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All Textbook Solutions for Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

In Problems 1-6, identify the absorbing states in the indicated transition matrix. ABCP=ABC.6.3.1010001 In Problems 1-6, identify the absorbing states in the indicated transition matrix. ABCP=ABC010.3.2.5001 In Problems 1-6, identify the absorbing states in the indicated transition matrix. ABCP=ABC001100010 In Problems 1-6, identify the absorbing states in the indicated transition matrix. ABCP=ABC100.3.4.3001 In Problems 1-6, identify the absorbing states in the indicated transition matrix. ABCDP=ABCD10000010.1.1.5.30001 In Problems 1-6, identify the absorbing states in the indicated transition matrix. ABCDP=ABCD01001000.1.2.3.4.7.1.1.1 In Problems 7-10, identify the absorbing states for each transition diagram, and determine whether or not the diagram represents an absorbing Markov chain.In Problems 7-10, identify the absorbing states for each transition diagram, and determine whether or not the diagram represents an absorbing Markov chain.In Problems 7-10, identify the absorbing states for each transition diagram, and determine whether or not the diagram represents an absorbing Markov chain.In Problems 7-10, identify the absorbing states for each transition diagram, and determine whether or not the diagram represents an absorbing Markov chain.In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? 0110 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? 1001 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? .3.701 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? .6.410 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? 100010001 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? 010001100 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? .9.10.1.90001 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? .5.50.4.3.3001 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? .90.10100.2.8 In Problems 11-20, could the given matrix be the transition matrix of an absorbing Markov chain? 1000010.7.3 In Problems 21-24.find a standard form for the absorbing Markov chain with the indicated transition diagram.In Problems 21-24.find a standard form for the absorbing Markov chain with the indicated transition diagram.In Problems 21-24.find a standard form for the absorbing Markov chain with the indicated transition diagram.In Problems 21-24.find a standard form for the absorbing Markov chain with the indicated transition diagram.In Problems 25-28, find a standard form for the absorbing Markov chain with the indicated transition matrix. ABCP=ABC.2.3.5100001 In Problems 25-28, find a standard form for the absorbing Markov chain with the indicated transition matrix. ABCP=ABC001010.7.2.1 In Problems 25-28, find a standard form for the absorbing Markov chain with the indicated transition matrix. ABCDP=ABCD.1.2.3.40100.5.2.2.10001 In Problems 25-28, find a standard form for the absorbing Markov chain with the indicated transition matrix. ABCDP=ABCD0.3.3.401000010.8.1.10 In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of trials needed to go from each nonabsorbing state to an absorbing state. ABCP=ABC100010.1.4.5 In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of trials needed to go from each nonabsorbing state to an absorbing state. ABCP=ABC100010.3.2.5 In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of trials needed to go from each nonabsorbing state to an absorbing state. ABCP=ABC100.2.6.2.4.2.4 In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of trials needed to go from each nonabsorbing state to an absorbing state. ABCP=ABC100.1.6.3.2.2.6 In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of trials needed to go from each nonabsorbing state to an absorbing state. ABCDP=ABCD10000100.1.2.6.1.2.2.3.3 In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of trials needed to go from each nonabsorbing state to an absorbing state. ABCDP=ABCD10000100.1.1.7.1.3.1.4.2 Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated initial-state matrices. For matrix P from Problem 29 with AS0=001BS0=.2.5.3 Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated initial-state matrices. For matrix P from Problem 30 with AS0=001BS0=.2.5.3 Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated initial-state matrices. For matrix P from Problem 31 with AS0=001BS0=.2.5.3 Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated initial-state matrices. For matrix P from Problem 32 with AS0=001BS0=.2.5.3 Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated initial-state matrices. For matrix P from Problem 33 with AS0=0001BS0=0010CS0=00.4.6DS0=.1.2.3.4 Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated initial-state matrices. For matrix P from Problem 34 with AS0=0001BS0=0010CS0=00.4.6DS0=.1.2.3.4 In Problems 41-48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has an absorbing state, then it is an absorbing chain.In Problems 41-48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has exactly two states and at least one absorbing state, then it is an absorbing chain.In Problems 41-48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has exactly three states, one absorbing and two nonabsorbing, then it is an absorbing chain.In Problems 41-48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has exactly three states, one nonabsorbing and two absorbing, then it is an absorbing chain.In Problems 41-48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If every state of a Markov chain is an absorbing state, then it is an absorbing chain.In Problems 41-48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain is absorbing, then it has a unique stationary matrix.In Problems 41-48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain is absorbing, then it is regular.In Problems 41-48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain is regular, then it is absorbing.In Problems 49-52, use a graphing calculator to approximate the limiting matrix for the indicated standard form. ABCDP=ABCD10000100.5.3.1.1.6.2.1.1 In Problems 49-52, use a graphing calculator to approximate the limiting matrix for the indicated standard form. ABCDP=ABCD10000100.1.1.5.30.2.3.5 In Problems 49-52, use a graphing calculator to approximate the limiting matrix for the indicated standard form. ABCDEP=ABCDE10000010000.4.50.10.40.3.3.4.40.20 In Problems 49-52, use a graphing calculator to approximate the limiting matrix for the indicated standard form. ABCDEP=ABCDE1000001000.5000.50.40.2.400.1.7.2 The following matrix P is a nonstandard transition matrix for an absorbing Markov chain: ABCDP=ABCD.2.2.600100.5.10.40001 To find a limiting matrix for P, follow the steps outlined below. Step 1 Using a transition diagram, rearrange the columns and rows of P to produce a standard form for this chain. Step 2 Find the limiting matrix for this standard form. Step 3 Using a transition diagram, reverse the process used in Step 1 to produce a limiting matrix for the original matrix P.Repeat Problem 53 for ABCDP=ABCD1000.3.60.1.2.3.500001 Verify the results in Problem 53 by computing Pk on a graphing calculator for large values of k.Verify the results in Problem 54 by computing Pk on a graphing calculator for large values of k.Show that S=x1x0,0x1, is a stationary matrix for the transition matrix ABCP=ABC100010.1.5.4 