Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Introduction to Business Statistics
Machine A produce 3% defectives, machine B produce 5% defectives, and machine C produces 10% defectives. Of the total output from these machines,60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a days production. a. What is the prior probability that the item came from machine C? b. If inspection finds the item to be defective, what is the revised probability that the item came from machine C?A tax accountant has three choices for the method of treating one of a client’s deductions. After this choice has been made, there are only two choices for how a second deduction can be treated. What is the total number of possibilities for the treatment of the two deductions?A committee consists of eight members, each of whom may or may not show up for the next meeting. Assuming that the members will be making independent decisions on whether or not to attend, how many different possibilities exist for the composition of the meeting?Ten prominent citizens have been nominated for a community’s “Citizen of the Year award. First- and seond-pIace trophies are awarded to the two persons receiving the highest and seiond-highest number of votes. In how many different ways can the trophies be awarded?5.53EA state’s license plate has 6 positions, each of which has 37 possibilities (letter, integer, or blank). If the buyer of a personalized plate wants his first three positions to be BMW, in how many ways can his request be satisfied?When we are considering n objects taken r at a time, with r1, why will the number of combinations be less than the number of permutations?An investment counselor would like to meet with 12 of his clients on Monday, but he has time for only 8 appointments. How many different combinations of the clients could be considered for inclusion into his limited schedule for that day?Flow many different combinations are possible if 6 substitute workers are available to fill 3 openings created by employees planning to take vacation leave next week?A roadside museum has 25 exhibits but enough space to display only 10 at a time. If the order of arrangement is considered, how many possibilities exist for the eventual display?A sales representative has 35 customers throughout the state and is planning a trip during which 20 will be visited. In how many orders can the visits be made?The owner of a charter fishing boat has found that 12% of his passengers become seasick during a half- day fishing trip. He has only two beds below deck to accommodate those who become ill. About to embark on a typical half-day trip, he has 6 passengers on board. What is the probability that there will be enough room below deck to accommodate those who become ill?6.55CE6.56CE6.57CE6.58CE6.59CE6.60CEA mining company finds that daily lost-work injuries average 1.2. If the local union contract has a clause requiring that the mine be shut down as soon as three workers incur lost-work injuries, on what percentage of the days will the mine be operational throughout the day?6.62CE6.63CE6.64CE6.65CESeven of the 15 campus police officers available for assignment to the auditorium in which a local politician is to speak have received advanced training in crowd control. If 5 officers are randomly selected for service during the speech, what is the probability that exactly 2 of them will have had advanced training in crowd control? What is the probability that at least 3 of them will have had advanced training?6.67CE6.68CE6.69CE6.70CE6.71CE6.72CE6.73CE6.74CE6.75CE6.76CE6.77CE6.78CE6.79CE6.80CE6.1EIndicate whether each of the following random variables is discrete or continuous. a. The diameter of aluminum rods coming off a production line b. The number of years of schooling employees have completed c. The Dow Jones Industrial Average d. The volume of milk purchased during a supermarket visitIndicate whether each of the following random variables is discrete or Continuous. a. The number of drive-through customers at your local McDonald’s today b. The amount spent by all customers at the local McDonald’s today c. The time, as reported by your digital watch d. The length of a pedestrians stride6.4E6.5EDetermine the mean, variance, and standard deviation of the following discrete probability distribution:Determine the mean, variance, and standard deviation of the following discrete probability distribution:6.8E6.9E6.10EA consultant has presented his client with three alternative research studies that could be conducted. If the client chooses alternative a, the consultant will have to hire 1 additional employee. Two new employees will have to be hired if the client chooses b, and 5 if the client chooses c. The probability that the client will select altern ative a is 0.1, with P(b)=0.5andP(c)=0.4 . Identify the discrete random variable in this situation and determine its expected value.6.12E6.13ELaura McCarthy, the owner of Riverside Bakery, has been approached by insurance underwriters trying to convince her to purchase flood insurance. According to local meteorologists, there is a 0.01probability that the river will flood next year. Riverside’s profits for thecoming year depend on whether Laura