MATH 1300: Finite Mathematics EXAM 1 21 September 2017

Transcription

1 MATH 1300: Finite Mathematics EXAM 1 21 September 2017 NAME:...Grading Version B... Question Answer 1 $37, $10, $ $ $ $ $ x = 1, y = 1 9 No solution $ $186, $

2 MATH 1300 Fall 2017 Exam 1: Name... (B) : Short answer questions. Each question is worth 5 points; there is no partial credit. You must show your work, box your final answers and write your final answers on your Answer Page. Answers without supporting work may be graded as incorrect. 1. A newborn child receives a $10,000 gift toward a college education from her grandparents. How much will the $10,000 be worth in 20 years if it is invested at 6.6% compounded quarterly? (Round your answer to the nearest cent.) $37, On Jan 1, 2006 a deposit was made into a savings account paying interest compounded quarterly. The balance on Jan 1, 2009 was $12, and the balance on April 1, 2009 was $12, How large was the deposit? (Round your answer to the nearest cent.) $10,338.10

3 MATH 1300 Fall 2017 Exam 1: Name... (B) 3 3. At the end of each month, $400 is deposited into a savings account paying 2.7% interest compounded monthly. The balance after 8 years will be $42, What is the amount of interest earned? (Round your answer to the nearest cent.) $ Consider a $77, year mortgage at interest rate 6% compounded monthly with a $500 monthly payment. How much of the first month s payment is applied to paying off the principal? (Round your answer to the nearest cent.) $111.98

4 MATH 1300 Fall 2017 Exam 1: Name... (B) 4 5. A loan of $105, is to be amortized over a 5-year term at 12% interest compounded monthly with monthly payments and a $10,000 balloon payment at the end of the term. What is the monthly payment for this loan? (Round your answer to the nearest cent.) $ Using the add-on method, what is the monthly payment for a $9000 loan at 7% interest for three years? (Round your answer to the nearest cent.) $302.50

5 MATH 1300 Fall 2017 Exam 1: Name... (B) 5 7. Consider a 20-year mortgage of $500,000 at 6.3% interest compounded monthly where the loan is interest only for ten years. What is the monthly payment during the last ten years? (Round your answer to the nearest cent.) $ Use the Gauss-Jordan elimination method to find all solutions of the system of equations: { x + 3y = 2 5x + 6y = 1 x = 1, y = 1

6 MATH 1300 Fall 2017 Exam 1: Name... (B) 6 9. Use the Gauss-Jordan elimination method to find all solutions of the system of equations: x 5y + 6z = 16 2x 10y + 12z = 34 2x + 10y 12z = 34 No solution 10. Perform the multiplication. [ ] [ ] [ ]

7 MATH 1300 Fall 2017 Exam 1: Name... (B) Find the inverse (if it exists) of the given matrix: [ [ ] ] 12-14: Workout questions. Each question is worth 5 points; partial credit is possible. You must show your work, box your final answers and write your final answers on your Answer Page. 12. Consider a 30-year $200,000 5/1 ARM having a 2.8% margin and based on the CMT index. Suppose the interest rate is initially 6% and the value of the CMT is 5.6% five years later. Assume that all interest rates use monthly compounding. Calculate the monthly payment for the first 5 years. (Round your answer to the nearest cent.) (Grading: 5 points total. If answer is incorrect, 1 point for each step.) i = = n = (12)(30) = ,000 = $ ( ) R

8 MATH 1300 Fall 2017 Exam 1: Name... (B) For the mortgage in Question 12, calculate the unpaid balance at the end of the first 5 years. (Round your answer to the nearest cent.) (Grading: 5 points total. If answer is incorrect, 1 point for each step. 5 points for correct technique with incorrect inputs from Question 12.) i = = n = (12)(25) = 300 P = 1 ( ) ( ) $186, For the mortgage in Question 12, calculate the monthly payment for the 6th year. (Round your answer to the nearest cent.) (Grading: 5 points total. If answer is incorrect, 1 point for each step. 5 points for correct technique with incorrect inputs from Questions 12 and 13.) r = 5.6% + 2.8% = 8.4% i = = n = (12)(25) = , = $ ( ) R

