Mathematical Applications for the Management, Life, and Social Sciences
11th Edition
ISBN: 9781305108042
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Chapter 7.7, Problem 19E
To determine
To calculate: The steady state vector if the transition matrix is
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Ff.253.
Employment
Employment
Last Year
This Year
Percentage
Industry
Industry
60
Small Business
20
Self-Employed
20
Small Business
Industry
10
Small Business
70
Self-Employed
20
Self-Employed
Industry
80
Small Business
10
Self-Employed
10
Assume that state 1 is Industry, that state 2 is Small Business, and that state 3 is Self-Employed.
(Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).)
(1) Find the transition matrix for this Markov process.
P =
Number 20 in the image attached
Chapter 7 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 7.1 - CHECKPOINT
1. If a coin is drawn from a box...Ch. 7.1 - CHECKPOINT
2. A ball will be drawn from a bag...Ch. 7.1 - CHECKPOINT
3. A coin is tossed, and a die is...Ch. 7.1 - 1. One ball is drawn at random from a bag...Ch. 7.1 - 2. One ball is drawn at random from a bag...Ch. 7.1 - 3. If you draw one card at random from a deck of...Ch. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - 6. A die is rolled. What is the probability...Ch. 7.1 - 7. An urn contains three red balls numbered 1, 2,...
Ch. 7.1 - 8. An urn contains three red balls numbered 1, 2,...Ch. 7.1 - 9. From a deck of 52 ordinary playing cards, one...Ch. 7.1 - 10. From a deck of 52 ordinary playing cards, one...Ch. 7.1 - 11. Suppose a fair coin is tossed two times....Ch. 7.1 - Prob. 12ECh. 7.1 - 13. Use Table 7.1 to determine the following...Ch. 7.1 - 14. (a) When a pair of distinguishable dice is...Ch. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - 17. Suppose a die is tossed 1200 times and a 6...Ch. 7.1 - 18. Suppose that a coin is tossed 3000 times and...Ch. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - 21. If the odds that a particular horse will win a...Ch. 7.1 - 22. If the odds that an event E will not occur are...Ch. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - 25. Car maintenance A car rental firm has 425...Ch. 7.1 - Prob. 26ECh. 7.1 - 27. Voting The table gives the average number of...Ch. 7.1 - Prob. 28ECh. 7.1 - 29. Sales promotion In a sales promotion, a...Ch. 7.1 - 30. Management A dry cleaning firm has 12...Ch. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - 33. Blood types Human blood is classified by blood...Ch. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - 39. Fraud A company selling substandard drugs to...Ch. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - 44. Quality control A supply of 500 plasma...Ch. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - 48. Quality control A computer store offers used...Ch. 7.1 - 49. Genetics A newly married couple plan to have...Ch. 7.1 - 50. Management A frustrated store manager is asked...Ch. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - 64. Ice cream The odds of an American home having...Ch. 7.1 - Prob. 65ECh. 7.1 - 66. Rain If the probability of rain today is ,...Ch. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.2 - CHECKPOINT
1. If a ball is drawn from a bag...Ch. 7.2 - Prob. 2CPCh. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - 5. An ordinary die is tossed. What is the...Ch. 7.2 - 6. A card is drawn at random from a deck of 52...Ch. 7.2 - 7. If the probability that event E will occur is...Ch. 7.2 - Prob. 6ECh. 7.2 - In Problems 7-8, a bag contains 5 red balls...Ch. 7.2 - Prob. 8ECh. 7.2 - Prob. 9ECh. 7.2 - 13. Suppose a die is biased (unfair) so that each...Ch. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - 15. A bag contains 4 white, 7 black, and 6 green...Ch. 7.2 - 16. In a game where only one player can win, the...Ch. 7.2 - 17. A cube has 2 faces painted red, 2 painted...Ch. 7.2 - Prob. 16ECh. 7.2 - 19. A ball is drawn from a bag containing 13 red...Ch. 7.2 - 20. A ball is drawn from a bag containing 13 red...Ch. 7.2 - 21. Drug use Forty-six percent of marijuana use...Ch. 7.2 - 22. Breast cancer According to the American Cancer...Ch. 7.2 - 23. Car maintenance A car rental firm has 425...Ch. 7.2 - 25. Linguistics Of 100 students, 24 can speak...Ch. 7.2 - 25. Linguistics Of 100 students, 24 can speak...Ch. 7.2 - 26. Management A company employs 65 people. Eight...Ch. 7.2 - Prob. 25ECh. 7.2 - Photography Rob Lee knows his camera will take a...Ch. 7.2 - 29. Salaries The table gives the percent of...Ch. 7.2 - Prob. 28ECh. 7.2 - 31. Workers The table gives the projected number...Ch. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - 37. Education A mathematics class consists of