buys the flood insurance and whether the river floods. The profits (which take into consideration the $10,000 premium for the flood insurance) for the four possible combinations of Laura’s choice and river conditions are: a. If Laura decides not to purchase flood insurance, use the appropriate discrete probability distribution to determine Riverside’s expected profit next year. b. If Laura purchases the flood insurance, what will be Riverside’s expected profit next year? c. Given the results in parts (a) and (b), provide Laura with a recommendation.In 2007, nearly 24 million tons of steel mill products went to construction and contracting companies. Transco Steel, a hypothetical manufacturer specializing in the production of steel for this market, is faced with aging production facilities and is considering the possible renovation of its plant. The company has reduced its alternatives to just three: (1) no renovation at all, (2) minor renovation, and (3) major renovation. Whichever strategy it chooses, the company’s profits will depend on the size of the construction and contracting industry in future years. Company executives have a subjective probability of 0.3 that the industry will not grow at all, a probability of 0.5 that it will grow moderately, and a probability of 0.2 that it will show a high rate of growth. The company’s estimated profits (in millions of dollars) for each combination of renovation strategy and industry growth possibility are: Source: Statistical Abstract of the United States 2009, p. 630. Given the executives’ subjective probabilities for the three possible states of industry growth, what will be the company’s expected profit if it chooses not to renovate the plant? If it chooses minor renovations to the plant? If it chooses major renovations to the plant? Based on these expected values, provide the company’s management with a recommendation as to which level of renovation they should choose.What is necessary for a process to be considered a Bernoulli process?When we are sampling without replacement, under what conditions can we assume that the constant assumption has been satisfactorily met?6.18E6.19EA city law-enforcement official has stated that 20% of the items sold by pawn shops within the city have been stolen. Ralph has just purchased 4 items from one of the citys pawn shops. Assuming that the official is correct, and for x= the number of Ralph’s purchases that have been stolen, determine the following: a. P(x=0) b. P(2x) c. P(1x3) d. P(x2) e.6.21EAccording to the National Marine Manufacturers Association, 50.0% of the population of Vermont were boating participants during the most recent year. For a randomly selected sample of 20 Vermont residents, with the discrete random variable x= the number in the sample who were boating participants that year, determine the following: Source: National Marine Manufacturers Association, NMMA Boating Industry Report, p. 3. a. E(x) b. P(x8) c. P(x=10) d. P(x=12) e. P(7x13)In the town of Hickoryville, an adult citizen has a 1 % chance of being selected for jury duty next year. If jury members are selected at random, and the Anderson family includes three adults, determine the probability that a. none of the Andersons will be chosen. b. exactly one of the Andcrsons will be chosen. c. exactly two of the Andersons will be chosen. d. all three Andersons will be chosenIt has been reported that the overall graduation rate for football players at Division I-A colleges and universities is 65%. Source: How Football Rates. “USA Today, December 20. 2005. p. 12C. a. If five players are randomly selected from the entire population of Division I-A football players, what is the probability that at least 2 of the 5 will graduate? b. In part (a), what is the probability that all 5 of the players will graduate?6.25EThe U.S. Department of Labor has reported that 30% of the 2.1 million mathematical and computer scientists in the United States are women. If 3 individuals are randomly selected from this occupational group, and x= the number of females, determine P(x=0),P(x=1),P(x=2),andP(x=3). Source: Bureau of the Census. Statistical Abstract of the United States 2002, p. 381.Alicia’s schedule includes three Tuesday/Thursday courses in which each professor uses a single coin flip to decide whether to give a short quiz each class day. Alicia is active on the university’s student advisory council, works two part-time jobs, and is helping to build a float for the upcoming homecoming parade. As a result of these activities and slightly inadequate planning on her part, she has had very little time to prepare for her Thursday classes being held tomorrow. What is the probability that Alicia will be “lucky” and have no surprise quizzes tomorrow? What is the probability that the worst will occur and she will have surprise quizzes in all three classes? What is the probability that she will escape with minimal damage and have a quiz in only one of the three classes?OfficeQuip is a small office supply firm that is currently bidding on furniture and office equipment contracts with four different potential customers who are of comparable size. For each contract, OfficeQuip would gain a profit of $50,000 if that