Discuss the generalization of this result to any absorbing Markov chain with two absorbing states and one nonabsorbing state.Show that S=x1x00,0x1, is a stationary matrix for the transition matrix ABCDP=ABCD10000100.1.2.3.4.6.2.1.1 Discuss the generalization of this result to any absorbing Markov chain with two absorbing states and two nonabsorbing state.An absorbing Markov chain has the following matrix P as a standard form: ABCDP=ABCD1000.2.3.1.40.5.3.20.1.6.3I0RQ Let wk denote the maximum entry in Qk. Note that w1=.6. (A) Find w2,w4,w8,w16, and w32 to three decimal places. (B) Describe Qk when k is large.Refer to the matrices P and Q of Problem 59. For k a positive integer, let Tk=I+Q+Q2++Qk. (A) Explain why Tk+1=TkQ+I. (B) Using a graphing calculator and part (A) to quickly compute the matrices Tk, discover and describe the connection between IQ1 and Tk when k is large.Loans. A credit union classifies car loans into one of four categories: the loan has been paid in full F. the account is in good standing G with all payments up to date, the account is in arrears A with one or more missing payments, or the account has been classified as a bad debt B and sold to a collection agency. Past records indicate that each month 10 of the accounts in good standing pay the loan in full, 80 remain in good standing, and 10 become in arrears. Furthermore, 10 of the accounts in arrears are paid in full, 40 become accounts in good standing, 40 remain in arrears, and 10 are classified as bad debts. (A) In the long run, what percentage of the accounts in arrears will pay their loan in full? (B) In the long run, what percentage of the accounts in good standing will become bad debts? (C) What is the average number of months that an account in arrears will remain in this system before it is either paid in full or classified as a bad debt?Employee training. A chain of car muffler and brake repair shops maintains a training program for its mechanics. All new mechanics begin training in muffler repairs. Every 3 months, the performance of each mechanic is reviewed. Past records indicate that after each quarterly review, 30 of the muffler repair trainees are rated as qualified to repair mufflers and begin training in brake repairs. 20 are terminated for unsatisfactory performance, and the remainder continue as muffler repair trainees. Also, 30 of the brake repair trainees are rated as fully qualified mechanics requiring no further training. 10 are terminated for unsatisfactory performance, and the remainder continue as brake repair trainees. (A) In the long run, what percentage of muffler repair trainees will become fully qualified mechanics? (B) In the long run, what percentage of brake repair trainees will be terminated? (C) What is the average number of quarters that a muffler repair trainee will remain in the training program before being either terminated or promoted to fully qualified mechanic?Marketing. Three electronics firms are aggressively marketing their graphing calculators to high school and college mathematics departments by offering volume discounts, complimentary display equipment, and assistance with curriculum development. Due to the amount of equipment involved and the necessary curriculum changes, once a department decides to use a particular calculator in their courses, they never switch to another brand or stop using calculators. Each year, 6 of the departments decide to use calculators from company A, 3 decide to use calculators from company B, 11 decide to use calculators from company C. and the remainder decide not to use any calculators in their courses. (A) In the long run, what is the market share of each company? (B) On average, how many years will it take a department to decide to use calculators from one of these companies in their courses?Pensions. Once a year company employees are given the opportunity to join one of three pension plans: A, B, or C. Once an employee decides to join one of these plans, the employee cannot drop the plan or switch to another plan. Past records indicate that each year 4 of employees elect to join plan A, 14 elect to join plan B. 7 elect to join plan C, and the remainder do not join any plan. (A) In the long run. what percentage of the employees will elect to join plan A ? Plan B ? Plan C ? (B) On average, how many years will it take an employee to decide to join a plan?Medicine. After bypass surgery, patients are placed in an intensive care unit (ICU) until their condition stabilizes. Then they are transferred to a cardiac care ward (CCW), where they remain until they are released from the hospital. In a particular metropolitan area, a study of hospital records produced the following data: each day 2 of the patients in the ICU died, 52 were transferred to the CCW, and the remainder stayed in the ICU. Furthermore, each day 4 of the patients in the CCW developed complications and were returned to the ICU, 1 died while in the CCW, 22 were released from the hospital, and the remainder stayed in the CCW. (A) In the long run, what percentage of the patients in the ICU are released from the hospital? (B) In the long run, what percentage of the patients in the CCW die without ever being released from the hospital? (C) What is the average number of days that a patient in the ICU will stay in the hospital?Medicine. The study discussed in Problem 65 also produced the following data for patients who underwent aortic valve replacements: each day 2 of the patients in the ICU died, 60 were transferred to the CCW, and the remainder stayed in the ICU. Furthermore, each day 5 of the patients in the CCW developed complications and were returned to the ICU, 1 died while in the CCW, 19 were released from the hospital, and the remainder stayed in the CCW. (A) In the long run, what percentage of the patients in the CCW are released from the hospital? (B) In the long run, what percentage of the patients in the ICU die without ever being released from the hospital? (C) What is the average number of days a patient in the CCW will stay in the hospital?Psychology. A rat is placed in room F or room B of the maze shown in the figure. The rat wanders from room to room until it enters one of the rooms containing food, L or R. Assume that the rat chooses an exit from a room at random and that once it enters a room with food it never leaves. (A) What is the long-run probability that a rat placed in room B ends up in room R ? (B) What is the average number of exits that a rat placed in room B will choose until it finds food?Psychology. Repeat Problem 67 if the exit from room B to room R is blocked.Given the transition matrix P and initial-state matrix S0 shown below, find S1 and S2, and explain what each represents: ABP=AB.6.4.2.8S0=.3.7 In Problems 2-6, P is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither. ABP=AB10.7.3 In Problems 2-6, P is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither. ABP=AB01.7.3 In Problems 2-6, P is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither. ABP=AB0110 In Problems 2-6, P is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither. ABCP=ABC.80.2010001 6RE In Problems 7-10, write a transition matrix for the transition diagram indicated, identify any absorbing states, and classify each Markov chain as regular, absorbing, or neither.In Problems 7-10, write a transition matrix for the transition diagram