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Please handwrite your responses to all homework assignments and turn them in to me in person (during class or when I am in my office). If (and only if) you cannot physically turn them in, please take a picture of your work and send it to me by email. For each problem or question, please include a brief explanation of your thinking process (not just what calculations you did and your answers: explain why you did what you did and why your reasoning makes sense). Note: I will provide you with feedback on your responses so that you can revise and resubmit your work. The miles per gallon (mpg) ratings for 40 cars are shown below. Use these data to answer the following questions. 11, 17, 18, 19, 19, 20, 21, 21, 22, 23, 25, 25, 25, 26, 26, 27, 27, 28, 29, 30, 30, 31, 31, 32, 32, 32, 33, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 45 1. Identify the minimum, lower quartile, median, upper quartile, and maximum values for this data set. Determine the median and both quartiles by hand (without using technology; average values to determine the median and quartiles as needed). 2. Create a box plot for these data by hand (use a ruler, graph paper, or other tools to make your box plot as accurate as possible). Based on your box plot, does it appear that the data are concentrated together, spread out evenly, or concentrated in some areas, but not in others? How do you know? 3. Are there any outliers among the 40 mpg ratings? To support your answer, calculate the upper and lower cutoffs needed to determine whether an outlier(s) exist and explain whether any value(s) exceed these cutoffs. 4. The rating of 20 mpg is what percentile? How do you know? 5. The rating of 39 mpg is what percentile? How do you know? 6. Would you prefer to have a car at the 12th percentile for mpg or would you rather have a car at the 83rd percentile for mpg? Why