contract were accepted, so the company could make as little as $0 or as much as $200,000. The four potential customers are making independent decisions, and in each case the probability that OfficeQuip will receive the contract is 0.40. When all the decisions have been made, what is the probability that OfficeQuip will receive none of the contracts? Exactly one of the contracts? Exactly two of the contracts? Exactly three of the contracts? All four contracts? Overall, what is OfficeQuip’s expected profit in this business-procurement venture?Four wheel bearings are to be replaced on a company vehicle, and the mechanic has selected the four replacement parts from a large supply bin. Unknown to the mechanic, 10% of the bearings are defective and will fail within the first 100 miles after installation. Vhat is the probability that the company vehicle will have a breakdown due to defective wheel bearings before it completes tomorrows 200-mile delivery route?It has been estimated that one in five Americans suffers from allergies. The president of Hargrove University plans to randomly select 10 students from the undergradu ate population of 1400 to attend a dinner at his home. Assuming that Hargrove students are typical in terms of susceptibility to allergies and that the college president’s home happens to contain iust about every common allerg en to which afflicted persons react, what is the probability that at least 8 of the students will be able to stay for the duration the dinner event? Source: Wcuhi Almanac and Book of Facts 2009. p. 187.Airlines book more seats than arc actually available, then “hump” would-be passengers whenever more people show up than there are seats. Through the first quarter of 2009, the rate at which passengers were humped was 1.40 per 1000 passengers. Assuming that, on average, the probability of any given passenger being bumped is 1.40/1000, or 0.00140: Source: U.S. Bureai of Transportaton Statistcs, June 2009. a. Emily is flying nonstop to visit Besco, Inc., for a job interview. What is the probability that she will be bumped? b. Ten members of the Besco board of directors will be flying nonstop to the firm’s annual meeting, and their flights are independent of each other. What is the probability that at least one of them will be bumped? c. Besco sales personnel made a total of 220 nonstop flights last year, and they experienced a total of four bumpings. Could the company’s experience be cons idered as very unusual?Every day, artists at Arnold’s House of Fine Figurines produce 5 miniature statues that must be sanded and painted. Past experience has shown that 10% of the statues have a defect that does not show up until after the statue has been sanded and painted. Whenever a statue is found to have this defect, Arnold must pay a specialist $20 to correct the defect and repaint the statue. Describe the probability distribution for the daily amount that Arnold must pay the specialist, and determine the average daily amount the specialist will receive.Under what circumstances should the hypergeometric distribution be used instead o the binomial distribution?Using the hypergeometric distribution, with N=4,n=2, and s=3, determine the following: a. P(x=0) b. P(x=1) c. P(x=2)Using the hypergeometric distribution, with N=5,n=2, and s=3, determine the following: P(x=0) b. P(x=1) c. P(x=2)In a criminal trial, there are 25 persons who have been approved by both parties for possible inclusion in the eventual jury of 12. Of those who have been approved, there are 14 women and 11 men. If the judge forms the final jury of 12 by randomly selecting individu als from the approved listing, what is the probability that at least half of the eventual jurors will be males?A computer firm must send a group of three specialists to give a technical presentation to a potential customer. Five such individuals are anxious to attend, but only two are considered to have strong interpersonal skills. Since the specialists have equal levels of seniority, they have agreed to place their names in a hat and allow management to randomly select the three to attend the presentation. What is the probability that there will be at least one person with strong interpersonal skills among the group that is sent?6.38E6.39E6.40E6.41E6.42EThe U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x= the number of divorces in this community during the coming year, determine the following: Source New York Almanac 2009, p. 294. E(x) P(x=1) P(x=4) P(x6) P(2x5)During the 12 P.M.