indicated, identify any absorbing states, and classify each Markov chain as regular, absorbing, or neither.In Problems 7-10, write a transition matrix for the transition diagram indicated, identify any absorbing states, and classify each Markov chain as regular, absorbing, or neither.In Problems 7-10, write a transition matrix for the transition diagram indicated, identify any absorbing states, and classify each Markov chain as regular, absorbing, or neither.A Markov chain has three states, A,B, and C. The probability of going from state A to state C in one trial is .5, the probability of going from state B to state A in one trial is .8. the probability of going from state B to state C in one trial is .2, the probability of going from state C to state A in one trial is .1, and the probability of going from state C to state B in one trial is .3. Draw a transition diagram and write a transition matrix for this chain.Given the transition matrix ABP=AB.4.6.9.1 find the probability of (A) Going from state A to state B in two trials (B) Going from state B to state A in three trials In Problems 13 and 14. solve the equation SP=S to find the stationary matrix S and the limiting matrix P. ABP=AB.4.6.2.8 In Problems 13 and 14. solve the equation SP=S to find the stationary matrix S and the limiting matrix P. ABCP=ABC.4.60.5.3.20.8.2 In Problems 15 and 16, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing slate and the average number of trials needed to go from each nonabsorbing state to an absorbing state. ABCP=ABC100010.3.1.6 In Problems 15 and 16, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing slate and the average number of trials needed to go from each nonabsorbing state to an absorbing state. ABCDP=ABCD10000100.1.5.2.2.1.1.4.4 In Problems 17-20, use a graphing calculator to approximate the limiting matrix for the indicated transition matrix. Matrix P from Problem 13 In Problems 17-20, use a graphing calculator to approximate the limiting matrix for the indicated transition matrix. Matrix P from Problem 14 In Problems 17-20, use a graphing calculator to approximate the limiting matrix for the indicated transition matrix. Matrix P from Problem 15 In Problems 17-20, use a graphing calculator to approximate the limiting matrix for the indicated transition matrix. Matrix P from Problem 16 Find a standard form for the absorbing Markov chain with transition matrix ABCDP=ABCD.6.1.2.10100.3.2.3.20001 In Problems 22 and 23, determine the long-run behavior of the successive state matrices for the indicated transition matrix and initial-state matrices. ABCP=ABC010001.2.6.2AS0=001BS0=.5.3.2 In Problems 22 and 23, determine the long-run behavior of the successive state matrices for the indicated transition matrix and initial-state matrices. ABCP=ABC100010.2.6.2AS0=001BS0=.5.3.2 Let P be a 22 transition matrix for a Markov chain. Can P be regular if two of its entries are 0 ? Explain.Let P be a 33 transition matrix for a Markov chain. Can P be regular if two of its entries are 0 ? Explain.A red urn contains 2 red marbles, 1 blue marble, and 1 green marble. A blue urn contains 1 red marble, 3 blue marbles, and 1 green marble. A green urn contains 6 red marbles, 3 blue marbles, and 1 green marble. A marble is selected from an urn, the color is noted, and the marble is returned to the urn from which it was drawn. The next marble is drawn from the urn whose color is the same as the marble just drawn. This is a Markov process with three states: draw from the red urn, draw from the blue urn, or draw from the green urn. (A) Draw a transition diagram for this process. (B) Write the transition matrix P. (C) Determine whether this chain is regular, absorbing, or neither. (D) Find the limiting matrix P, if it exists, and describe the long-run behavior of this process.Repeat Problem 26 if the blue and green marbles are removed from the red urn.Show that S=xyz0, where 0x1, 0y1, 0z1, and x+y+z=1, is a stationary matrix for the transition matrix ABCDP=ABCD100001000010.1.3.4.2 Discuss the generalization of this result to any absorbing chain with three absorbing states and one nonabsorbing state.Give an example of a transition matrix for a Markov chain that has no limiting matrix.Give an example of a transition matrix for an absorbing Markov chain that has two different stationary matrices.Give an example of a transition matrix for a regular Markov chain for which .3.1.6 is a stationary matrix.Give an example of a transition matrix for an absorbing Markov chain for which .3.1.6 is a stationary matrix.Explain why an absorbing Markov chain that has more than one state is not regular.Explain why a regular Markov chain that has more than one state is not absorbing.A Markov chain has transition matrix P=.4.6.2.8 For S=.3.9, calculate SP. Is S a stationary matrix? Explain.In Problems 36 and 37, use a graphing calculator to approximate the entries (to three decimal places) of the limiting matrix, if it exists, of the indicated transition matrix. ABCDP=ABCD.2.3.1.400100.80.20010 In Problems 36 and 37, use a graphing calculator to approximate the entries (to three decimal places) of the limiting matrix, if it exists, of the indicated transition matrix. ABCDP=ABCD.10.3.6.2.4.1.3.3.50.2.9.100 Product switching. A company's brand X has 20 of the market. A market research firm finds that if a person uses brand X, the probability is .7 that he or she will buy it next time. On the other hand, if a person does not use brand X (represented by X ), the probability is .5 that he or she will switch to brand X next time. (A) Draw a transition diagram. (B) Write a transition matrix. (C) Write the initial-state matrix. (D) Find the first-stale matrix and explain what it represents. (E) Find the stationary matrix. (F) What percentage of the market will brand X have in the long run if the transition matrix does not change?Marketing. Recent technological advances have led to the development of three new milling machines: brand A, brand B, and brand C. Due to the extensive retooling and startup costs, once a company converts its machine shop to one of these new machines, it never switches to another brand. Each year, 6 of the machine shops convert to brand A machines. 8 convert to brand B machines, 11 convert to brand C machines, and the remainder continue to use their old machines. (A) In the long run, what is the market share of each brand? (B) What is the average number of years that a company waits before converting to one of the new milling machines?40RE Employee training. In order to become a fellow of the Society of Actuaries, a person must pass a series of ten examinations. Passage of the first two preliminary exams is a prerequisite for employment as a trainee in the actuarial department of a large insurance company. Each year, 15 of the trainees complete the next three exams and become associates of the Society of Actuaries, 5 leave the company, never to return, and the remainder continue as trainees. Furthermore, each year, 17 of the associates complete the remaining five exams and become fellows of the Society of Actuaries, 3 leave the company, never to return, and the remainder continue as associates. (A) In the long run, what percentage of the trainees will become fellows? (B) In the long run, what percentage of the associates will leave the company? (C) What is the average number of years