Math 1313 Homework 24 Section 7.2 1. The choices for problem number 4 part a (mean) from the book are given below a. 13.1857 b. 6.4615 c. 11.3754 d. 5.478 e. 7.8750 2. The choices for problem number 6 part a (mean) from the book are given below a. 231.8570 b. 202.8750 c. 199.7451 d. 211.3754 e. 205.4782 3. The choices for problem number 14 from the book are given below. a. 37.2 b. 39.5 c. 26.1 d. 30.2 e. 27.9 4. The choices for problem number 18 from the book are given below. a. 4.0502 b. 2.2613 c. 3.4691 d. 1.9908 e. 2.8712 5. The choices for problem number 28 from the book are given below. a. 0.05 b. 0.10 c. 0.11 d. 0.08 e. 0.23 6. The choices for problem number 36 from the book are given below. a. 16 : 17 b. 19 : 31 c. 17 : 8 d. 8 : 17 e. 31 : 17 7. The choices for problem number 44 from the book are given below. a. 0.5878 b. 0.7692 c. 0.7271 1 Math 1313 Homework 24 Section 7.2 d. 0.2369 e. 0.3997 8. Find the expected value of a random variable having the following probability distribution: 2 3 4 5 6 7 8 0.350 0.200 0.245 0.125 0.066 0.010 0.004 x P(X=x) a. b. c. d. e. 2.890 3.403 3.205 2.998 3.580 9. Find the expected value of a random variable having the following probability distribution: x P(X=x) a. b. c. d. e. -5 0.12 -1 0.16 0 0.28 1 0.22 5 0.12 8 0.1 0.473 0.635 0.125 0.860 1.024 10. Find the expected value of a random variable having the following probability distribution: x P(X=x) -3 3/10 -1 1/5 0 1/14 1 1/7 5 2/7 a. 1 33 b. 70 c. 19 35 d. 109 140 e. 33 140 2 Exercise Set 7.2: Central Tendency, Expected Value, and Odds Find each of the following measures of central tendency for the given data set. Round any nonterminating decimals to the nearest ten-thousandth. A. The mean B. The median C. The mode 10. x P ( X = x) 10 14 17 24 30 0.384 0.117 0.291 0.157 0.051 1. 34, 27, 23, 56, 34, 42, 30, 23 2. 140, 100, 75, 80, 110, 90 3. 75, 83, 71, 81, 83, 71, 84, 75, 83 4. 10, 5, 8, 5, 7, 10, 8, 5, 3, 8, 3, 9, 3 5. 65, 40, 71, 2, 65, 65, 2, 40, 71, 2, 71, 40 x P ( X = x) 6. 210, 222, 210, 186, 191, 203, 191, 210 6 0 7 12 15 0.319 0.166 0.307 0.056 0.152 x P ( X = x) 3 1 6 15 18 0.170 0.278 0.148 0.266 0.138 11. 7. Value Frequency 10 9 12 10 15 4 18 5 20 3 24 7 12. 8. Value Frequency 75 12 84 20 86 20 95 28 Use the given probability distribution table to find the expected value. 9. x P ( X = x) 2 3 5 9 11 0.165 0.210 0.332 0.138 0.155 MATH 1313 Finite Mathematics with Applications 13. x P ( X = x) 10 20 30 40 50 60 0.21 0.53 0.10 0.08 0.03 0.05 453 Exercise Set 7.2: Central Tendency, Expected Value, and Odds 14. x P ( X = x) 0 15 30 45 60 75 0.21 0.43 0.10 0.08 0.03 0.15 Number of Main Dishes Frequency 1 25 2 78 3 53 4 49 5 31 6 14 18. 15. x P ( X = x) 4 2 0 2 0.429 0.156 0.325 0.090 x P ( X = x) 6 0.233 0.207 0.139 0.421 Number of Passengers Frequency 0 7 1 154 2 297 3 229 4 54 5 9 16. 1 0 8 Answer the following. Round any nonterminating decimals to the nearest tenthousandth, unless otherwise indicated. 17. Suppose that random variable X is defined to be the number of main dishes included in a restaurant's to-go orders. The frequency distribution for this random variable is given below. Find the expected value of this random variable. 454 Suppose that random variable X is defined to be the number of passengers (not including the driver) observed in cars and vans in a city's high occupancy vehicle lane. The frequency distribution for this random variable is given below. Find the expected value of this random variable. 19. Suppose that random variable X is defined to be the number of items of clothing per order that customers leave with a dry cleaner for cleaning. The frequency distribution for this random variable is given below. Find the expected value of this random variable. Number of Items Frequency 1 138 2 221 3 105 4 80 5 28 6 16 7 9 8 3 University of Houston Department of Mathematics Exercise Set 7.2: Central Tendency, Expected Value, and Odds 20. Suppose that random variable X is defined to be the number of books that a student needs to purchase during a given semester. The frequency distribution for this random variable is below. Find the expected value. 