-1 P.M. noon hour, arrivals at a curbside banking machine have been found to be Poisson distributed with a mean of 1.3 persons per minute. If x= number of arrivals during a given minute, determine the following: E(x) P(x=0) P(x=1) P(x2) P(1x3)During the winter heating season in a northern state, Howards Heating and Cooling Service receives an average of 3.1 emergency service calls per day from heati ng customers in their area. Howard has increased personnel and equipment resources to better handle such calls, and his company is now able to satisfy a maximum of 8 emergency service calls per day. During a typical day during the heating season, and assuming the daily number ofemergency service calls to be Poisson distributed, what is the probability that Howard will receive more emergency service calls tomorrow than his company is able to handle? Considering this probability, would it seem advisable for Howard to increase or to decrease the level of personnel and equipment he devotes to handling such calls?6.46E6.47E6.48E6.49EA manufacturing plant’s main production line breaks down an average of 2.4 times per day. Whenever the line goes down, it costs the company $500 in maintenance, repairs, and lost production. What is the probability that the production line will break down at least 3 times tomorros’? What is the approximate expected value for the amount of money that production line breakdowns will cost the company each day?6.51EAccording to a recent survey, 35% of the adult citizens of Mayville have a charge account at Marcy’s Department Store. Mr. Marcy’s nephew is going to trial for embezzlement, and nine jurors are to be randomly selected from the adult citizenry. What is the probability that at least four of the jurors will be charge-account holders?7.64CE7.65CEDuring an annual heating season, the average gas bill for customers in a New England community heating their homes with gas was $457. Assuming a normal distribution and a standard deviation of $80: a. What proportion of homes heating with gas had a gas bill over $382? b. What proportion of homes heating with gas had a gas bill between $497 and $537? c. What amount was exceeded by only 2.5% of the homes heating with gas? d. What amount was exceeded by 95% of the homes heating with gas?It has been reported that the average monthly cell phone bill is $50. Assuming a normal distribution and a standard deviation of $10, what is the probability that a randomly selected cell phone subscriber’s bill last month was less than S35? More than $70? source: Statistical Abtract of the United States 2009. p. 706.During 2004, the average number of flying hours for aircraft operated by regional airlines in the United States was 2389. Assume a normal distribution and a standard deviation of 300 hours. Source: Statistical Abstract of the United States 2006. p. 701. a. What proportion of aircraft flew more than 2200 hours during the year? b. What proportion of aircraft flew between 2000 and 2400 hours during the year? c. What number of annual flying hours was exceeded by only 15% of the aircraft? d. What number of annual flying hours was exceeded by 75% of the aircraft?During fiscal 2008, the average daily volume for FedFx Corporation was 7,000,000 packages per day. Assuming a normal distribution and a standard deviation of 800,000 packages per day, on what proportion of the days was the volume between 6,000,000 and 6,500,000 packages? Source: FedEx Corporation, 2008 Anrol Report. p. 28.For itemized tax returns in the $60,000—$75,000 income group for the most recent year reported, the avera ge charitable contribution was $1935. Assume a normal distribution and a standard deviation of $400. a. For a randomly selected household from this income group, what is the probability that the household made charitable contributions of at least S 1600? b. For a randomly selected household from this income group, what is the probability that the household made charitable contributions of between $2200 and $2400? c. What level of contributions was exceeded by only 20% of the itemized returns in this income group? d. What level of contributions was exceeded by 40% of the itemized returns in this income group?Of the 1.0 million persons of voting age in Maine, 72% voted in the 2008 presidential election. For a randomly selected group of 30 Maine residents who were of voting age at that time, what is the probability that at least 20 of these persons voted in the presidential election? Source: nonprofitiote org. July 15. 2009.A public relations agency tells its client that 80% of the residents in a 50-mile radius believe the company is “an industry leader.” Skeptical, the company commissions a survey in which just 320 of the 500 persons interviewed felt the company was an industry leader. If the public relations agency’s claim is correct, what is the probability that interviews with 500 people would yield 320 or fewer who felt the company was an industry leader?Given the results of Exercise 7.72, evaluate the claim made by the public relations agency.A researcher is studying a particular process and has identified the following times, in minutes, between consecutive occurrences: 1.8, 4.3, 2.3, 2.1, 5.6, 1.5, 4.5, 1.8, 2.4, 2.6, 3.2, 3.5, 1.6, 2.1, and 1.9. Given this information, what would be the researcher’s best estimate for the mean of the exponential distribution? What would be her best estimate for the mean of the corresponding Poisson distribution?A safety researcher has found that fourth to sixth graders engaging in unorganized activities on school grounds experienced in juries at the rate of 2.4 injuries per 100 thousand student-days. On the average, how many student-days elapse between injuries to fourth to sixth graders in unorganized activities at school, and what is the probability that the next such injury will occur before 45 thousand student-days have passed?The number of defects in rolls of