that a trainee remains in this program before either becoming a fellow or being discharged?Genetics. A given plant species has red, pink, or white flowers according to the genotypes RR. RW, and WW, respectively. If each of these genotypes is crossed with a red-flowering plant, the transition matrix is NextgenerationRedPinkWhiteThisgenerationRedPinkWhite100.5.50010 If each generation of the plant is crossed only with red plants to produce the next generation, show that eventually all the flowers produced by the plants will be red. (Find the limiting matrix.)Smoking. Table 2 gives the percentage of U.S. adults who were smokers in the given year. The following transition matrix P is proposed as a model for the data, where S represents the population of U.S. adult smokers. FiveyearslaterSSCurrentyearSS.74.26.03.97=P (A) Let S0=.301.699 and find S1,S2, and S3. Compute the matrices exactly and then round entries to three decimal places. (B) Construct a new table comparing the results from part (A) with the data in Table 2. (C) According to this transition matrix, what percentage of the adult U.S. population will be smokers in the long run?(A) Using Figure 3, estimate the median annual income of a male with some college and a female who holds a bachelor’s degree. Within which educational category is there the greatest difference between male and female income? The least difference? (B) Using Figure 4, estimate the population of Kinshasa in the years 2016 and 2030.Which of the cities is projected to have the greatest increase in population from 2016 to 2030 ? The least increase? The greatest percentage increase? The least percentage increase?(A) Using Figure 6 estimate the revenue and costs in 2017. In which years is a profit realized? In which year is the greatest loss experienced? (B) Using Figure 7 estimate the U.S. consumption of nuclear energy in 2030. Estimate the percentage of total consumption that will come from renewable energy in the year 2030,Repeat Example 1 for the following intervals: (A) 649.5699.5 (B) 299.5499.5 The weights (in pounds) were recorded for 20 kindergarten children chosen at random: (A) Use a graphing calculator to draw a histogram of the data, choosing the five class intervals 32.537.5,37.542.5 and so on. (B) What is the probability that a kindergarten child chosen at random from the sample weighs less than 42.5 pounds? More than 42.5 pounds?(A) Construct a frequency table and histogram for the following data set using a class interval width of 2 starting at 0.5 (B) Construct a frequency table and histogram for the following data set using a class interval width of 2 starting at 0.5. (c) How are the two histograms of parts (A) and (B) similar? How are the two data sets different?(A) Construct a frequency table and histogram for the data set of part (A) of Problem 1 using a class interval width of 1, starting at 0.5. (B) Construct a frequency table and histogram for the data set of part (B) of Problem 1 using a class interval width of 1, starting at 0.5. (c) How are the histogram of part (A) and (B) different?Gross domestic product. Graph the data in the following table using a bar graph.Corporation revenues. Graph the data in the following table using a bar graph.Gold production. Use the double bar graph on world gold production to determine the country that showed the greatest increase in gold production from 2010 to 2015. Which country showed the greatest percentage increase? The greatest percentage decrease?Gasoline prices .Graph the data in the following table using divided bar graph. (Source: American Petroleum Institute)Postal service. Graph the data in the following table using a broken line graph.Postal service. Refer to Problem 9. If the data were presented in a bar graph, would horizontal bars or vertical bars be used? Could the data be presented in a pie graph? Explain.Federal income. Graph the data in the following table using a pie graph.Gasoline prices. In April 2017 the average price of a gallon of gasoline in the United States 57 was $2.47. Of this amount, 126 cents was the cost of crude oil, cents the cost of refining, 20 cents the cost of distribution and marketing, and 44 cents the amount of tax. Use a pie graph to present this data.Starting salaries. The starting salaries (in thousands of dollars) of 20 graduates, chosen at random from the graduating class of an urban university, were determined and recorded in the following table: (A) Construct a frequency and relative frequency table using a class interval width of 4 starling at 30.5. (B) Construct a histogram. (C) What is the probability that a graduate chosen from the sample will have a starting salary above $42,500 ? Below $38,500 ? (D) Construct a histogram ussing a graphing calculator Commute times. Thirty-two people were chosen at random from among the employees of a large corporation. Their commute times (in hours) from home to work were recorded in the following table: (A) Construct a frequency and relative frequency table using a class interval width of 0.2, starting at 0.15 (B) Construct a histogram. (C) What is the probability that a person chosen at random from the sample will have a commuting time of at least an hour? Of at most half an hour? (D) Construct a histogram using a graphing calculator Common stocks. The following table shows price-earnings ratios of 100 common stocks chosen at random from the New York Stock Exchange. (A) Construct a frequency and relative frequency table using a class interval of 5, starting at 0.5. (B) Construct a histogram. (C) Construct a frequency polygon. (D) Construct a cumulative frequency and relative cumulative frequency table. What is the probability that a price earnings ratio drawn at random from the sample will fall between 4.5 and 4.5 ? (E) Construct a cumulative frequency polygon.Mouse weights. One hundred healthy mice were weighed at the beginning of an experiment with the following results: (A) Construct a frequency and relative frequency table using a class interval 2 of starting at 41.5. (B) Construct a histogram. (C) Construct a frequency polygon. (D) Construct a cumulative frequency and relative cumulative frequency table. What is the probability of a mouse weight drawn at random from the sample lying between 5.5 and 53.5 ? (E) Construct a cumulative frequency polygon.Population growth. Graph the data in the following table using a broken-line graph.Aims epidemic. One way to gauge the toll of the AIDS epidemic in Sub-Saharan Africa is to compare life expectancies with the figures that would have been projected in the absence of AIDS. Use the broken-line graphs shown to estimate the life expectancy of a child born in the year 2012.What would the life expectancy of the same child be in the absence of AIDS? For which years of birth is the life expectancy less than 50 years? If there were no AIDS epidemic, for which years of birth would the life expectancy be less than 50 years.Nutrition. Graph the data in the following table using a double bar graph.Greenhouse gases. The U.S. Environmental Protection Agency estimated that of all emissions 2014 of greenhouse gases by the United States in, carbon dioxide accounted for 81, methane for 11, nitrous oxide for 6, and fluorinated gases for 6. Use a pie graph to present this data. Find the central angles of the graph.Nutrition. Graph the nutritional information