23. Number of Books Frequency 0 156 1 143 2 167 3 358 4 408 5 268 21. The table below gives the number of days it takes a patient to recover from a virus and the probability associated with each number of days. Find the number of days a patient should expect it to take to recover from the virus. Number of Rooms Probability 0 0.02 1 0.13 2 0.22 3 0.28 4 0.35 24. Number of Days Probability 4 0.03 5 0.08 6 0.21 7 0.42 8 0.17 9 0.09 22. The table below gives the number of hours that students who made As on an exam spent studying for the exam and the probability associated with each length of time. Find the expected number of hours that a student needs to study to make an A on the exam. Number of Hours Probability 0 0.05 1 0.16 2 0.28 3 0.22 4 0.19 5 0.10 MATH 1313 Finite Mathematics with Applications The table below gives the number of rooms in a small hotel and the probability that each number of rooms will be rented on any given Saturday night. Find the expected number of rooms that will be rented on a Saturday night. The table below gives the number of days it takes for packages to be delivered from an online retailer and the probability associated with each number of days. Find the number of days a customer should expect it to take for his or her package to arrive. Number of Days Probability 3 0.01 4 0.14 5 0.46 6 0.25 7 0.14 25. Find the expected value of one spin of the fair spinner below. 3 6 8 4 10 26. Find the expected value of one spin of the fair spinner below. 5 9 6 12 455 Exercise Set 7.2: Central Tendency, Expected Value, and Odds 27. 28. 29. 30. Suppose that there are 6 dimes, 12 nickels and 14 quarters in a bag and one coin is drawn from the bag. What is the expected value of the draw in dollars? (Round to the nearest cent.) Suppose that there are 10 dimes, 15 nickels and 8 quarters in a bag and one coin is drawn from the bag. What is the expected value of the draw in dollars? (Round to the nearest cent.) Suppose that there are 6 quarters, 28 dimes and 24 pennies in a bag and one coin is drawn from the bag. What is the expected value of the draw in dollars? (Round to the nearest cent.) 32. 33. 34. 35. The probability that event E c occurs is 0.32. Find the odds in favor of event E occurring. 37. The probability that event E c occurs is 0.18. Find the odds against event E occurring. 38. The probability that event E c occurs is 0.77. Find the odds against event E occurring. Answer the following. Round any nonterminating decimals to the nearest tenthousandth. 39. The odds in favor of event E occurring are 7 to 5. Find the probability that event E occurs. 40. The odds in favor of an event E occurring are 8 to 3. Find the probability that event E occurs. 41. The probability that event E occurs is 0.78. Find the odds in favor of event E occurring. The odds against an event E occurring are 2 to 7. Find the probability that event E occurs. 42. The probability that event E occurs is 0.62. Find the odds in favor of event E occurring. The odds against an event E occurring are 6 to 3. Find the probability that event E occurs. 43. The probability that event E occurs is 0.92. Find the odds against event E occurring. The odds in favor of an event E occurring are 1 to 8. Find the probability that event E does not occur. 44. The probability that event E occurs is 0.84. Find the odds against event E occurring. The odds in favor of an event E occurring are 3 to 10. Find the probability that event E does not occur. 45. The probability that event E c occurs is 0.56. Find the odds in favor of event E occurring. The odds against an event E occurring are 4 to 5. Find the probability that event E occurs. 46. The odds against an event E occurring are 7 to 6. Find the probability that event E occurs. Suppose that there are 30 quarters, 17 dimes and 13 nickels in a bag and one coin is drawn from the bag. What is the expected value of the draw in dollars? (Round to the nearest cent.) Answer the following. 31. 36. 456 University of Houston Department of Mathematics Exercise Set 7.2: Central Tendency, Expected Value, and Odds 47. Find the probability that a salesman will close a sale of a new computer system, given that his odds of closing the sale are 7 to 5. 48. Find the probability that Natasha will win her next tennis match, given that her odds of winning are 10 to 2. 49. The odds that it will rain tomorrow are 4 to 5. A. What is the probability that it will rain tomorrow? B. What is the probability that it will not rain tomorrow? 50. The odds that a delivery service will deliver a package by noon tomorrow are 9 to 1. A. What is the probability that the package will arrive by noon tomorrow? B. What is the probability that the package will not arrive by noon tomorrow? 51. The odds that a football team will win its next game are 3 to 1. What is the probability that the team will lose its next game? 52. The odds that a women's doubles team will win a championship are 7 to 4. What is the probability that the team will not win the championship? 53. The odds that a machine will break down are 1 to 8. What is the probability that the machine will break down? 54. The odds that a concert will start on time are 2 to 10. What is the probability that the concert will start on time? MATH 1313 Finite Mathematics with Applications 457