aluminum sheet average 3.5 defects per 100 feet. The company presid ent is accompanying overseas visitors on a tour of the plant, and they have just arrived at the aluminum-sheet machine. If they remain at the machine long enough to observe 32 feet of aluminum being produced, what is the probability that they will have left the area before the next defect occurs?The mileage death rate for motorcycle riders has been estimated to he about 39 deaths per 100 million miles of motorcycle travel. A national motorcycling association has 1200 members who travel a total of 2 million miles each year on their motorcycles. What is the probability that the next highway fatality experienced by the association will not occur until more than a year from now? Until more than 2 years from now?The “20-ounce” package of mozzarella cheese distributed by a food company actually has a weight that is normally distributed, with =21 ounces and =0.2 ounces. a. What is the probability that a randomly selected package of this cheese will actually contain at least 20.5 ounces? b. What is the probability that a randomly selected package of this cheese will actually contain between 20.5 and 21.3 ounces? c. A shopper randomly selects 8 of these packages. What is the probability that 3 or more of them will contain at least 21.2 ounces of cheese?State Police Academy graduates from a large gradua ting class have scored an average of 81.0 on a profic iency test, and the scores are normally distributed with =8.5. Graduates are randomly paired and assigned to barracks throughout the state. Madeleine has scored 83.0 on the test. What is the probability that she will be paired with someone whose score was within 5.0 points of her own?The trainer for a professional football team has found that, on the average, his team experiences 2.3 sprained ankles per 1000 game minutes. If a game lasts 60 minutes, and the number of game minutes between ankle sprains is exponentially distributed, determine the probability that the next ankle sprain will occur a. during the team’s next game. b. sometime during the team’s next ten games. c. at the moment the 2-minute warning is sounded in the next game.The precooked weight of hamburgers at a gourmet hamburger restaurant has been normally distributed with a mean of 5.5 ounces and a standard deviation of 0.15 ounces. A dining-column journalist from the local newspaper enters the restaurant and orders a hamburger. What is the probability that he will receive a hamburger that had a precooked weight less than 5.3 ounces? If, in a separate visit to the restaurant, the journalist is accomp anied by three colleagues who also order a hamburger, what is the probability that at least 2 of these 4 customers will receive a hamburger that had a precooked weight greater than 5.7 ounces?Boxes are filled with sugar by a machine that is set to deliver an average of 20.3 ounces. The weightsare normally distributed with a standard deviation of 0.3 ounces. If a consumer advocate buys a package of the product and then proceeds to weigh the contents, what is the probability that the package she has purchased will have a content weight between 20 and 21 ounces? If the consumer advocate plans to purchase 100 boxes of the product, then file suit against the company if more than 5 of the boxes have content weights below the 20-ounce stated weight on the package, what is the probability that she will end up filing suit against the company?In Exercise 7.82, the company would like to put in a greater weight “cushion” to help protect itself from consumer advocates. If the company wants to have just 2% of the packages contain less than 20 ounces, to what average weight must the filling machine be set?Discount Micros, a computer mail-order company, has received 2000 desktop computers from a major manufacturer. Unknown to the mail-order company, 250 of the computers have a hard disk that was improperly installed at the factory. A consulting firm purchases 40 computers from Discount Micros. If the order is filled by random selection from the 2000 computers just received, what is the probability that the shipment to the consulting firm will include no more than 2 defective computers? At least 1, but no more than 3 detective computers?The U-Drive car rental corporation has found that the cars in the company’s rental fleet experience punctures at the rate of 1.25 punctures per 10,000 miles, and the number of punctures per distance traveled is Poisson distributed. Ed and Harriet are taking advantage of a U-Drive promotion in which there is no mileage charge. During their vacation, they plan to drive from Roston to Los Angeles and back, a total distance of 6164 miles. a. What is the probability that Ed and Harriet will not have to change any tires during their vacation? b. While traveling west, what is the probability that Ed and Harriet will experience a punctured tire before they make it to Denver, 2016 miles away? c. For what mileage is the probability 0.80 that Ed and Harriet will experience a puncture before they reach this distance?Ronnie Rogers, the customer relations manager for a large computer manufacturer, has recently studied the duration of telephone calls received by the company’s