2) A major airline keeps track of data on how their passengers redeem frequent flyer miles. They found that in the last year, 58% of passengers redeemed them to purchase tickets for domestic travel, 44% redeemed them to purchase tickets for international travel, and 16% redeemed them to purchase tickets for domestic and international travel. a) What is the probability that a passenger redeemed frequent flyer miles to purchase a ticket for domestic or international travel? (2 points) b) What is the probability that a passenger did not redeem frequent flyer miles to purchase a ticket for domestic or international travel? (2 points) c) Are two events D -{redeeming miles to purchase a ticket for domestic travel; and I -{ redeeming miles to purchase a ticket for international travel) disjoint (or mutually exclusive)? Explain. (4 points)Instructions: 1. Your assignment should be uploaded on Brightspace in a single pdf file. You may submit more than one version, but only the latest will be considered 2. Your answers should be typed. Handwritten answers would not be evaluated. 3. Remember to include personal ethics statement in your file. 4. You may use Minitab, Excel, R or other software for any calculations. However, make sure to explain all calculation steps and how you arrived at your answer. 5. Part 1 of the assignment needs to be done on MyLab Statistics. 1) Eastland College instructors and students are asking to review a new computer tutorial. Peter, the author of the tutorial, wants to analyze the feedback. He gets a spreadsheet. List the variables in the data set. Indicate whether each variable is categorical or quantitative. If the variable is categorical, indicate whether it is nominal or ordinal. (6 points) Number of Tutorial Level of visits Time (minutes) Name Status Access ID satisfaction per week spent per week Ann Instructor AB235 Moderately helpful 3 60 Boris Student BC1090 Very helpful 120 Parul Student PR1841 Not helpful 30 Paul Instructor PG145 Somewhat helpful 2 453) It has been reported that men are more likely than women to participate in online auctions. A recent study found that 50% of Internet shoppers are women and that 30% of Internet shoppers have participated in online auctions. Moreover, 25% of online shoppers were men and had participated in online auctions. a) Construct the contingency table with marginal values. (4 points) b) What is the probability that a randomly chosen participant will be a woman who does not participate in online auction? (1 point) c) Given that a participant participates in an online auction, what would be its probability of being a man? (2 points) d) Are gender and participation in online auctions independent? Explain. (3 points)4) Suppose a company manufactures components for electronic devices. In the manufacturing process, if an unacceptable level of defects occurs, an engineer must decide how to correct the problem. The engineer can order the three minor adjustments listed below to try to fix the problem where each is listed with the probability that it is the cause of the defects: motherboard adjustment (25%) memory adjustment (35%) case adjustment (40%). Suppose that upon further investigation, the engineer has determined the following conditional probabilities: P(Fixed | Case) = 0.80, P(Fixed | Memory ) = 0.50, and P(Fixed | Motherboard) = 0.10. That is, the probability that a simple case adjustment will correct the problem is 0.80, and so on. a) Draw the probability tree for this question. (3 points) b) What is the probability that a minor adjustment will correct the problem? (2 points) 5) A shareholder believes that in one year, there is a 25% chance that his stock will be worth $75, a 45% chance that it will be worth $100, and a 30% chance that it will be worth $140. a) Find the stock's expected value in one year. (2 points) b) Find the standard deviation of the stock's worth in one year. (4 points)