Quantitative Methods For Business 1st Edition John Buglear - Solutions

13.4 An automobile manufacturer produces a certain model of car.The fuel economy figures of these cars are normally distributed with a mean mileage per gallon (mpg) of 36.8 and a standard deviation of 1.3.(a) What is the probability that one of these cars will have an mpg of more than 37.5?(b) What
13.3 The colour dye used in the manufacture of certain garments fades after a mean of 96 machine washes, with a standard deviation of 7 washes. If the number of washes before fading follows a normal distribution, what proportion of the garments will first fade:(a) after 100 washes?(b) before 90
13.2* A confectionery company produces 100 g ‘Real Chocolate’ bars that have a mean chocolate content of 70 g with a standard deviation of 0.8 g. The variation in chocolate content is normally distributed. What is the probability that a chocolate bar chosen at random contains:(a) more than 71
13.1 Find the areas of the Standard Normal Distribution that represent the following probabilities:(a) P(Z 1.44)(b) P(Z0.29)(c) P(Z 2.06)(d) P(Z 1.73)(e) P(0.52 Z 1.99)(f) P(2.31 Z 1.08)(g) P(0.97 Z 0.65)
12.20 Select the appropriate description for each term on the left-hand side from the list on the right-hand side.(i) simulation (a) consists of probabilities of incidents over time(ii) np (b) four factorial, twenty-four(iii) the binomial distribution (c) the variance of the binomial
12.19 A builder completes a large project for a property company who, due to cash flow problems, offer him a small seaside hotel in lieu of payment. The builder, who has no desire to enter the hotel business, has found a buyer for the hotel, but this deal will not be completed until 12 weeks after
12.18 A book trader has taken out a 13-week lease on a small unit in a shopping mall prior to it being fitted out as a new outlet by a major retailer. The trader intends to sell remaindered books,‘coffee table classics’ selling for £3 each and children’s books selling at £1 each. She has a
12.17 A restaurant serves fresh locally grown strawberries as part of its‘Wimbledon working lunch’ menu for ten working days in the early summer. The supplier provides 100 kg per day and sells to the hotel at a price that varies according to the probability distribution:Price per kg (£) 1.00
12.16 Orders for the Potchtar Mail Order Company are sent in batches of 50 by the Post Office. The number of orders arriving each working day varies according to the following probability distribution:Number of orders Probability 150 0.05 200 0.15 250 0.30 300 0.30 350 0.15 400 0.05 These orders
12.15* Furgon Van Hire rents out trucks and vans. One service they offer is a same-day rental deal under which account customers can call in the morning to hire a van for the day. Five vehicles are available for hire on these terms. The demand for the service varies according to the following
12.14 A company produces mouse mats that are 20 cm long and 20cm wide. These mats are cut from sheets of material that are one metre long and one metre wide. Precise machine setting means that 25 mouse mats can be cut from each sheet of material.Problems that have arisen in the laminating process
12.13 Everyone working in a large open plan office takes cups of tea or coffee back to their desk to drink. The mean number of spilled cups of hot drinks in an eight-hour working day is 24. What is the probability that an hour passes in which:(a) there are no spillages?(b) there are two
12.12 The mean number of violent incidents at the Koshmar pub is 14 per week. As a result of being injured at work the pub bouncer will be off for a day.(a) What is the probability that the day passes without any violent incidents?(b) What is the probability that the day passes with no more than
12.11 An office worker receives an average of 22.5 email messages per day. If his working day lasts seven and a half hours, what is the probability that:(a) he receives no emails in an hour?(b) he receives one email in an hour?(c) he receives two or fewer emails in an hour?(d) he receives more than
12.10 Wasim’s word processing skills are good. On average he only makes 0.5 mistakes on each page he types. What is the probability that in a document ten pages long he makes:(a) no mistakes?(b) less than four mistakes?(c) no more than six mistakes?(d) at least eight mistakes?
12.9* The mean number of accidents per day at a large building site is 1.0. What is the probability that a day passes when there are:(a) no accidents?(b) two accidents?(c) four or fewer accidents?(d) more than three accidents?