technical support department. The call lengths are exponentially distributed, with a mean duration of 8 minutes. Experience has taught Bonnie that lengthy calls usually can be more efficiently handled by a technical support manager, rather than by the less experienced personnel who receive the initial technical inquiry. To avoid havi ng the higher-paid managers virtually take over the task of handling technical support, Bonnie would like to have only the longest 10% of the calls redirected to a technical support manager. How long must a technical support call last before it qualifies for redirection to a technical support manager?A storage warehouse in a relatively remote part of a county is protected by a homemade burglary detection system. Once actuated by an intruder, the system sounds a horn and flashes a light for 15 minutes, then saves battery power by shutting down and resetting itself until the next intrusion is detected. Police in three patrol cars havethis part of the county as one of their responsibilities, and they routinely drive by the warehouse facility during the hours from dark to dawn. On average, a patrol car passes the warehouse every 20 minutes, and the time between patrol car arrivals is exponentially distributed. It’s the middle of the night and a burglar has just broken into the storage warehouse and set off the alarm. What is the probability that the alarm will shut off before the next police patrol car drives by?What is the difference between a continuous probability distribution and a discrete probability distribution?What is a probability density function and how is it relevant to the determination of probabilities associated with a continuous random variable?Why is the total area beneath a probability density function equal to 1.0?7.4EIt has been stated that the nomal distribution is really a “family” of distributions. Expain.7.6E7.7E7.8E7.9EThe Canada Urban Transit Association has reported that the average revenue per passenger trip during a given year s’as $1.55. If we assume a normal distribution and a standard deviation of =0.20 , what proportion of passenger trips produced a revenue of Source: American Public Transit Associations APTA 2009 Transit Fact Book, p. 35. a. less than $1.55? b. between $1.15 and $1.95? c. between $1.35 and $1.75? d. between $0.95 and $1.55?7.11EIn 2009, the average charge for tax preparation by H=20 what proportion of H&R Block’s tax preparation fees were source: hrblock.com, July 14, 2009. a. more than $187? b. between $147 and $227? c. between $167 and $207? d. more than $227?It has been reported that the average hotel check-in time, from curbside to delivery of bags into the room, is 12.0 minutes. An Li has just left the cab that brought her to her hotel. Assuming a normal distribution with a standard deviation of 2.0 minutes, what is the probability that the time required for An Li and her bags to get to the room will be: a. greater than 14.0 minutes? b. between 10.0 and 14.0 minutes? c. less than 8.0 minutes? d. between 10.0 and 16.0 minutes?The average American family of four spends $5000 per year on food prepared at home. Assuming a normal distribution with a standard deviation of $1000 and a randomly selected American family of four, what is the probability that the family’s annual spending for food prepared at home will be: Source: Business Briefing. Pittsburgh Tribune-Review, July 5. 2009. p. E 1. a. more than $8000? b. between SS000 and S7000? c. less than $6000? d. between $3000 and $6000?7.15EThe normal distribution is really a family of distributions. Is the standard normal distribution also a family of distributions? Explain.In the standard normal distribution, approximately what values of z correspond to the a. first and third quartiles? b. first and ninth deciles? c. 23rd and 77th percentiles?A Continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score: x=1000 x=750 x=1100 x=950 x=12257.19E7.20E7.21E7.22E7.23E7.24E7.25E7.26EFor the normal distribution described in Exercise 7.11, what is the probability that a randomly selected first mortgage would have been for an amount a. between $305,000 and $325,000? b. over $325,000? c. under $390000?7.28EFor the normal distribution described in Exercise 7.15, what is the probability that Jamals commuting time to work today will be a. less than 29 minutes? b. between 29 and 33 minutes? c. more than 32 minutes?For the normal distribution described in Exercise 7.15, what commuting time will be exceeded on only 10% of Jamal’s commuting days?For the normal distribution described in Exercise 7.11, what first-mortgage amount would have been exceeded by only 5% of the mortgage customers?7.32EIt has been reported that households in the West spend an annual average of S6050 for groceries. Assume a normal distribution with a standard deviation of $1500. Sotxce: David Stuckey and Sam Ward, Home Cooked, USA Today, July 25, 2006. p. 1A. a. What is the probability that a randomly selected Western household spends more than $6350 for groceries? b. How much money would a Western household have to spend on groceries per year in order to be at the 99th percentile (i.e., only I % of Vestern households would spend more on groceries)?Andre is a