values are minutes after the bell rings. 22669563500What proportion of time does Mr. Wilder end class within one minute of when the bell went off? Shade the appropriate area on the graph to show how you found the answer.On the density curve below, draw two vertical lines where you think the median and the mean of the distribution are. Label each line, and describe in words what feature of the curve you are using to locate each measure.3583940-190500As gasoline prices have increased in recent years, many drivers have expressed concern about the taxes they pay on gasoline for their cars. In the United States, gasoline taxes are imposed by both the federal government and by individual states. The boxplot below shows the distribution of the state gasoline taxes, in cents per gallon, for all 50 states on January 1, 2006.a) Based on the boxplot, what are the approximate values of the median and the interquartile range of the distribution of state gasoline taxes, in cents per gallon? Mark and label the boxplot to indicate how you found the approximated values.b) The federal tax imposed on gasoline was 18.4 cents per gallon at the time the state taxes were in effect. The federal gasoline tax was added to the state gasoline tax for each state to create a new distribution of combined gasoline taxes. What are approximate values, in cents per gallon, of the median and interquartile range of the new distribution of combined gasoline taxes? Justify your answer.To determine the amount of sugar in a typical serving of breakfast cereal, a student randomly selected 60 boxes of different types of cereal from the shelves of a large grocery store. The student noticed that the side panels of some of the cereal boxes showed sugar content based on one-cup servings, while others showed sugar content based on three-quarter-cup servings. Many of the cereal boxes with side panels that showed three-quarter-cup servings were ones that appealed to young children, and the student wondered whether there might be some difference in the sugar content of the cereals that showed different-size servings on their side panels. To investigate the question, the data were separated into two groups. One group consisted of 29 cereals that showed one-cup serving sizes; the other group consisted of 31 cereals that showed three-quarter-cup serving sizes. The boxplots shown below display sugar content (in grams) per serving of the cereals for each of the two serving sizes.0-127000Write a few sentences to compare the distributions of sugar content per serving for the two serving sizes of cereals.After analyzing the boxplots on the preceding page, the student decided that instead of a comparison of sugar content per recommended serving, it might be more appropriate to compare sugar content for equal-size servings. To compare the amount of sugar in serving sizes of one cup each, the amount of sugar in each of the cereals showing three-quarter-cup servings on their side panels was multiplied by 4/3. The bottom boxplot shown below displays sugar content (in grams) per cup for those cereals that showed a serving size of three-quarter-cup on their side panels.0000What new information about sugar content do the boxplots above provide?Based on the boxplots shown on this page, how would you expect the mean amounts of sugar per cup to compare for the different recommended serving sizes? Explain. ................
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