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Written Homework Assignment #3 Sections 3.2-3.3 MATH-138 Statistics Directions: On a separate sheet of paper, write out your solutions to the questions below. Then scan your written work, save it as a PDF file, and submit it on Canvas. Late assignments will receive a grade of zero unless prior arrangements are made with me. This assignment is worth 33 points. Note: Do NOT calculate the standard deviation by hand. 1. (3 points) Find the (a) range, (b) standard deviation (using your calculator), and (c) variance for the given sample data. Then answer the given questions. According to the "freshman 15" legend, college freshman gain 6.8 kilograms (or 15 pounds) during their freshman year. Listed below are the amounts of weight change (in kilograms) for a simple random sample of freshman included in the study. Positive values correspond to students who gained weight and negative values correspond to students who lost weight. 11 3 0 23225-27 2 4 8 1 0 -5 2 Is a weight gain of 6.8 kilograms (or 15 pounds) unusual? Why or why not? If 6.8 kilograms (or 15 pounds) is not unusual, does that support the legend of the "freshman 15"? (4 points) 2. (3 points) Listed below are the average salaries for a simple random sample of NCAA football coaches. How does the standard deviation change if the highest salary is omitted? Why? (Note: Your explanation should not include calculations.) $150,000 $300,000 $350,147 $232,425 $360,000 $1,231,421 $810,000 $229,000 3. The five-number summary for midterm scores (number of points; the maximum possible score was 50 points) from an intro stats class is: Min 01 Median Q3 Max 39 43.5 48.5 13.5 32 a. Calculate the fences for a modified boxplot. Be sure to write the formulas and show your work. (3 points) b. Are any of the midterms scores outliers? Explain. (2 points)
C. Construct a modified boxplot and be sure to label each value from the five-number summary, the fences, and any outliers. Make sure you include the proper scale. Note: The second lowest score was a 24. (6 points) d. Would you expect the mean midterm score of all students who took the midterm to be higher or lower than the median? Explain. (2 points) e. What are the best measures for the center and spread of this distribution? Why? (2 points) 4. (3 points) Light bulbs are measured in lumens (light output), watts (energy used), and hours (life). A standard white light bulb has a mean life of 675 hours and a standard deviation of 50 hours. A soft white light bulb has a mean life of 700 hours and a standard deviation of 35 hours. In a test at a local science competition, both light bulbs lasted 750 hours. Use z-scores to determine which light bulb's life span was more notable. Round your answers to two decimal places. 5. (2 points) The ASQ (American Society for Quality) regularly conducts a salary survey of its membership, primarily quality management professionals. A quality control specialist calculated the z-score associated with his own salary and found it was -2.50. Write a complete sentence explaining what this means. 6. (3 points) Heights of men have a bell-shaped distribution with a mean of 176 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of men between a. 169 cm and 183 cm? b. 155 cm and 197 cm?