12.8 Two in five people can associate a particular piece of music with the product it is used to promote in an advertising campaign.Identify the probability that in a group of ten people:(a) none will recognize it(b) less than half will recognize it(c) exactly six will recognize it(d) more than six
12.7 An egg packing company thinks that a tenth of all the eggs they buy from farms are contaminated with harmful bacteria that could result in food poisoning. What is the probability that in a pack of ten eggs:(a) none of the eggs contains harmful bacteria?(b) more than two eggs contain harmful
12.6 The producers of a TV survival programme advertise for potential participants and then select random samples of ten people to appear in the programme. If 30% of the people who apply to take part in the programme are smokers, what is the probability that:(a) a team consists entirely of
12.5 ‘Fast’ Gary and Mickey ‘the Mule’ import alcoholic beverages from France into the UK. They are offered a consignment of packs of bottled beers. Each pack contains ten bottles. The price for the consignment is low because due to problems at the bottling plant 20% of the bottles have no
12.4 A large party of Russian managers is to visit a car plant in the UK. They will be shown round the plant in small groups of five.Twenty per cent of the managers speak English. If the groups are selected at random, what is the probability that:(a) there is no English speaker in a group?(b) there
12.3 A lingerie manufacturer produces ladies’ knickers in packs of five pairs. Quality control has been erratic and they estimate that one in every ten pairs of knickers leave the factory without the trim sewn on. What is the probability that in a pack of five pairs of knickers:(a) there are no
12.2* If 30% of the adult population have made an airline booking through the Internet work out the probability that out of four people:(a) none has made an Internet booking(b) one has made an Internet booking(c) two have made an Internet booking(d) three have made an Internet booking(e) all four
12.1 There are three very old X-ray security machines in the departure complex of an airport. All three machines are exactly the same.The probability that a machine breaks down in the course of a day is 0.2. If they are all in working order at the beginning of a day, and breakdowns are independent
11.20 Select the appropriate description for each term on the lefthand side from the list on the right-hand side.(i) maximax (a) a decision rule based on lowest pay-offs(ii) sensitivity analysis (b) the expected monetary value of a decision(iii) minimax regret (c) working out EMVs in a multistage
11.19 Lord Du Raq owns a crumbling castle in Scotland. The revenue from visitors is no longer sufficient to cover the upkeep of the property and he must decide what to do. A national heritage organization has offered to buy the property for £8m. Alternatively he could have a theme park constructed
11.18 Seela Energy wants to build a nuclear power station on a remote coastline in Northern Europe. They need new capacity, as without it they will incur a loss of €100m because they will have to use inefficient old capacity to meet demand. At an early stage during the time it will take to build
11.17 Scientists at the Medicament Drug Company have synthesized a new drug which they believe will be an effective treatment for stress and anxiety. The company must decide whether to proceed with the commercial development of the new drug or not. If they decide not to develop it, no further costs
11.16 Kenny Videnia, a film producer, has to decide whether to bid for the film rights of a modestly successful novel. He believes that there is a 0.9 chance that he will be successful. If the bid is unsuccessful he will have to meet legal and administrative costs of $0.5m. If he is successful he
11.15* Miners at the Gopher Gold Mine in Siberia have put in a series of wage and condition demands that would cost $50m to the management and threaten to strike if the demands are not met.The management have to decide right away whether to increase short-term production to build up a stockpile of
11.14 An arable farmer is thinking of sowing scientifically modified crops next year. She believes that if she did so her profits would be £75,000, compared to £50,000 if she sowed unmodified crops. A neighbouring farmer has made it clear that if his crops are contaminated he will demand
11.13 Kholodny plc installs ventilation systems. At present its order book is rather thin and it has no work for the forthcoming period. It has been offered two contracts abroad, of which it can take only one. The first contract is to install a ventilation system in the Presidential Palace of the