9 MATH 1300 Fall 2017 Exam 1: Name... (B) 9 Potentially Helpful Formulas F = (1 + i) n P P = F (1 + i) n r eff = APY = (1 + i) m 1 F = (1 + i)n 1 i R P = R = 1 (1 + i) n i P (1 + rt) 12t R

10 MATH 1300: Finite Mathematics EXAM 2 19 October 2017 NAME:...Version B... SECTION:... INSTRUCTOR:... Question Answer 1 W = 2x + 3y 2 See exam booklet 3 See exam booklet 4 x = 12, y = 2 5 Y = 0.06x y (12,000 x y) -or- Y = 0.02x 0.01y See exam booklet 7 See exam booklet 8 low = $2000, medium = $2000, high = $ C = 2.50x y (600 x) (550 y) -or- C = 1.5x + y See exam booklet 11 See exam booklet 12 x = 600, y = R S T 15 9

11 MATH 1300 Fall 2017 Exam 2: Name... (B) : Work out questions. Each question is worth 5 points; partial credit is possible. You must show your work, box your final answers and write your final answers on your Answer Page. Answers without supporting work may be graded as incorrect. Questions 1-4: A nutritionist working for NASA must meet certain minimum nutritional requirements and yet keep the weight of the food at a minimum. He is now considering a combination of two foods which are packaged in tubes. Each tube of Food A contains 4 units of protein, 2 units of carbohydrates and 2 units of fat. A tube of Food A weighs 2 pounds. Each tube of Food B contains 3 units of protein, 6 units of carbohydrates and 1 units of fat. A tube of Food B weighs 3 pounds. The minimum nutritional requirements are 54 units of protein, 36 units of carbohydrates and 20 units of fat. Let x be the number of tubes of Food A and let y be the number of tubes of Food B. 1. Write the objective equation for this problem. (5 points. W is not necessary.) W = 2x + 3y 2. Write the inequalities associated with this problem. (5 points. 1 point for each inequality.) x 0 y 0 4x + 3y 54 2x + 6y 36 2x + y 20

12 MATH 1300 Fall 2017 Exam 2: Name... (B) 3 3. Graph your inequalities on the grid below. (5 points. 1 point for each line, 1 point for correct feasible set position, 1 point for all correct.) F S Use the vertices of the feasible set and the objective equation to find the number of tubes of Food A and Food B that will meet the minimum nutritional requirements and minimize weight. (5 points. 1 point for each vertex, 1 point for final answer.) (0, 20) W = 60 (18, 0) W = 36 (3, 14) W = 48 (12, 2) W = 30 x = 12, y = 2

13 MATH 1300 Fall 2017 Exam 2: Name... (B) 4 Questions 5-8: An investor has $12,000 to invest in three types of stocks, low-risk, medium-risk and high-risk. She invests according to three principles. The amount invested in low-risk stocks will be at most $2000 more than the amount invested in medium risk stocks. At least $4000 will be invested in low-risk and medium-risk stocks combined. No more than $10,000 will be invested in medium-risk and high-risk stocks combined. The expected yield for these investments are 6% for low-risk stocks, 7% for medium-risk stocks and 8% for high-risk stocks. The investor wishes to maximize the yield on the investments. Let x be the amount to be invested in low-risk stocks and y be the amount to be invested in medium-risk stocks. 5. Write the objective equation for this problem. (5 points. Y is not necessary. Full credit for any mathematically equivalent equation.) Y = 0.06x y (12,000 x y) or Y = 0.02x 0.01y Write the inequalities associated with this problem. (5 points. 0.5 points for x 0 and y 0, 1 point each for other inequalities.) x 0 y 0 12,000 x y 0 x y x + y 4000 y + (12,000 x y) 10,000

14 MATH 1300 Fall 2017 Exam 2: Name... (B) 5 7. Graph your inequalities on the grid below. (5 points. 1 point for each line, 1 point for correct feasible set position.) F S Use the vertices of the feasible set and the objective equation to find the amount of money that the investor invest in each type of stock to maximize yield. (5 points. 1 point for each vertex, 1 point for final answer.) (2000, 10000) Y = 820 (2000, 2000) Y = 900 (3000, 1000) Y = 890 (7000, 5000) Y = 770 low = $2000, medium = $2000, high = $8000

