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Written Homework Assignment #6 Supplementary Topics MATH-138 Statistics your Directions: On a separate sheet of paper write out your solutions to the questions below. Then scan 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 43 points. 1. A regional survey was carried out to gauge public opinion on the controversial Arizona Immigration Law (results are shown below). For parts b-g, write both the fraction and the percent. Round to two decimal places where appropriate. (Hint: Before you begin answering the questions below, find the totals for each column and row.) Response Favor Democrat Republican Independent 50 93 35 Oppose 85 45 60 Don't Know 5 7 20 a. How many respondents are Republican and favor the law? (1 point) b. What percent of respondents are Independent? (2 points) c. What percent oppose the law? (2 points) d. Of respondents who are Democrat, what percent oppose the law? (2 points) e. of respondents who oppose the law, what percent are Democrat? (2 points) f. Give the marginal distribution for responses. (3 points) g. Give the conditional distribution for responses for Independents. (3 points) h. Are responses independent of party affiliation? (1 point) For questions 2-4, don't forget to use P notation (identify what you're taking the probability of). 2. For purposes of making on-campus bousing assignments, a college classifies its students as Seniors, Juniors, and Underclassmen. Of the students who choose to live on campus, 10% are Seniors, 20% are Juniors, and the rest are Underclassmen. The most desirable dorm is the newly constructed Gold dorni, and 60% of the Seniors elect to live there. 15% of the Juniors also live there, along with only 5% of the Underclassmen. Round your answers to three decimal places. a. Create a tree diagram for the scenario above. (4 points) c. b. What is the probability that a mandomly selected resident lives in the Gold dorm? (1 points) What is the probability that a randomly selected resident is a Senior given they live in the Gold dorm? (2 points)
I 3. A survey of an introductory statistics class asked students whether or not they ate breakfast the morning of the survey. Results are as follows. Be sure to include both the fraction and decimal rounded to three decimal places. Breakfast Yes No. Total 58 66 124 Sex Male Female 125 69 194 Total 183 135 318 a. What is the probability that a randomly selected student is female? (1 point) b. What is the probability that a randomly selected student ate breakfast? (1 point) c. What is the probability that a randomly selected student is a female who ate breakfast? (2 points) d. What is the probability that a randomly selected student is female, given that the student ate breakfast? (2 points) e. What is the probability that a randomly selected student ate breakfast, given that the student is female? (2 points) f. Does it appear that whether or not a student ate breakfast is independent of the student's sex? Explain using a valid probability formula to support your answer. (2 points) 4. A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had alarm systems, and 22% had both CD players and alarm systems. Leave your answers as decimals and round to three decimal places. a. Create a Venn Diagram for the scenario above. Remember to use probabilities, not percentages. (4 points) b. What is the probability one of these cars selected at random had neither a CD player nor an alarm system? (1 point) c. What is the probability that a car had a CD player unprotected by an alarm system? (1 point) d. What is the probability a car with an alarm system had a CD player? (2 points) e. Are having a CD player and an alarm system disjoint events? Explain. (2 points) 2
Written Homework Assignment #5 Sections 5.1-5.3 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 20 points. 1. According to online resources, about 8% of all males have some color perception defect, most commonly red-green colorblindness. How would you assign random numbers to conduct a simulation based on this percentage? (2 points) 2. Suppose you buy five boxes of cereal. In each box is a picture of a famous athlete. 20% of the cereal boxes contain Michael Phelps, 30% Lamar Jackson, and the rest Elena Delle Donne. Estimate the probability that you end up with a complete set of the pictures. a. Explain how you would use randomly generated numbers to model the likelihood that you end up with a complete set of pictures. (2 points) b. Run 20 trials and create a table of your findings. For your table, use the headings "Trial", "Components", "Outcome". (4 points) For example: Trial Components (the list of numbers generated by your calculator) Outcome (complete set of pictures or not) 1 2 w c. What is the probability that you end up with a complete set of the pictures? (2 points)
ATH-J ssroo P DRITIONS E 3. A Harris Poll (MetLife Survey of the American Teacher 2009) found that 67% of teachers are very satisfied with their careers. Suppose we select three teachers randomly from the population of all teachers in the United States. (2 points each) a. What is the probability that all three are very satisfied with their careers? b. What is the probability that none of the three is satisfied? c. What is the probability that at least one teacher is satisfied? 4. Suppose two calculators are to be randomly selected, in succession, without replacement, from a box that contains four defective and nine good calculators. After each selection, the calculator is checked to see whether it is good or defective. What is the probability that the first calculator selected is good, and the second calculator selected is defective? (2 points) 5. From a box containing five red balls and three green balls, three balls are to be randomly selected, in succession, without replacement. What is the probability that the third ball is the first green ball selected? (2 points)