in the following table using a double bar graph.Nutrition. Refer to Problem 21. Suppose that you are trying to limit the fat in your diet to at most 30 of your calories, and your calories down to 2000 per day. Should you order the quarter-pound bacon cheeseburger with mayo for lunch? How would such a lunch affect your choice of breakfast and dinner? Discuss.Education. For statistical studies, U.S. states are often grouped by region: Northeast, Midwest, South, and West. The 1965 total public school enrollment (in millions) in each region was 8.8,11.8,13.8, and 7.6 respectively. The projected 2020 enrollment was 7.8,10.8,20.4 and 13.6 respectively. Use two pie graphs to present this data and discuss any trends suggested by your graphs.Study abroad. Would a pie graph be more effective or less effective than the bar graph shown in presenting information on the most popular destinations of U.S. college students who study abroad? Justify your answer.Median age. Use the broken-line graph shown to estimate the median age in 1900 and 2000.In which decades did the median age increase? In which did it decrease? Discuss the factors that may have contributed to the increases and decreases.State prisoners. In 1980 in the United States, 6 of the inmates of state prisons were incarcerated for drug offenses. 30#37; for property crimes, 4 for public order offenses, and 60 for violent crimes; in 2014 the percentages were 16,19,12 and 53 respectively. Present the data using two pie graphs. Discuss factors that may account for the shift in percentages between 1980 and 2014.Grade point Averages. One hundred seniors were chosen at random from a graduating class at a university and their grade-point averages recorded 23. Education. For statistical studies, U.S. states are often grouped by region: Northeast, Midwest, South, and West. The 1965 total public school enrollment (in millions) in each region was 8.8,11.8,13.8 and 7.6 respectively. The projected 2020 enrollment was 7.8,10.8,20.4, and 13.6, respectively. Use two pie graphs to present this data and discuss any trends suggested by your graphs. (A) Construct a frequency and relative frequency table using a class interval of 0.2 starting at 1.95. (B) Construct a histogram. (C) Construct a frequency polygon. (D) Construct a cumulative frequency and relative cumulative frequency table. What is the probability of a GPA drawn at random from the sample being over 2.95 (E) Construct a cumulative frequency polygon.For many sets of measurements the median lies between the mode and the mean. But this is not always so. (A) In a class of seven students, the scores on an exam were 52,89,89,92,93,96,99. Show that the mean is less than the mode and that the mode is less than the median. (B) Construct hypothetical sets of exam scores to show that all possible orders among the mean, median, and mode can occur.Find the mean for the sample measurements 3.2,4.5,2.8,5.0, ansd 3.6.Compute the mean for the grouped sample data listed in Table 2. .Add the salary $100,000 to those in Example 3 and compute the median and mean for these eight salaries.Find the median for the grouped data in the following table:Compute the mode(s), median, and mean for each data set: (A) 2,1,2,1,1,5,1,9,4 (B) 2,5,1,4,9,8,7 (C) 8,2,6,8,3,3,1,5,1,8,3 In Problems 1-4, find the mean of the data set. (If necessary, review Section B.1). 5,8,6,7,9 s In Problems 1-4, find the mean of the data set. (If necessary, review Section B.1). 12,15,18,21 In Problems 1-4, find the mean of the data set. (If necessary, review Section B.1). 1,2,0,2,4 In Problems 1-4, find the mean of the data set. (If necessary, review Section B.1). 85,75,65,75 In Problems 5-8, find the indicated sum. (If necessary, review Section B.1). i=16xiifxi=i+3fori=1,2,,6 In Problems 5-8, find the indicated sum. (If necessary, review Section B.1). i=15xiifxi=100ifori=1,2,,5 In Problems 5-8, find the indicated sum. (If necessary, review Section B.1). i=610xifiifxi=2iandfi=3ifori=6,7,,10 In Problems 5-8, find the indicated sum. (If necessary, review Section B.1). i=58Xifiifxi=i2andfi=ifori=5,6,7,8 Find the mean, median, and mode for the sets of ungrouped data given in Problems 9 and 10. 1,2,2,3,3,3,3,4,4,5 Find the mean, median, and mode for the sets of ungrouped data given in Problems 9 and 10. 1,1,1,1,2,3,4,5,5,5 Find the mean, median, and/or mode, whichever are applicable, in Problems 11 and 12.Find the mean, median, and/or mode, whichever are applicable, in Problems 11 and 12.Find the mean for the sets of grouped data in Problems 13 and 14.Find the mean for the sets of grouped data in Problems 13 and 14.Which single measure of central tendency-mean, median, or mode-would you say best describes the following set of measurements? Discuss the factors that justify your preferences Which single measure of central tendency mean, median, or mode would you say best describes the following set of measurements? Discuss the factors that justify your preference.A data set is formed by recording the results of 100 rolls of a fair die. (A) What would you expect the mean of the data set to be? The median? (B) Form such a data set by using a graphing calculator to simulate 100 rolls of a fair die, and find its mean and median A data set is formed by recording the sums on 200 rolls of a pair of fair dice (A) What would you expect the mean of the data set to be? The median? (B) Form such a data set by using a graphing calculator to simulate 200 rolls of a pair of fair dice, and find the mean and median of the set.(A) Construct a set of four numbers that has mean 300, median 250, and mode 175. (B) Let constructing m1m2m3. Devise four numbers and discuss that has a procedure mean m1 for median m2, and mode m3.(A) Construct a set of five numbers that has mean 200 median 150, and mode 50. (B) Let m1m2m3. Devise and discuss a procedure for constructing a set of five numbers that has mean m1 median m2, and mode m3.Price earnings ratios. Find the mean, median, and mode for the data in the following table Gasoline tax. Find the mean, median, and mode for the data in the following table. (Source: American Petroleum Institute.)Light bulb lifetime. Find the mean and median for the data in the following table.Price earnings ratios. Find the mean and median for the data in the following table.Student loan debt. Find the mean median, and mode for the data in the following table l that gives the percentages by stale of students graduating from college in 2015 who had student loan debt.Tourism Find the mean, median, and mode for the data in the following table.Mouse weights. Find the mean and median for the data in the following table.Blood cholesterol levels. Find the mean and median for the data in the following table.Immigration Find the mean, median, and mode for the data in the following table.Grade point averages. Find the mean and median for the grouped data in the following table.Entrance examination scores. Compute the median for the grouped data of entrance examination scores given in Table 1 on page 514 Presidents. Find the mean and median for the grouped data in the following table (A) When is the sample standard deviation of a set of measurements equal to 0 ? (B) Can the population standard deviation of a set of measurements ever be greater than the range? Explain why or why not.Find the standard deviation for the sample measurements 