15 MATH 1300 Fall 2017 Exam 2: Name... (B) 6 Questions 9-12: A coffee supplier has warehouses in Seattle and San Jose. The coffee supplier receives orders from coffee retailers in Salt Lake City and Reno. The retailer in Salt Lake City needs 600 pounds of coffee and the retailer in Reno needs 550 pounds of coffee. The Seattle warehouse has 1100 pounds available and the warehouse in San Jose has 700 pounds available The shipping costs are as follows: $2.50 per pound from Seattle to Salt Lake City; $3.00 per pound from Seattle to Reno; $4.00 per pound from San Jose to Salt Lake City; $2.00 per pound from San Jose to Reno. Let (x, y) correspond to x pounds of coffee shipped from Seattle to Salt Lake City and y pounds of coffee shipped from Seattle to Reno. The coffee supplier wishes to find the (x, y) that minimizes the company s the shipping costs. 9. Write the objective equation for this problem. (5 points. C is not necessary. Full credit for any mathematically equivalent equation.) C = 2.50x y (600 x) (550 y) or C = 1.5x + y Write the inequalities associated with this problem. (5 points. 0.5 points for x 0 and y 0, 1 point each for other inequalities.) x 0 y x y 0 x + y 1100 (600 x) + (550 y) 700

16 MATH 1300 Fall 2017 Exam 2: Name... (B) Graph your inequalities on the grid below. (5 points. 1 point for each line, 1 point for correct feasible set position.) F S Use the vertices of the feasible set and the objective equation to find the values of x and y which will minimize the shipping costs. (5 points. 1 point for each vertex, 1 point for final answer, 5 points maximum.) (0, 450) C = 3950 (450, 0) C = 2825 (600, 0) C = 2600 (600, 500) C = 3100 (550, 550) C = 3225 (0, 550) C = 4050 x = 600, y = 0

17 MATH 1300 Fall 2017 Exam 2: Name... (B) Of the 171 students who took a math exam, 90 correctly answered Question 1, 95 correctly answered Question 2 and 46 answered both questions correctly. How many students answered Question 2 correctly but not Question 1? Use unions, intersections and/or complements of sets R, S and T to write an expression for the Venn diagram below. R S T R S T

18 MATH 1300 Fall 2017 Exam 2: Name... (B) Let S and T be subsets of the universal set U. Suppose n(u) = 25, n(s) = 11, n(t ) = 12 and n(s T ) = 16. Find n(s T ). 9

19 MATH 1300: Finite Mathematics EXAM 3 16 November 2017 NAME:...Version B... SECTION:... INSTRUCTOR:... (B) Question Answer 1 19, , ,036, See exam booklet

20 MATH 1300 Fall 2017 Exam 3: Name... (B) : Short answer questions. Each question is worth 5 points; there is no partial credit. You must show your work, box your final answers and write your final answers on your Answer Page. Answers without supporting work may be graded as incorrect. 1. How many different possibilities are there for 28 athletes to win first, second, and third places? 19, Two seven-member teams play a game. After the game, each of the members of the winning team shakes hands once with each member of both teams. How many handshakes take place? 70

21 MATH 1300 Fall 2017 Exam 3: Name... (B) 3 3. An electronics store receives a shipment of 40 graphing calculators, including 8 that are defective. Four of the calculators are selected to be sent to a local high school. How many of the selections will contain no defective calculators? 35, The student council at a certain college is made up of three freshmen, four sophomores, five juniors, and six seniors. A yearbook photographer would like to line up two council members from each class for a picture. How many different pictures are possible if each group of classmates stands together? 1,036,800

22 MATH 1300 Fall 2017 Exam 3: Name... (B) 4 5. Suppose that a red die and a green die are tossed and the numbers on the sides that face upward are observed. What is the probability that the numbers add up to 8? (Write your answer as a fraction in lowest terms.) Suppose that P r(e) = 0.8, P r(f ) = 0.6, and P r(e F ) = 0.5. Find P r(e F ). 0.3