16...Ch. 7.2 - 38. Parts delivery Repairing a copy machine...Ch. 7.2 - Oil drilling The table summarizes the opinions of...Ch. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - 44. Job bids Three construction companies have bid...Ch. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.3 - CHECKPOINT
1. Suppose that one ball is drawn from...Ch. 7.3 - Prob. 2CPCh. 7.3 - 1. A card is drawn from a deck of 52 playing...Ch. 7.3 - Prob. 2ECh. 7.3 - 3. A die has been “loaded so that the probability...Ch. 7.3 - 4. A die has been “loaded” so that the probability...Ch. 7.3 - 5. A bag contains 9 red balls numbered 1, 2, 3, 4,...Ch. 7.3 - Prob. 6ECh. 7.3 - 7. A bag contains 4 red balls and 6 white balls....Ch. 7.3 - 8. A fair die is rolled. Find the probability that...Ch. 7.3 - 9. A fair coin is tossed 3 times. Find the...Ch. 7.3 - 10. A fair coin is tossed 14 times. What is the...Ch. 7.3 - 11. A die is thrown twice. What is the probability...Ch. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - 15. (a) A box contains 3 red balls, 2 white balls,...Ch. 7.3 - Prob. 16ECh. 7.3 - 17. Two balls are drawn from a bag containing 3...Ch. 7.3 - Prob. 18ECh. 7.3 - 19. A bag contains 9 nickels, 4 dimes, and 5...Ch. 7.3 - Prob. 20ECh. 7.3 - 21. A red ball and 4 white balls are in a box. If...Ch. 7.3 - 22. From a deck of 52 playing cards, two cards are...Ch. 7.3 - 23. One card is drawn at random from a deck of 52...Ch. 7.3 - Prob. 24ECh. 7.3 - 25. Two balls are drawn without replacement from a...Ch. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Carbon emissions The table gives the results of a...Ch. 7.3 - Prob. 30ECh. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - 43. Quality control Each computer component that...Ch. 7.3 - Prob. 44ECh. 7.3 - 45. Lactose intolerance Lactose intolerance...Ch. 7.3 - 46. Quality control If 3% of all light bulbs a...Ch. 7.3 - 47. Quality control To test its shotgun shells, a...Ch. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - 53. Maintenance Twenty-three percent of the cars...Ch. 7.3 - Prob. 54ECh. 7.3 - 55. Testing An unprepared student must take a...Ch. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - 58. Racing Suppose that the odds that Blackjack...Ch. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - 62. Crime In an actual case.’ probability was used...Ch. 7.4 - CHECKPOINT
1. Urn I contains 3 gold coins, urn II...Ch. 7.4 - Prob. 2CPCh. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 4ECh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 6ECh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 12ECh. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - Prob. 14ECh. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - 17. Lactose intolerance Lactose intolerance...Ch. 7.4 - 18. Genetics What is the probability that a couple...Ch. 7.4 - 19. Marksmanship Suppose that a marksman hits the...Ch. 7.4 - 20. Majors In a random survey of students...Ch. 7.4 - Quality control Suppose a box contains 3 defective...Ch. 7.4 - Prob. 22ECh. 7.4 - 23. Alcoholism A small town has 8000 adult males...Ch. 7.4 - Prob. 24ECh. 7.4 - 27. Pregnancy test A self-administered pregnancy...Ch. 7.4 - 29. Survey In a Student Activity Participation...Ch. 7.4 - Prob. 30ECh. 7.5 - CHECKPOINT
1. If a state permits either a letter...Ch. 7.5 - Prob. 2CPCh. 7.5 - Prob. 3CPCh. 7.5 - Prob. 4CPCh. 7.5 - Prob. 5CPCh. 7.5 - 1. Compute .
Ch. 7.5 - Prob. 2ECh. 7.5 - 3. Compute .
Ch. 7.5 - 4. Compute .
Ch. 7.5 - 5. Compute .
Ch. 7.5 - Prob. 6ECh. 7.5 - 7. How many four-digit numbers can be formed from...Ch. 7.5 - Prob. 8ECh. 7.5 - 9. Compute .
Ch. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - 15. Compute .
Ch. 7.5 - 16. Compute .
Ch. 7.5 - 17. Compute .
