M130 Sample Final Exam

M130 Sample Final Exam Use the following preference schedule to answer questions #1 - #4. Number of Voters 71 22 15 63 1 st choice 2 nd Choice 3 rd choice 4 th choice A B C D D C B A D B C A C A B D 1) Under the extended plurality method who comes in 3 rd? A) A B) B C) C D) D 2) Which candidate wins the election under the Borda count method? A) A B) B C) C D) D 3) The candidate that comes in 2 nd place using the recursive Borda count method is A) A B) B C) C D) D 4) Which candidate has a majority? A) A B) B C) C D) D E) No candidate has a majority. Refer to the weighted voting system[ 51 : 39,21,18,17 ] and the Banzhaf definition of power to answer questions #5 - #7. 5) The winning coalitions for the weighted voting system are A) { 39,21,18,17 }, { 39,21,18 }, { 39,21,17 }, { 39,18,17 }, { 21,18,17 }, { 39,21 }, { 39,18},{ 39,17} B) { 39,21,18,17 }, { 39,21,18 }, { 39,21,17 }, { 39,18,17 }, { 21,18,17 } C) { 39,21,18,17 }, { 39,21,18 }, { 39,21,17 }, { 39,18,17 }, { 21,18,17 }, { 39,21 }, { 39,18},{ 39,17},{ 21,18 }, { 21,17 }, { 18,17} D) { 39,21,18,17 }, { 39,21,18 }, { 39,21,17 }, { 39,18,17 }, { 21,18,17 }, { 39,21 }, { 39,18},{ 39,17},{ 21,18 }, { 21,17 } 6) Which player(s) are critical in the coalition{,18,17 } A) None of the players are critical. B) All of the players are critical. C) Only players 21 and 18 are critical. D) 21 is the only critical player. 21? 7) What is the Banzhaf power distribution? A) 1 1 1 1,,, 4 4 4 4 1,0,0, 2 1 1 1,,, 5 5 5 5 B) 0 C) D) 1 1 1,,, 2 6 6 1 6 E) None of the above

Refer to the weighted voting system [ : 9,6,5] 8) What are the sequential coalitions for this system? A) 9,6,5, 9,6, 9, 5 B) 9,6,5, 9,6, 9,5, 6, 5 C) 9,6,5, 9,5,6, 6,9,5, 6,5,9, 5,9,6, 5,6, 9 D) 9,6,5, 6,9,5, 5,9, 6 9) Which player is pivotal in the sequential coalition 5,6, 9? A) 9 B) 6 C) 5 D) There is no pivotal player. 13 and the Shapley-Shubik definition of power to answer questions #8 - #10. 10) What is the Shapley-Shubik power distribution for the weighted voting system? A) 2 1 1,, 3 6 6 1,0, 1 1 1,, 3 3 3 B) 0 C) Use the following to answer questions #11 - #13 D) 3 2 1,, 6 6 6 E) None of the above A 1 11) Which of the following is NOT a fair share for player C? A) B) C) D) C 1 B 1 A 2 B 2 C 2 12) What does player B receive under the Method of Markers? A) B) C) D) 13) What are all the leftover items under the Method of Markers? A) B) C) D) There are no items left over.

Use the following to answer questions #14 - #16 Marcia retires from her job, leaving 3 items to be divided among her co-workers. They decide to divide the items up using the method of sealed bids. Their bids on each item are as follows: Mad Max Sarah Connor James T. Kirk Spirograph $20 $6 $13 Millenium Falcon model $1,500 $2,200 $5,000 Atari 2600 $400 $293 $150 14) What is Sarah Connor s fair share? A) $2,499 B) $833 C) $1,575 D) $742 15) Who gets the Atari 2600? A) Mad Max B) Sarah Connor C) James T. Kirk D) No one gets the Atari 2600 16) After the final allocation, how much will James T. Kirk have to pay in? A) $1,721 B) $3,279 C) $5,000 D) $2,537 Use the following to answer questions #17 - #20. There are 40 seats available in the Toy Doll House of Commons. The Cabbage Patch Kids have a population of 134. The Garbage Pal Kids have a population of 115. The Barbies have a population of 201. 17) What is the standard divisor? A) 450 B) 40 C) 11.25 D) 17.87 18) Which of the following is the best interpretation of the standard divisor? A) The number of dolls each seat represents B) How many seats each doll gets C) The total number of dolls D) The total number of seats 19) What are the standard quotas for the Cabbage Patch Kids, Garbage Pal Kids, and Barbies respectively? A) 12, 11, 17 B) 11, 10, 17 C) 12, 10, 18 D) 11.91, 10.2, 17.87 20) Under Hamilton s Method, what is the final apportionment? A) 12, 11, 17 B) 12, 10, 18 C) 11, 10, 19 D) 13, 10, 17

21) Which of the following illustrates an Euler circuit for the graph below? A) C, D, E, A, B, F, D, C B) C, D, E, A, B, C C) C, D, E, A, B, F, D, B, C D) No Euler circuit possible. 22) In the graph below, once the minimum number of deadheads are added, how many edges are in the Euler circuit? A) 19 B) 18 C) 17 D) 16 Use the graph to the right to answer questions #23 - #25. 23) The cheapest link algorithm yields a Hamilton circuit of weight A) 32 B) 28 C) 29 D) 25 24) The nearest neighbor algorithm from vertex D yields the following Hamilton circuit A) A, B, C, D, E, A B) A, C, D, E, B, A C) A, D, E, B, C, A D) A, D, C, B, E, A 25) How many Hamilton circuits are possible in the graph including mirror images? A) 120 B) 10 C) 24 D) 5 Use the graph to answer questions #26 - #27. EXTRA COPY OF GRAPH: 26) Using Kruskal s algorithm, what is the weight of the minimum spanning tree? A) 36 B) 37 C) 38 D) 39 27) How many edges are in the minimum spanning tree? A) 9 D) 12 B) 10 C) 11