23 MATH 1300 Fall 2017 Exam 3: Name... (B) 5 7. Gamblers usually give odds against an event happening. For instance, if a bookie gives the odds 4 to 1 that a certain team will win an event, he is stating that the probability that the team will win is 1 5 or 0.2. Also, if a bettor bets $1 that the team will win and they do win, then the bettor will receive $5 (his original bet plus a profit of $4). Suppose a bookie has set the odds for the eventual winner in a four-team league as follows: Team A (3 to 2), Team B (3 to 2), Team C (3 to 1), and Team D (4 to 1). What is the probability that Team A will win the league? (Write your answer as a fraction in lowest terms.) Let S be a sample space and E and F be events associated with S. Suppose that P r(e) = 0.6, P r(f ) = 0.2 and P r(e F ) = 0.1. Calculate P r(e F ). (Write your answer as a fraction in lowest terms.) 3 8

24 MATH 1300 Fall 2017 Exam 3: Name... (B) 6 9. A factory produces fuses, which are packaged in boxes of 16. Three fuses are selected at random from each box for inspection. The box is rejected if at least one of these three fuses is defective. What is the probability that a box containing six defective fuses will be rejected? (Round your answer to four decimal places.) A die is rolled 36 times. What is the probability of getting exactly 7 threes? (Round your answer to four decimal places.)

25 MATH 1300 Fall 2017 Exam 3: Name... (B) An airport limousine has five passengers and stops at nine different hotels. What is the probability that two or more people will be staying at the same hotel? (Assume that each person is just as likely to stay in one hotel as another. Round your answer to four decimal places.) A bag contains seven red marbles and nine white marbles. If a sample of four marbles contains at least one white marble, what is the probability that all the marbles in the sample are white? (Round your answer to four decimal places.)

26 MATH 1300 Fall 2017 Exam 3: Name... (B) : Workout questions. Each question is worth 5 points; partial credit is possible. You must show your work, box your final answers and write your final answers on your Answer Page. 13. At a local college, four sections of economics are taught during the day and two sections are taught at night. 60 percent of the day sections are taught by full-time faculty. 35 percent of the evening sections are taught by full-time faculty. Construct a tree diagram showing the probabilities associated with this problem. (5 points. Subtract one point for each incorrect branch.) 6 10 Full Time Day Part Time 1 3 Night 7 20 Full Time Part Time 14. Calculate the probability that a student is taught by part-time faculty. (Write your answer as a fraction in lowest terms.) (5 points. 2 points for each path, 1 additional point for correct arithmetic. Full credit for correct technique and arithmetic with bad inputs from question 13.) ( ) ( )

27 MATH 1300 Fall 2017 Exam 3: Name... (B) If Jane has a part-time teacher for her economics course, what is the probability that she is taking a night class? (Round your answer to four decimal places if necessary.) (5 points. Full credit for correct conditional probability formula and correct technique with bad inputs from questions 13 and/or 14.) Pr (N P ) = Pr(N P ) Pr(P ) =

28 Student: Charles Brock Date: 11/30/17 Instructor: Steven Goldschmidt Course: Math 1300 FS2017 Assignment: Final Exam Review 1. Solve the following system of equations using the Gauss-Jordan elimination method. 4x 4y = 4 8x 8y = 8 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution is x = and y =. (Simplify your answer.) B. There are infinitely many solutions. If y is any real number, x =. (Type an expression using y as the variable.) C. There is no solution. 2. Use the Gauss-Jordan elimination method to find all solutions of the system of equations. x + 2 y = 7 3 x + y = 7 x + 8 y = 13 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution is x = and y =. (Simplify your answers.) B. There are infinitely many solutions. If y is any real number, x =. (Type an expression using y as the variable.) C. There is no solution. 3. Use Gauss-Jordan elimination to find the solution to the following system of equations. x + y + z = 1 x + 5y 19z = 29 7x 6y 12z = 0 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution is x =, y =, and z =. (Simplify your answer.) B. There are infinitely many solutions. If z is any real number, x = and y =. (Type an expression using z as the variable.) C. There is no solution.