fearless circus performer who gets shot from a special cannon during the grand finale of the show and is supposed to land on a safety net at the other side of the arena. The distance he travels varics but is normally distributed with a mean of 150 feet and a standard deviation of 10 feet. The landing net is 30 feet long. a. 10 maximize Andre’s probability of landing on the net, how far away from the cannon should he position the nearest edge of the net? b. Given the net position in part (a), what is the probability that Andre will be able to return for tomorrow night’s show?Drying times for newly painted microwave oven cabinets are normally distributed with a mean of 2.5 minutes and a standard deviation of 0.25 minutes. After painting, each cabinet is mated with its electronic modules and mechanical components. The production manager must decide how much time to allow after painting before these other components are installed. If the time is too short, the paint will smudge and the unit will have to be refinished. If the time is too long, production efficiency will suffer. A consultant has concluded that the time delay should be just enough to allow 99.8% of the cabinets to dry completely, with just 0.2% ending up being smudged and sent back for refinishing. Given this information, for what time setting should the production manager set the automatic timer that pauses the production line while each cabinet dries?KleerCo supplies an under-hood, emissionscontrol air pump to the automotive industry. The pump is vacuum powered and works while the engineis operating, cleaning the exhaust by pumping extra oxygen into the exhaust system. If a pump fails before the vehicle in which it is installed has covered 50,000 miles, federal emissions regulations require that it be replaced at no cost to the vehicle owner. The company’s current air pump lasts an average of 6.3,000 miles, with a standard deviation of 10,000 miles. The number of miles a pump operates before becoming ineffective has been found to be normally distributed. a. For the current pump design, what percentage of the company’s pumps will have to be replaced at no charge to the consumer? b. What percentage of the company’s pumps will fail at exactly 50,000 miles? c. What percentage of the company’s pumps will fail between 40,000 and 55,000 miles? d. For what number of miles does the probability become 80% that a randomly selected pump will no longer be effective?7.37E7.38EWhat is the correction for continuity and why is it employed when the normal distribution is used in approximating the binomial distribution?Under what circumstances is it permissible to use the normal distribution in approximating the binomial distribution?In a certain binomial distribution, =0.25 and n=40 . In using the normal approximation, a. What are the mean and standard deviation of the corresponding normal distribution? b. If x= the number of “successes” among the 40 observations, determine the following: P(x=8), P(12x16),P(10x12),P(x14).In a certain binomial distribution, =0.30 and n=20 . In using the normal approximation, a. What are the mean and standard deviation of the corresponding normal distribution? b. If x=the number of “successes” among the 20 observations, determine the following: P(x=5),P(4x7),P(1x5),P(x7).7.43E7.44E7.45E7.46E7.47ERepeat Exercise 7.46, but without using the correction for continuity (i.e., the discrete random variable, x , is not replaced by the interval x0.5 to x+0.5). Does your answer differ appreciably from that obtained in Ixcrcise 7.46? If not, comment on the need for using the correction for continuity when x can take on a large number of possible values.What is the relationship between the Poisson distribution and the exponential distribution?Every day, drivers arrive at a tollbooth. If the Poisson distribution were applied to this process, what would be an appropriate random variable? What would be the exponential-distribution counterpart to this random variable?The main switchboard at the Home Shopping Network receives calls from customers. If the Poisson distribution were applied to this process, what would be an appropriate random variable? What would be the exponential-distribution counterpart to this random variable?A random variable is Poision distributed with =1.5 occurences per minute. For the corresponding exponential distribution, and x= minutes until the next arrival, identify the mean of x and determine the following: a. P(x0.5) b. P(x1.0) c. P(x1.5) d. P(x2.0)A random variable is Poision distributed with =0.02 occurences per minute. For the corresponding exponential distribution, and x= minutes until the next arrival, identify the mean of x and determine the following: a. P(x30.0) b. P(x40.0) c. P(x50.0) d. P(x60.0)A random variable is Poision distributed with =0.50 arrivals per minute. For the corresponding exponential distribution, and x= minutes until the next arrival, identify the mean of x and determine the following: a. P(x0.5) b. P(x1.5) c. P(x2.5) d. P(x3.0)The owner of a self-service carwash has found that customers take an average of 8 minutes to wash and dry their cars. Assuming that the self-service times tend to be exponentially distributed, what is the