Ch. 7.5 - Prob. 18ECh. 7.5 - 19. Compute .
Ch. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - 23. Binz, not Benz Mercedes Benz E-Class sedans...Ch. 7.5 - 24. Ice cream cones Baskin-Robbins’logo includes...Ch. 7.5 - Prob. 25ECh. 7.5 - License plates If a state wants each of its...Ch. 7.5 - 28. Racing Eight horses are entered in a race. In...Ch. 7.5 - Prob. 29ECh. 7.5 - 30. Testing An examination consists of 12...Ch. 7.5 - Prob. 31ECh. 7.5 - Prob. 32ECh. 7.5 - 33. Management A department store manager wants to...Ch. 7.5 - 34. Call letters The call letters for radio...Ch. 7.5 - Prob. 35ECh. 7.5 - 36. Testing How many ways can a 10-question...Ch. 7.5 - Prob. 37ECh. 7.5 - Prob. 38ECh. 7.5 - Prob. 39ECh. 7.5 - 40. Astronauts If 8 people are qualified for the...Ch. 7.5 - 41. Sales A traveling salesperson has 30 products...Ch. 7.5 - Prob. 42ECh. 7.5 - Prob. 43ECh. 7.5 - Prob. 44ECh. 7.5 - Prob. 45ECh. 7.5 - Prob. 46ECh. 7.5 - 47. Committees In how many ways can a committee...Ch. 7.5 - Prob. 48ECh. 7.6 - CHECKPOINT
1. If three wires (red, black, and...Ch. 7.6 - Prob. 2CPCh. 7.6 - 1. Education If a child is given cards with A, C,...Ch. 7.6 - Prob. 2ECh. 7.6 - Politics A poll asks voters to rank Social...Ch. 7.6 - 4. Photography Two men and a woman are lined up to...Ch. 7.6 - 5. License plates Suppose that all license plates...Ch. 7.6 - Prob. 6ECh. 7.6 - 7. ATMs
(a) An automatic teller machine requires...Ch. 7.6 - 8. Keys Keys for antique General Motors cars had...Ch. 7.6 - 9. Phone numbers If the first digit of a...Ch. 7.6 - Prob. 10ECh. 7.6 - 11. Rewards As a reward for a record year, the Ace...Ch. 7.6 - 12. Mutual funds The retirement plan for a company...Ch. 7.6 - 13. Testing In a 10-question matching test with 10...Ch. 7.6 - Prob. 14ECh. 7.6 - Quality control A box of 12 transistors has 3...Ch. 7.6 - Prob. 16ECh. 7.6 - 17. Quality control A retailer purchases 100 of a...Ch. 7.6 - Prob. 18ECh. 7.6 - 19. Banking To see whether a bank has enough...Ch. 7.6 - 20. Diversity A high school principal must select...Ch. 7.6 - 21. Diversity Suppose that an employer plans to...Ch. 7.6 - 22. Lottery Four men and three women are...Ch. 7.6 - Prob. 23ECh. 7.6 - 24. Sales A car dealer has 12 different cars that...Ch. 7.6 - 25. Diversity Suppose that two openings on an...Ch. 7.6 - Prob. 26ECh. 7.6 - 27. Management Suppose that an indecisive company...Ch. 7.6 - 28. Quality control Suppose that 10 computer chips...Ch. 7.6 - Prob. 29ECh. 7.6 - Prob. 30ECh. 7.6 - Prob. 31ECh. 7.6 - 32. Evaluation Employees of a firm receive annual...Ch. 7.6 - Prob. 33ECh. 7.6 - Prob. 34ECh. 7.6 - 35. Poker A flush (5 cards from the same suit) is...Ch. 7.6 - Prob. 36ECh. 7.6 - Prob. 37ECh. 7.7 - Prob. 1CPCh. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Prob. 2ECh. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Prob. 5ECh. 7.7 - Prob. 6ECh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - In Problems 9-12, use the given transition matrix...Ch. 7.7 - Prob. 10ECh. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Prob. 14ECh. 7.7 - 15. Use the matrix and initial probability vector...Ch. 7.7 - Prob. 16ECh. 7.7 - In Problems 17-20, find the steady-state vector...Ch. 7.7 - Prob. 18ECh. 7.7 - Prob. 19ECh. 7.7 - Prob. 20ECh. 7.7 - Politics Use the following information for...Ch. 7.7 - Prob. 22ECh. 7.7 - Church attendance Use the following information...Ch. 7.7 - Church attendance Use the following information...Ch. 7.7 - Church attendance Use the following information...Ch. 7.7 - Prob. 26ECh. 7.7 - Car selection Use the following information for...Ch. 7.7 - Prob. 28ECh. 7.7 - Prob. 29ECh. 7.7 - Prob. 30ECh. 7.7 - Prob. 31ECh. 7.7 - Car selection Use the following information for...Ch. 7.7 - 33. Population demographics Suppose a government...Ch. 7.7 - Prob. 34ECh. 7.7 - Prob. 35ECh. 7.7 - Prob. 36ECh. 7.7 - Prob. 37ECh. 7.7 - Prob. 38ECh. 7.7 - Prob. 39ECh. 7.7 - Prob. 40ECh. 7 - 1. If one ball is drawn from a bag containing 9...Ch. 7 - 2. Suppose a ball is drawn from a bag containing 9...Ch. 7 - 3. If the probability that an event E occurs is...Ch. 7 - 4. Suppose that a fair coin is tossed two times....Ch. 7 - 5. Suppose that a fair coin is tossed three times....Ch. 7 - 6. A card is drawn at random from an ordinary deck...Ch. 7 - 7. A deck of 52 cards is shuffled. A card is...Ch. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - 11. A bag contains 4 red balls numbered 1, 2, 3, 4...Ch. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - 19. Bag A contains 3 red, 6 black, and 5 white...Ch. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - 23. How many combinations of 8 things taken 5 at a...Ch. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - 26. Find the steady-state vector associated with...Ch. 7 - 27. Senior citizens In a certain city, 30,000...Ch. 7 - Prob. 28RECh. 7 - 29. United Nations Of 100 job applicants to the...Ch. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Productivity Suppose that in a study of leadership...Ch. 7 - 33. Quality control A product must pass an initial...Ch. 7 - Prob. 34RECh. 7 - 36. Purchasing A regional survey found that of...Ch. 7 - 38. Management A personnel director ranks 4...Ch. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - 43. License plates The RBC Heritage Classic...Ch. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - 48. Quality control A supplier has 200 compact...Ch. 7 - 49. Stocks Mr. Way must sell stocks from 3 of the...Ch. 7 - 50. Quality control A sample of 6 fuses is drawn...Ch. 7 - Income levels Use the following information for...Ch. 7 - Prob. 50RECh. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - 10. A cat hits the letters on a computer keyboard...Ch. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - Prob. 13TCh. 7 - Prob. 14TCh. 7 - Prob. 15TCh. 7 - 16. Computer chips come from two suppliers, with ...Ch. 7 - 17. A placement test is given by a university to...Ch. 7 - 18. Lactose intolerance affects about of...Ch. 7 - Prob. 19TCh. 7 - Prob. 20TCh. 7 - Prob. 21TCh. 7 - 22. A publishing company has determined that a new...
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- In a college class, 70% of the students who receive an “A” on one assignment will receive an “A” on the next assignment. On the other hand, 10% of the students who do not receive an “A” on one assignment will receive an “A” on the next assignment. Find and interpret the steady state matrix for this situation.arrow_forward1. The Galápagos penguin is the only penguin species found north of the equator, and it is considered endangered. The population of the Galápagos penguin changes on a yearly basis as a discrete dynamic [40] system. Suppose that initially there are 40 chicks and 40 breeding adults, that is xo = Suppose 40 also that the yearly transition matrix is A = = 0 [o. 0.125 2 0.75 (a) Which entry in the transition matrix gives the annual birthrate of chicks per adult? Which entry tells us the proportion of chicks that will survive to become adults? (b) Calculate the state vector x1. (c) Find the eigenvalues and corresponding eigenvectors for matrix A. (d) Express xo as a linear combination of eigenvectors. (e) Find the long-term distribution, after n years. State the long term ratio of chicks to adults. marks] (f) From your result to part (e), is the Galápagos penguin likely to survive?arrow_forward1. Abigail spends her entire weekly allowance on either candy or toys. If she buys candy one week, she is 60% sure to buy toys the next week. The probability that she buys toys in two successive weeks is 25%. (a) Create a transition diagram that describes this scenario. (b) Create a transition matrix that describes this scenario. Is this scenario ergodic or absorbing? Explain. (c) Suppose that this week, Abigail spends all of her money (100%) on candy. Using matrix multiplication, predict the probability that Abigail buys toys or candy next week, the following week, and three weeks from now. (d) Find the eigenvalues and eigenvectors for this transition matrix. (e) In the long run, what is the probability that Abigail will spend her money on toys? Explain.arrow_forward
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