29 4. Solve the following system of equations using the Gauss-Jordan elimination method. x 3y + 3z = 3 2x + 6y 6z = 5 x + 3y 3z = 1 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution is x =, y =, and z =. (Simplify your answer.) B. There are infinitely many solutions. If z is any real number, x = and y =. C. There is no solution. 5. Perform the multiplication Select the correct choice below and, if necessary, fill in the answer box to complete your choice = A (Type an integer or decimal for each matrix element.) B. The product is undefined. 6. In a certain town, the proportions of voters voting Democratic and Republican by various age groups is summarized by matrix A, and the population of voters in the town by age group is given by matrix B. Interpret the entries of the matrix product BA. Under Over 50 Dem. Rep = A B = Under Over 50 In the matrix BA, the first entry means that there are voters (1) and the second entry means that there are voters (2). (1) between 30 and 50 under 30 over 50 voting Republican voting Democratic (2) between 30 and 50 voting Republican over 50 under 30 voting Democratic

30 7. Find the inverse of the given matrix Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The inverse of the given matrix is. (Type an integer or decimal for each matrix element.) B. The matrix is not invertible. 8. It is found that the number of married and single adults in a certain town are subject to the following statistics. Suppose that x and y denote the number of married and single adults, respectively, in a given year (say as of January 1) and let m and s denote the corresponding numbers for the following year. Complete parts a through d. 0.4 x y = m 0.1 x y = s (a) Write this system of equations in matrix form. x y = m s (Type an integer or decimal for each matrix element.) (b) Solve the resulting matrix equation for X = x. y x y = m (Type an integer or decimal for each matrix element.) s (c) Suppose that in a given year there were found to be 100,000 married adults and 60,000 single adults. How many married (respectively, single) adults were there the preceding year? In the preceding year, there were married adults and single adults. (d) How many married (respectively, single) adults were there two years ago? Two years ago, there were married adults and single adults. 9. A nutritionist, working for NASA, must meet certain minimum nutritional requirements and yet keep the weight of the food at a minimum. He is considering a combination of two foods, which are packaged in tubes. Each tube of food A contains 4 units of protein, 2 units of carbohydrates, and 2 units of fat and weighs 3 pounds. Each tube of food B contains 3 units of protein, 6 units of carbohydrates, and 1 unit of fat and weighs 2 pounds. The requirement calls for 48 units of protein, 42 units of carbohydrates, and 18 units of fat. How many tubes of each food should be supplied to the astronauts? The number of tubes of food A is. The number of tubes of food B is.

31 10. Mr. Smith decides to feed his pet Doberman pinscher a combination of two dog foods. Each can of brand A contains 4 units of protein, 1 unit of carbohydrates, and 2 units of fat and costs 80 cents. Each can of brand B contains 1 unit of protein, 1 unit of carbohydrates, and 4 units of fat and costs 50 cents. Mr. Smith feels that each day his dog should have at least 7 units of protein, 4 units of carbohydrates, and 12 units of fat. How many cans of each dog food should he give to his dog each day to provide the minimum requirements at the least cost? Mr.Smith should give his dog can(s) of brand A and can(s) of brand B to provide the minimum requirements at the least cost. 11. Mr. Jones has $18,000 to invest in three types of stocks, low-risk, medium-risk, and high-risk. He invests according to three principles. The amount invested in low-risk stocks will be at most $2,000 more than the amount invested in medium-risk stocks. At least $8,000 will be invested in low- and medium-risk stocks. No more than $15,000 will be invested in mediumand high-risk stocks. The expected yields are 6% for low-risk stocks, 7% for medium-risk stocks, and 8% for high-risk stocks. How much money should Mr. Jones invest in each type of stock to maximize his total expected yield? Mr. Jones should invest $ in low-risk stocks, $ in medium-risk stocks, and $ in high-risk stocks. 12. A foreign-car dealer with warehouses in New York and Baltimore receives orders from dealers in Philadelphia and Trenton. The dealer in Philadelphia needs 4 cars and the dealer in Trenton needs 8. The New York warehouse has 5 cars and the Baltimore warehouse has 9. The cost of shipping cars from Baltimore to Philadelphia is $120 per car, from Baltimore to Trenton $90 per car, from New York to Philadelphia $100 per car, and from New York to Trenton $70 per car. Find the number of cars to be shipped from each warehouse to each dealer to minimize the shipping cost. Let (x, y) correspond to x cars shipped from Baltimore to Trenton, y cars shipped from Baltimore to Philadelphia. Find (x, y). Choose the correct answer below. A. The minimum cost is achieved at ( 3, 4), ( 7, 0), or anywhere on the line segment connecting these two points. B. The minimum cost is achieved at ( 3, 4) and ( 7, 0). C. The minimum cost is achieved at ( 7, 0). D. The minimum cost is achieved at ( 3, 4). 13. A shipping company is buying new trucks. The high-capacity trucks cost $50,000 and hold 340 cases of merchandise. The low-capacity trucks cost $30,000 and hold 220 cases of merchandise. The company has budgeted $ 1,080,000 for the new trucks and has a maximum of 30 people qualified to drive the trucks. Due to availability limitations, the company can purchase at most 15 high-capacity trucks. How many of each type of truck should the company purchase to maximize the number of cases shipped at one time? To maximize the number of cases of merchandise that can be shipped simultaneously, the company should purchase high-capacity trucks and low-capacity trucks.