1.2,1.4,1.7,1.3,1.5.Find the standard deviation for the grouped sample data shown below.1E In Problems 1-8, find the indicated sum. (If necessary, review Section B.1). i=15xi102ifx1=8,x2=9,x3=10,x4=11,x5=12 In Problems 1-8, find the indicated sum. (If necessary, review Section B.1). i=14xi+32ifx1=4,x2=3,x3=2,x4=3 In Problems 1-8, find the indicated sum. (If necessary, review Section B.1). i=13xi+152ifx1=20,x2=15,x3=10 In Problems 1-8, find the indicated sum. (If necessary, review Section B.1). i=13xi42fiifx1=0,x2=4,x3=8,f1=1,f2=1,f3=1 In Problems 1-8, find the indicated sum. (If necessary, review Section B.1). i=13xi42fiifx1=0,x2=4,x3=8,f1=2,f2=1,f3=2 In Problems 1-8, find the indicated sum. (If necessary, review Section B.1). i=15xi152fiifxi=5i,fi=2fori=1,2,...,5 In Problems 1-8, find the indicated sum. (If necessary, review Section B.1). i=14xi3.52fiifxi=i+1,fi=3fori=1,2,3,4 (A) Find set of the ungrouped mean and sample standard data deviation of the following set of ungrouped sample data. 4235316423 (B) What proportion of the measurements lies within 1standard deviation of the mean? Within 2 standard deviations? Within 3 standard deviations? (C) Based on your answers to part (B), would you conjecture that the histogram is approximately bell shaped? (D) Explain. To confirm your conjecture, construct a histogram with class interval width 1 starting at 0.5.(A) Find the mean and standard deviation of the following set of ungrouped sample data. 3512154513 (B) What proportion of the measurements lies within 1 standard deviation of the mean? Within 2 standard deviations? Within 3 standard deviations? (C) Based on your answers to part (B), would you conjecture that the histogram is approximately bell shaped? Explain. (D) To confirm your conjecture, construct a histogram with class interval width 1, starting at 0.5.In Problems 11 and 12, find the standard deviation for each set of grouped sample data using formula (5) on page 525.In Problems 11 and 12, find the standard deviation for each set of grouped sample data using formula (5) on page 525.In Problems 13-18, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The range for a set of sample measurements is less than or equal to the range of the whole population.In Problems 13-18, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The range for a set of measurements is greater than or equal to 0.In Problems 13-18, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The sample standard deviation is less than or equal to the sample variance.In Problems 13-18, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. Given a set of sample measurements that are not all equal, the sample standard deviation is a positive real number In Problems 13-18, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If x1,x2 is the whole population, then the population standard deviation is equal to one-half the distance from x1 to x2 In Problems 13-18, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The sample variance of a set of measurements is always less than the population variance.A data set is formed by recording the sums in 100 rolls of a pair of dice. A second data set is formed by recording the results of 100 draws of a ball from a box containing 11 balls numbered 2 through 12 (A) Which of the two data sets would you expect to have the smaller standard deviation? Explain. (B) To obtain evidence for your answer to part (A) Use a graphing calculator to simulate both experiments and compute the standard deviations of each data set.A data set is formed by recording the results of rolling a fair die 200 times. A second data set is formed by rolling a pair of dice 200 times each time recording the minimum of the two numbers. (A) Which of the two data sets would you expect to have the smaller standard deviation? Explain. (B) To obtain evidence for your answer to part (A), use a graphing calculator to simulate both experiments and compute the standard deviations of each data set.Find the mean and standard deviation for each of the sample data sets given in Problems 21-28. Use the suggestions in the remarks following Examples 1 and 2 to perform some of the computations. Earnings per share. The earnings per share (in dollars) for 12 companies selected at random from the list of Fortune 500 companies are:Find the mean and standard deviation for each of the sample data sets given in Problems 21-28. Use the suggestions in the remarks following Examples 1 and 2 to perform some of the computations. Checkout times. The checkout times (in minutes) for 12 randomly selected customers at a large supermarket during the store’s busiest time are Find the mean and standard deviation for each of the sample data sets given in Problems 21-28. Use the suggestions in the remarks following Examples 1 and 2 to perform some of the computations. Quality control. The lives (in hours of continuous use) of 100 randomly selected flashlight batteries are Find the mean and standard deviation for each of the sample data sets given in Problems 21-28. Use the suggestions in the remarks following Examples 1 and 2 to perform some of the computations. Stock analysis. The price-earnings ratios of 100 randomly selected stocks from the New York Stock Exchange are Find the mean and standard deviation for each of the sample data sets given in Problems 21-28. Use the suggestions in the remarks following Examples 1 and 2 to perform some of the computations. Medicine. The reaction times (in minutes) of a drug given to a random sample of 12 patients are:Find the mean and standard deviation for each of the sample data sets given in Problems 21-28. Use the suggestions in the remarks following Examples 1 and 2 to perform some of the computations. Nutrition animals. The mouse weights (in grams) of a random sample of 100 mice involved in a nutrition experiment are:Find the mean and standard deviation for each of the sample data sets given in Problems 21-28. Use the suggestions in the remarks following Examples 1 and 2 to perform some of the computations. Reading scores. The grade-level reading scores from a reading test given to a random sample of 12 students in an urban high school graduating class are:Find the mean and standard deviation for each of the sample data sets given in Problems 21-28. Use the suggestions in the remarks following Examples 1 and 2 to perform some of the computations. Grade point average. The grade-point averages of a random sample of 100 students from a university’s graduating class are Find p and q for a single roll of a fair die, where success is a number divisible by 3 turning up.In Example 2, find the probability of the outcome FSSSF Using the same die experiment as in Example 3, what is the probability of rolling (A) Exactly one 3 ? (B) At least one 3 ?Use the binomial formula to expand q+p4.Repeat Example 5, where the binomial experiment consists of two rolls of a die instead of three rolls.Compute the mean and standard deviation for the random variable in Matched Problem 5.Repeat Example 7 for four patients. The probability of recovering after a particular type of operation is. 4 Eight patients undergo this operation. For the binomial distribution, (A) Write the probability function. (B) Construct a table. (C) Construct a histogram. (D) Find the mean and standard deviation.Evaluate nCxpxqnx for the values of n,x, and p given in Problems 1-6. n=5,x=1,p=12 