probability that a customer will require more than 10 minutes to complete the job?A taxi dispatcher has found that successive calls for taxi service are exponentially distributed, with a mean time between calls of 5.30 minutes. The dispatcher must disconnect the telephone system for 3 minutes in order to have the push-button mechanism repaired. What is the probability that a call will be received while the system is out of service?During 2008, U.S. general aviation pilots had 1.20 fatal crashes per 100,000 flying hours. Harriet Arnold is president of Arnold’s Flying Service, a company that operates a total of 50 sightseeing planes based in 20 regions of the United States. Altogether, the planes in this fleet are in the air about 40,000 hours per year. Ever since a fatal crash last year involving one of the company’s planes that took off under questionable weather conditions, the company has been getting close scrutinyfrom both government safety officials and the national media. Harriet believes her planes are just as safe as anyone else’s, but is concerned that even one more fatal accident within the coming year might be too much for the now-struggling company to overcome. Assuming an exponential distribution for x= thousands of flying hours between fatal crashes, what is the probability that Arnold’s Flying Service will not experience a fatal crash until at least a year from today? Until at least 2 years from today? What number of flying hours would be assoc iated with a 90% probability of experiencing no crashes within that number of flying hours from today? Source:The Bureau of Labor Statistics reports the fatality rate for workers in the rail transportation industry is 0.006 fatalities per 200000 worker-hours. During 2007, rail transportation workers put in a total of 545 million worker-hours. Assuming that (1) an exponential distribut ion applies for the number of worker-hours between fatalities in this industry, and (2) the annual 545 million worker-hours of activity continues in the industry, what is the expected number of worker-hours until the next fatality occurs in this industry? If a given rail transport ation company requires 1,000,000 worker-hours each year, what is the probability that the next fatal injury in this company will not occur until at least 30 years from now? Source: Bureau of Labor Statistics, Census of Fatal Occupational Injuries, 2007.A computer statistical package has simulated 1000 random observations from a normal distribution with =50 and =10. Sketch the approximate box and-whisker display for the resulting data.7.60E7.61E7.62E8.42CE8.43CE8.44CE8.45CE8.46CE8.47CE8.48CE8.49CE8.50CE8.51CE8.52CE8.53CE8.54CE8.55CE8.56CE8.57CE8.58CE7.1AE7.2AE7.3AE7.4AE8.1AE8.2AE8.3AE8.4AE8.1E8.2E8.3E8.4E8.5E8.6E8.7E8.8EFor a random variable that is normally distributed, with =80and=10 , determine the probability that a simple random sample of 25 items will have a mean that is a. greater than 78. b. between 79 and 85. c. less than 85.8.10E8.11E8.12E8.13E8.14E8.15EThe tensile strength of spot welds produced by a robot welder is normally distributed, with a mean of 10,000 pounds per square inch and a standard deviation of 800 pounds per square inch. For a simple random sample of n=4 welds, what is the probability that the sample mean will be at least 10,200 pounds per square inch? Less than 9900 pounds per square inch?8.17E8.18E8.19E8.20E8.21E8.22E8.23E8.24E8.25E8.26E8.27EThe Temployee Company supplies temporary workers to industry and has found that 58% of the positions it is asked to fill require a knowledge of Microsoft Excel. The firm currently has 25 individuals available who know Microsoft Excel. If TemployeeCompany receives 50 inquiries for temporary workers next week, how likely is it that the company will not have enough Microsoft Excel-skilled people on hand?8.29E8.30E8.31E8.32E8.33E8.34E8.35E8.36E8.37E8.38E8.39E8.40E8.41E9.80CE9.81CE9.82CE9.83CE9.84CE9.85CE9.86CE9.87CE9.88CE9.89CE9.90CE9.91CE9.92CE9.93CE9.94CE9.95CE9.96CE9.97CE9.98CE9.99CE9.100CEThere are 1254 machinery rebuilding and repairing companies in the United States. A tool manufacturer wishes to survey a simple random sample of these firms to find out what proportion of them are interested in a new tool design. If the tool manufacturer would like to be 95% confident that the sample proportion is within 0.01 of the actual population proportion, how many machinery rebuilding and repairing companies should be included in the sample? Source: infousa.com, July 21, 2009.9.102CE9.103CE9.104CE9.105CE9.106CEA truck loaded with 8000 electronic circuit boards has just pulled into a firm’s receiving dock. The supplier claims that no more than 3% of the boards fall outside the most rigid level of industry performance specifications. In a simple random sample of 300 boards from this shipment, 12 fall outside these specifications. Construct the 95% confidence interval for the percentage of all boards in this shipment that fall outside the specifications, then comment on whether the supplier’s claim would appear to be correct.9.108CE9.109CE9.110CE9.111CE2.1IC2.2IC2.3IC9.1AE9.2AE9.3AE9.4AE10.1AE10.2AE10.3AE10.4AE11.1AE11.2AE11.3AE11.4AE9.1E9.2E9.3E9.4E9.5E9.6E9.7E9.8E9.9E9.10E9.11E