32 14. Draw a three-circle Venn diagram and shade the portion corresponding to the set. R ( S T) Choose the correct diagram below. A. B. U R S R S U T T C. D. R S U R S U T T 15. An electronics store receives a shipment of 30 graphing calculators, including 4 that are defective. Four of the calculators are selected to be sent to a local high school. A. How many selections can be made using the original shipment? B. How many of these selections will contain no defective calculators? 16. Refer to the map in the figure below. How many of the routes from A to B pass through the point C? How many routes are there from A to B? A C B 17. An urn contains 15 numbered balls, of which 9 are red and 6 are white. A sample of 5 balls is to be selected. Complete parts (a) through (d). (a) How many different samples are possible? (b) How many samples contain all red balls? (c) How many samples contain 2 red balls and 3 white balls? (d) How many samples contain at least 4 red balls?

33 18. A bag of 10 apples contains 3 rotten apples and 7 good apples. A shopper selects a sample of 3 apples from the bag. (a) How many different samples are possible? (b) How many samples contain all good apples? (c) How many samples contain at least 1 rotten apple? 19. How many different committees can be formed from 8 teachers and 39 students if the committee consists of 2 teachers and 3 students? In how many ways can the committee of 5 members be selected? 20. If a "word" is interpreted to be a sequence of letters, how many four-letter words with no repeated letters contain two vowels? (Note that y is not considered a vowel.) There are words. (Simplify your answer.) 21. An urn contains six green balls and five white balls. A sample of four balls is selected at random from the urn. (a) Find the probability that the four balls have the same color. (b) Find the probability that the sample contains more green balls than white balls. (a) The probability that the four balls have the same color is. (Type an integer or a simplified fraction.) (b) The probability that the sample contains more green balls than white balls is. (Type an integer or a simplified fraction.) 22. A factory produces fuses, which are packaged in boxes of 14. Three fuses are selected at random from each box for inspection. The box is rejected if at least one of these three fuses is defective. What is the probability that a box containing six defective fuses will be rejected? The probability that the box containing six defective fuses will be rejected is. (Type an integer or a simplified fraction.) 23. A man, a woman, and their seven children randomly stand in a row for a family picture. What is the probability that the parents will be standing next to each other? The probability that the parents will be standing next to each other is. (Type an integer or a simplified fraction.)

34 24. Let S be a sample space and E and F be events associated with S. Suppose that Pr(E) = 0.7, Pr(F) = 0.2 and Pr(E F) = 0.1. Calculate the following probabilities. a. Pr(E F) c. Pr E F b. Pr(F E) d. Pr E F a. Pr(E F) = (Type an integer or a simplified fraction.) b. Pr(F E) = (Type an integer or a simplified fraction.) c. Pr E F = (Type an integer or a simplified fraction.) d. Pr E F = (Type an integer or a simplified fraction.) 25. A bag contains five red marbles and eight white marbles. If a sample of four marbles contains at least one white marble, what is the probability that all the marbles in the sample are white? The probability is. (Round to four decimal places as needed.) 26. Suppose that we have a white urn containing four white balls and one red ball and we have a red urn containing one white ball and six red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. The probability that the second ball is red is. 27. One ordinary quarter and a fake quarter with two heads are placed in a hat. One quarter is selected at random and tossed twice. If the outcome is "HH," what is the probability that the fake quarter was selected? Pr( fake HH ) = (Type an integer or a simplified fraction.) Ordinary H H T T H T Fake H H 28. Suppose 500 athletes are tested for a drug, one in twenty-five has used the drug, the test has a 99% specificity and the test has a 100% sensitivity. That is, the probability of a false positive is 1% and there is no chance that the user of the drug will go undetected. If an athlete in the group tests positive, what is the probability that he or she has used the drug? Pr(used POS) = (Type an integer or decimal rounded to the nearest hundredth as needed.) used not used POS NEG POS NEG