Evaluate nCxpxqnx for the values of n,x, and p given in Problems 1-6. n=5,x=2,p=12 Evaluate nCxpxqnx for the values of n,x, and p given in Problems 1-6. n=6,x=3,p=.4 Evaluate nCxpxqnx for the values of n,x, and p given in Problems 1-6. n=6,x=6,p=.4 Evaluate nCxpxqnx for the values of n,x, and p given in Problems 1-6. n=4,x=3,p=23 Evaluate nCxpxqnx for the values of n,x, and p given in Problems 1-6. n=4,x=3,p=13 In Problems 7-12, a fair coin is tossed four times. What is the probability of obtaining A head on the first toss and tails on each of the other losses?In Problems 7-12, a fair coin is tossed four times. What is the probability of obtaining Exactly one head?In Problems 7-12, a fair coin is tossed four times. What is the probability of obtaining At least three tails?In Problems 7-12, a fair coin is tossed four times. What is the probability of obtaining Tails on each of the first three tosses?In Problems 7-12, a fair coin is tossed four times. What is the probability of obtaining No heads?In Problems 7-12, a fair coin is tossed four times. What is the probability of obtaining Four heads?In Problems 13-18 construct a histogram for the binomial distribution Px=nCXpxqnx, and compute the mean and standard deviation if n=3,p=14 In Problems 13-18 construct a histogram for the binomial distribution Px=nCXpxqnx, and compute the mean and standard deviation if n=3,p=34 In Problems 13-18 construct a histogram for the binomial distribution Px=nCXpxqnx, and compute the mean and standard deviation if n=4,p=13 In Problems 13-18 construct a histogram for the binomial distribution Px=nCXpxqnx, and compute the mean and standard deviation if n=5,p=13 In Problems 13-18 construct a histogram for the binomial distribution Px=nCXpxqnx, and compute the mean and standard deviation if n=5,p=0 In Problems 13-18 construct a histogram for the binomial distribution Px=nCXpxqnx, and compute the mean and standard deviation if n=4,p=1 In Problems 19-24, round answers to four decimal places. A fair die is rolled four times Find the probability of obtaining A 6,6,5, and 5 in that order.In Problems 19-24, round answers to four decimal places. A fair die is rolled four times Find the probability of obtaining Two 6s and two 5s in any order In Problems 19-24, round answers to four decimal places. A fair die is rolled four times Find the probability of obtaining Exactly two 6s In Problems 19-24, round answers to four decimal places. A fair die is rolled four times Find the probability of obtaining Exactly three 6s In Problems 19-24, round answers to four decimal places. A fair die is rolled four times Find the probability of obtaining No 6s In Problems 19-24, round answers to four decimal places. A fair die is rolled four times Find the probability of obtaining At least two 6s If a baseball player has a batting average of 350 what is the probability that the player will get the following number of hits in the next four times at bat? (A) Exactly 2 hits (B) At least 2 hits If a true-false test with 10 questions is given, what is the probability of scoring (A) Exactly 70 just by guessing? (B) 70 or better just by guessing?A multiple-choice test consists of 10 questions, each with choices A,B,C,D,E (exactly one choice is correct). Which is more likely if you simply guess at each question: all your answers are wrong, or at least half are right? Explain.If 60 of the electorate supports the mayor, what is the probability that in a random sample of 10 voters, fewer than half support her?Construct a histogram for each of the binomial distributions in Problems 29-32. Compute the mean and standard deviation for each distribution. Px=6Cx.4x.66x Construct a histogram for each of the binomial distributions in Problems 29-32. Compute the mean and standard deviation for each distribution. Px=6Cx.6x.46x Construct a histogram for each of the binomial distributions in Problems 29-32. Compute the mean and standard deviation for each distribution. Px=8Cx.3x.78x Construct a histogram for each of the binomial distributions in Problems 29-32. Compute the mean and standard deviation for each distribution. Px=8Cx.7x.38x A random variable represents the number of successes in 20 Bernoulli trails each with probability of success p=.85 (A) Find the mean and standard deviation of the random variable. (B) Find the probability that the number of successes lies within 1 standard deviation of the mean.A random variable represents the number of successes in 20 Bernoulli trails each with probability of success p=.45 (A) Find the mean and standard deviation of the random variable. (B) Find the probability that the number of successes lies within 1 standard deviation of the Mean.In Problems 35 and 36 a coin is loaded so that the probability of a head occurring on a single toss is 34. In five tosses of the coin, what is the probability of getting All heads or all tails?In Problems 35 and 36 a coin is loaded so that the probability of a head occurring on a single toss is 34. In five tosses of the coin, what is the probability of getting Exactly 2 heads or exactly 2 tails?Find conditions on p that guarantee the histogram for a binomial distribution is symmetrical about x=n/2. Justify your answer Consider two binomial distributions for 1,000 repeated Bernoulli trials the first for trials wit p=.15, and the second for trials with p=.85. How are the histograms for the two distributions related? Explain A random variable represents the number of heads in ten tosses of a coin. (A) Find the mean and standard deviation of the random variable. (B) Use a graphing calculator to simulate 200 repetitions of the binomial experiment, and compare the mean and standard deviation of the numbers of heads from the simulation to the answers for part (A).A random variable represents the number of times a sum of 7 or 11 comes up in ten rolls of a pair of dice. (A) Find the mean and standard deviation of the random variable. (B) Use a graphing calculator to simulate 100 repetitions of the binomial experiment, and compare the mean and standard deviation of the numbers of 7s or 11s from the simulation to the answers for part (A).Management training each year a company selects a number of employees for a management training program at a university. On average, 70 of those sent complete the program. Out of 7 people sent, what is the probability that (A) Exactly 5 complete the program? (B) 5 or more complete the program?Employee turnover. If the probability of a new employee in a fast-food chain still being with the company at the end of 1 year is 6, what is the probability that out of 8 newly hired people, (A) 5 will still be with the company after 1 year? (B) 5 or more will still be with the company after 1 year?Quality control A manufacturing process produces, on average, 6 defective items out of 100. To control quality, each day a sample of 10 completed items is selected at random and inspected. If the sample produces more than 2 defective items, then the whole day’s output is inspected, and the manufacturing process is reviewed. What is the probability of this happening, assuming that the process is still producing 6 defective items?Guarantees. A manufacturing process produces, on average 3 defective items. The company ships 10 items in each box and wants to guarantee no more than 1 defective item per box. If this guarantee applies to each box, what