Use the following digraph to answer questions #28- #32 28) What tasks must be completed before task E? A) A, B, C only B) A, B only C) C only D) There are no tasks that need to be completed before task E. 29) The decreasing time algorithm generates the priority list A) F, B, A, E, C, D B) D, C, E, A, B, F C) A, B, C, D, E, F D) A, B, C, E, F, D 30) The length of the critical path is A) 19 B) 22 C) 17 D) 16 31) The critical path algorithm generates the priority list A) F, E, D, C, B, A B) A, B, C, D, E, F C) D, F, E, B, C, A D) A, C, B, E, F, D 32) Schedule the tasks on two processors using the priority list A, B, C, D, E, F.

33) Walt purchases a stereo/cd player for $35. He marks the price up by 50% for retail sale. However, after two months he marks the price down 25%. What is the price to the customer? A) $43.75 B) $52.50 C) $39.38 D) $65.63 34) Calculate the mean and median of the data: 78, 82, 85, 87, 90, 92, 99, 102, 103, 108, 110, 112 A) Mean: 92; Median: 99 B) Mean: 95.5; Median: 95.67 C) Mean: 99; Median: 99 D) Mean: 95.67; Median: 95.5 35) Based off the box plot to the right, which of the following is true about the Mean and Median? A) Mean > Median B) Mean < Median C) Mean = Median D) Cannot be determined 36) Michelle received her test results for her Spanish exam. Her raw score was 84 out of a possible 90 points. Her test score was in the 91 th percentile. Which of the following statements are true regarding her test? 1: Michelle scored 84 percent on her exam 2: Michelle scored 76 percent on her exam 3: Michelle scored 93 percent on her exam A) Statements 1 and 4 B) Statements 2 and 5 C) Statements 3 and 6 4: 91 percent of the class has an exam score higher than or equal to Michelle 5: 9 percent of the class has an exam score higher than or equal to Michelle 6: 93 percent of the class has an exam score higher than or equal to Michelle D) Statements 3 and 5 E) Statements 1 and 6 37) A survey was taken from college students on the number of hours studied each night. The hours studied per week are: Hours 1 2 3 4 5 6 Frequency 26 20 15 8 5 1 Find the Mean and Median number of hours studied. A) Mean: 2.32; Median: 2 B) Mean: 2; Median: 3 C) Mean: 3; Median: 3 D) Mean: 12.5; Median: 11.5 38) Use the pie graph to the right to determine the total number of vehicles if there are 45 bicycles. A) There are 45 vehicles. B) There are 150 vehicles. C) There are 100 vehicles. D) The total number of vehicles cannot be determined. 39) The standard deviation of the following data set is: {5, 8, 10, 4} A) 5. 6875 B) 6. 75 C) 5.6875 D) 22. 75

Use the following to answer questions #40- #42 At Ice Cream Palace they have a sundae bar. The options are as follows: Ice Cream: chocolate, vanilla, strawberry, butter pecan Sauce: hot fudge, caramel, strawberry sauce, pineapple sauce Topping: rainbow sprinkles, whipped cream, none Nuts: walnuts, almonds, none 40) How many different sundaes are possible? A) 48 B) 144 C) 14 D) 96 41) How many sundaes have strawberry ice cream and pineapple sauce? A) 9 B) 12 C) 2 D) 6 42) What is the probability that someone will order a sundae with almonds? A) 48 B) 0.33 C) 0.25 D) 0.5 43) The odds that Thundercat will win the next race are 4 to 9. What is the probability that Thundercat will win? A) 0.44 B) 2.25 C) 0.31 D) 0.69 44) There is a 3 in 10 chance that Miss Fancy Buttons will win the last race. What are the odds that Miss Fancy Buttons will win? A) 3 to 10 B) 10 to 3 C) 3 to 7 D) 7 to 3 45) You have $600 to invest. If you put it in the Smart Fund there is a 19% chance that it will increase in value by $180 within a year, but there is a 81% chance that it will decrease in value by $100. What is your expected gain or loss from an investment in the Smart Fund? A) $19.00 gain B) $19.00 loss C) $46.80 gain D) $46.80 loss 46) Calculate the grade a student should receive if quizzes are worth 30% of the final grade, homework worth 30% and exams worth 40%. Quiz average is 88%, homework average is 95% and exam average is 79%. A) 28.8% B) 85.25% C) 87.3% D) 86.5%

Use the following normal distribution to answer questions #47 - #48. Consider the normal distribution of coral snake length: Mean length: 64 cm Standard deviation length: 2 cm 47) What percentage of coral snakes are between 58 cm and 66 cm in length? A) 83.85% B) 49.85% C) 15.85% D) 50% 48) If 250 coral snakes are surveyed, about how many coral snakes will be longer than 66 cm? A) 40 B) 180 C) 142 D) 36