35 29. Find the five-number summary and the interquartile range for the given set of numbers, and then draw the box plot. 8, 9, 10, 14, 15, 17, 18, 20, 21, 22, 26 The five-number summary: min =, Q 1 =, Q 2 =, Q 3 =, max =. The interquartile range is. Which graph is representative of the above data? A. B. C. D An urn contains 4 red balls and 9 white balls. A sample of 2 balls is slected at random and the number of red balls observed. Determine the probability distribution for this experiment and draw its histogram. The probability to draw zero red balls is, to draw one red ball is, and to draw two red balls is. (Simplify your answers.) Choose the correct histogram below. A. B. C. D In a certain carnival game the player selects two balls at random from an urn containing 3 red balls and 5 white balls. The player receives $ 5 if he draws two red balls and $ 1 if he draws one red ball. He loses $ 2 if no red balls are in the sample. Determine the probability distribution for the experiment of playing the game and observing the player's earnings. The probability to draw two red balls is, to draw one red ball is, and to draw zero red balls is. (Simplify your answers.) 32. A coin is tossed 8 times. Find the probability that the number of tails is exactly three. The probability that the number of tails is exactly three is. (Round to four decimal places as needed.) 33. A coin is tossed 12 times. Find the probability of tossing four or five tails. The probability of tossing four or five tails is. (Round to four decimal places as needed.)

36 34. A single die is rolled eight times. Find the probability that 4 appears at most four times. The probability that the number 4 appears at most four times is. (Round to four decimal places as needed.) 35. Thirteen percent of U.S. residents are in their forties. Consider a group of six U.S. residents selected at random. Find the probability that two or three of the people in the group are in their forties. The probability that two or three of the people in the group are in their forties is. (Round to four decimal places as needed.) 36. The table gives the relative frequency of the number of cavities for two groups of children trying different brands of toothpaste. Calculate the sample means to determine which group had fewer cavities. Number of cavities Relative frequency Group A Group B Find the sample mean for group A. (Type an integer or a decimal.) Find the sample mean for group B. (Type an integer or a decimal.) Determine which group had fewer cavities. Group B Group A 37. In a carnival game, the player selects two coins from a bag containing two silver dollars and five slugs. (Slugs are fake, worthless coins that look like real coins.) Write down the probability distribution for the winnings and determine how much the player would have to pay so that he would break even, on the average, over many repetitions of the game. The player should pay per play to break even. (Round to the nearest cent as needed.) 38. The promoter of a football game is concerned that it will rain. She has the option of spending $ 7,600 on insurance that will pay $ 38,000 if it rains. She estimates that the revenue from the game will be $ 58,600 if it does not rain and $ 24,600 if it does rain. What must the chance of rain be if she is ambivalent about this insurance? Choose the correct answer below. 20% 33% 42% 24% 39. Compute the variance of the probability distribution in the table below. Outcome Probability σ = (Type an integer or a decimal.)