is the probability that the box will fail to meet the guarantee?Quality control. A manufacturing process produces, on average, 5 defective items out of 100. To control quality, each day a random sample of 6 completed items is selected and inspected. If success on a single trial (inspection of 1 item) is finding the item defective, then the inspection of each of 6 items in the sample constitutes a binomial experiment. For the binomial distribution, (A) Write the probability function. (B) Construct a table. (C) Draw a histogram. (D) Compute the mean and standard deviation Management training. Each year a company selects 5 employees for a management training program at a university. On average, 40 of those sent complete the course in the top 10 of their class. If we consider an employee finishing in the top 10 of the class a success in a binomial experiment, then for the 5 employees entering the program, there exists a binomial distribution involving P ( x successes out of 5 ).For the binomial distribution, (A) Write the probability function. (B) Construct a table. (C) Draw a histogram. (D) Compute the mean and standard deviation Medical diagnosis A tuberculosis patient is given a chest x-ray .Four tuberculosis x-ray specialists examine each x-ray independently. If each specialist can detect tuberculosis 80 of the time when it is present, what is the probability that at least 1 of the specialists will detect tuberculosis in this patient?Harmful drug side effect. A pharmaceutical laboratory claims that a drug causes serious side effects in 20 people out of 1,000, on average. To check this claim, a hospital administers the drug to 10 randomly chosen patients and finds that 3 suffer from serious side effects if the laboratory's claims are correct, what is the probability that the hospital gets these results?Genetics. The probability that brown-eyed parents, both with the recessive gene for blue eyes, will have a child with brown eyes is. 75.If such parents have 5 children, what is the probability that they will have (A) All blue-eyed children? (B) Exactly 3 children with brown eyes? (C) At least 3 children with brown eyes?Gene mutation the probability of gene mutation under a given level of radiation is 3105. What is the probability of at least 1 gene mutation if 105 genes are exposed to this level of radiation?Epidemics. If the probability of a person contracting influenza on exposure is. 6 consider the binomial distribution for a family of 6 that has been exposed. For this distribution, (A) Write the probability function. (B) Construct a table. (C) Draw a histogram. (D) Compute the mean and standard deviation Drug side effect the probability that a given drug will produce a serious side effect in a person using the drug is .02. In the binomial distribution for 450 people using the drug, what are the mean and standard deviation?Testing A multiple-choice test is given with 5 choices (only one is correct) for each of 10 questions. What is the probability of passing the test with a grade of 70 better just by guessing?Opinion polls. An opinion poll based on a small sample can be unrepresentative of the population. To see why, assume that 40 of the electorate favors a certain candidate. If a random sample of 7 is asked their preference, what is the probability that a majority will favor this candidate?Testing. A multiple-choice test is given with 5 choices (only one is correct) for each of 5 questions. Answering each of the 5 questions by guessing constitutes a binomial experiment with an associated binomial distribution. For this distribution, (A) Write the probability function. (B) Construct a table (C) Draw a histogram. (D) Compute the mean and standard deviation.Sociology. The probability that a marriage will end in divorce within 10 years is. 35. What are the mean and standard deviation for the binomial distribution involving 1,000 marriages?Sociology. If the probability is .55 that a marriage will end in divorce within 20 years, what is the probability that out of 6 couples just married, in the next 20 years (A) None will be divorced? (B) All will be divorced? (C) Exactly 2 will be divorced? (D) At least 2 will be divorced?What percentage of the light bulbs in Example 1 can be expected to last between 500 and 750 hours?Refer to Example 1. What is the probability that a light bulb chosen at random lasts between 400 and 500 hours?In Example 3, Use the normal curve to approximate the probability that in the sample there are (A) From 5 to 9 users of the credit card (B) More than 10 users of the card In Example 3, Use the normal curve to approximate the probability that in the sample there are (A) From 5 to 9 users of the credit card (B) More than 10 users of the card Suppose in Example 4 that the manufacturing process produces 40 defective pens per 1,000, on average. What is the approximate probability that in the sample of 400 pens there are (A) At least 10 and no more than 20 defective pens? (B) 27 or more defective pens?In Problems 1-6, use Appendix C to find the area under the Standard normal curve from 0 to the indicated measurement. 2.00 In Problems 1-6, use Appendix C to find the area under the Standard normal curve from 0 to the indicated measurement. 3.30 In Problems 1-6, use Appendix C to find the area under the Standard normal curve from 0 to the indicated measurement. 1.24 In Problems 1-6, use Appendix C to find the area under the Standard normal curve from 0 to the indicated measurement. 1.08 In Problems 1-6, use Appendix C to find the area under the Standard normal curve from 0 to the indicated measurement. 2.75 In Problems 1-6, use Appendix C to find the area under the Standard normal curve from 0 to the indicated measurement. 0.92 In Problems 7-14, use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis 1,1 In Problems 7-14, use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis 2,2 In Problems 7-14, use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis 0.4,0.7 10E In Problems 7-14, use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis 0.2,1.8 In Problems 7-14, use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis 2.1,0.9 In Problems 7-14, use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis ,0.1 In Problems 7-14, use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis 0.6,In Problems 15-20, given a normal distribution with mean 15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number. 22 In Problems 15-20, given a normal distribution with mean 15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number. 6.4 In Problems 15-20, given a normal distribution with mean 15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number. 1.8.In Problems 15-20, given a normal distribution with mean 15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number. 13.5 In Problems 15-20, given a normal distribution with mean 15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number. 10.9 In Problems 15-20, given a normal distribution with mean 15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number. 48.6 In Problems 21.26, given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement 27.2 In Problems 21.26, given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement 36.1 In Problems 21.26, given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement 12.8

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