37 40. A manufacturer produces widgets that are packaged in boxes of 150. The probability of a widget being defective is Find the mean and standard deviation for the number of defective widgets in a box. The mean, μ, is The standard deviation, σ, is. (Round to the nearest hundredth as needed.). (Round to the nearest thousandth as needed.) 41. For a certain type of light, the number of hours a bulb will burn before requiring replacement has a mean of 3000 hours and a standard deviation of 200 hours. Suppose that 6000 such bulbs are installed in an office building. Estimate the number that will require replacement between 2600 and 3400 hours from the time of installation. At least bulbs will require replacement between 2600 and 3400 hours from the time of installation. (Round to the nearest whole number as needed.) 42. At the end of each month, for two years, $ 8,000 will be withdrawn from a savings account paying 1.5% interest compounded monthly. Calculate the present value of this decreasing annuity. The present value is $. (Do not round until the final answer. Then round to the nearest cent as needed.) 43. At the end of each month, $ 400 is deposited into a savings account paying 2.2% interest compounded monthly. The balance after 10 years will be $ 53, What is the amount of interest earned? The amount of interest earned is $. (Round to the nearest cent as needed.) 44. Consider a $ 45,410, 20-year mortgage at interest rate 12 % compounded monthly with a $500 monthly payment. (a) How much interest is paid the first month? (b) How much of the first month's payment is applied to paying off the principal? (c) What is the unpaid balance at the end of 15 years? (d) How much interest is paid during the 181st month? (a) The interest paid the first month is $. (Round to the nearest cent as needed.) (b) $ of the first month's payment is applied to paying off the principal. (Round to the nearest cent as needed.) (c) The unpaid balance at the end of 15 years is $. (Do not round until the final answer. Then round to two decimal places as needed.) (d) The interest paid during the 181st month is $. (Round to the nearest cent as needed.)

38 45. A car manufacturer is offering the choice of a 0.9% loan compounded monthly for 72 months or $ 1400 cash back on the purchase of a $ 19,000 new car. Complete parts (a) through (c) below. (a) If a car buyer takes the 0.9% loan offer, how much will the monthly payment be? The car buyer's monthly payment will be $. (Do not round until the final answer. Then round to the nearest cent as needed.) (b) If the car buyer takes the $ 1400 cash-back offer and can borrow money from a local bank at 11% interest compounded monthly for six years, how much will the monthly payment be? The car buyer's monthly payment will be $. (Do not round until the final answer. Then round to the nearest cent as needed.) (c) Which of the two offers is more favorable for the car buyer? A. The 0.9% loan offer is more favorable for the car buyer because the monthly payment is lower than for the $1400 cash-back offer. B. The $1400 cash-back offer is more favorable for the car buyer because the monthly payment is lower than for the 0.9% loan offer. C. The $1400 cash-back offer is more favorable for the car buyer because the monthly payment is higher than for the 0.9% loan offer. D. The 0.9% loan offer is more favorable for the car buyer because the monthly payment is higher than for the $1400 cash-back offer. E. Neither offer is more favorable than the other for the car buyer. 46. A loan of $ 105, is to be amortized over a 10-year term at 12% interest compounded monthly with monthly payments and a $30,000 balloon payment at the end of the term. Calculate the monthly payment. The monthly payment is $. (Do not round until the final answer. Then round to two decimal places as needed.) 47. If someone is 19 years old, deposits $ 1000 each year into a traditional IRA for 51 years at 6% interest compounded annually, and retires at age 70, how much money will be in the account upon retirement? The future value of the traditional IRA is $. (Round to the nearest cent as needed.) 48. Use the add-on method to determine the monthly payment for a $ 1,000 loan at 16% interest for one year. The monthly payment is $. (Round to the nearest cent as needed.) 49. Consider a 15-year mortgage of $ 100,000 at 6.0% interest compounded monthly where the loan is interest only for ten years. What is the monthly payment during the first ten years? last five years? The monthly payment for the first ten years is $. (Round to the nearest cent as needed.) The monthly payment for the last five years is $. (Round to the nearest cent as needed.)

39 50. Consider a 20-year $ 250,000 5/1 ARM having a 2.8% margin and based on the CMT index. Suppose the interest rate is initially 6% and the value of the CMT is 5.7% five years later. Assume that all interest rates use monthly compounding. (a) Calculate the monthly payment for the first 5 years. (b) Calculate the unpaid balance at the end of the first 5 years. (c) Calculate the monthly payment for the 6th year. (a) The monthly payment for the first five years is $. (Round to the nearest cent as needed.) (b) The unpaid balance after 5 years is $. (Round to the nearest cent as needed.) (c) The monthly payment for the 6th year is $. (Round to the nearest cent as needed.)