11.12 A member of a successful girl band is considering leaving the band to pursue a solo career. If she stays with the band she estimates that there is a 60% chance that the band will continue to be successful and she would earn £1.7m over the next three years. If the band’s success does not
11.11 A freight company has to transport a container by road from Amsterdam to Tabriz. There are two routes that are viable. Route A is longer but less dangerous than Route B. If the container reaches its destination successfully the company will receive a fee of €15,000. Fuel and other direct
11.10* A sportswear company markets a premium brand of trainers.At present the revenue from sales of these trainers is £17m a year. They have been negotiating with representatives of a top US sports star in order to obtain his endorsement of the product.The cost to the company of the endorsement
11.9 Cloppock Cotton is a farming collective in a central Asian republic. Their operations have been reliant on a government subsidy paid out to cotton farmers to support the production since cotton is a key export commodity. There are rumours that the government will reduce the subsidy for the
11.8 Pashley Package Holidays has to decide whether to discount its holidays to destinations abroad next summer in response to poor consumer confidence in international travel following recent military events. If they do not discount their prices and consumer confidence in air travel remains low
11.7 V. Nimania plc builds water treatment facilities throughout the world. One contract it has concerns an installation in an area prone to outbreaks of a dangerous disease. The company has to decide whether or not to vaccinate the employees who will be working there. Vaccination will cost
11.6 Zak ‘the Snack’ Cusker rents out a pitch for his stall at a music festival. The night before the festival he has to decide whether to load his van with ice-cream products, or burgers or a mix of burgers and ice-cream products. The takings he can expect(in £) depend on the weather, as
11.5* Ivana Loyer claims she has been unfairly dismissed by her employers. She consults the law firm of Zackon and Vorovat, who agree to take up her case. They advise her that if she wins her case she can expect compensation of £15,000, but if she loses she will receive nothing. They estimate that
11.4 A film production company is about to release a new movie.They estimate that there is a 5% chance that the film will make a profit of $14m, a 30% chance that it will make a profit of $1m, a 25% chance that it will break even and a 40% chance that it will make a loss of $2 m. What is the
11.3 An insurance company calculates that the probability that in a year a motor insurance policyholder makes a claim arising from a major accident is 0.03, the probability that s/he makes a claim as a result of a minor accident is 0.1, and the probability that s/he makes a claim as a result of
11.2 A graduate wants to pursue a career in a profession. She will need to gain membership of the professional institute by passing three stages of examinations. If she becomes a full member of the institute she anticipates that she will be able to earn£50,000 per year. If she fails the final
11.1* Heemy Pharmaceuticals marketed a drug that proved to be an effective treatment but unfortunately resulted in side effects for some patients. On the basis of initial clinical research the probability that a patient who is treated with the drug suffers no side effect is 0.85, the probability of
10.20 Select the appropriate definition for each term on the left-hand side from the list on the right-hand side.(i) compound probability (a) basing a probability on opinion(ii) multiplication rule (b) outcomes that cannot occur together(iii) collectively exhaustive (c) P(A and B) P(A) *
10.19 You win a prize in a raffle. The prize, donated by an airline, consists of three return tickets to a destination in Africa; Cairo, Dar-es-salaam and Entebbe. The seats you are allocated on the journeys will be either Business or Economy, the only seat types the airline offers, and will be
10.18 Thursday, Friday and Saturday are the busiest nights at the Jopper bar. Police records show that on 12 of the last 50 Thursdays, 15 of the last 50 Fridays, and 16 of the last 50 Saturdays they were summoned to deal with a disturbance at the bar. Construct a tree diagram and use it to find the
10.17 The Strachovania Insurance Company offers quotations for motor insurance by telephone. The company employs permanent staff to do this work but as a result of a dramatic rise in the number of telephone enquiries 35% of quotations are provided by temporary staff. Unfortunately 22% of the
10.16 Florrie’s Fashion Store and Mary’s market stall both sell a particular style of sweatshirt. They are the only outlets for the garment in the area, with Florrie’s accounting for 70% of the total number sold and Mary’s accounting for the remainder. Unfortunately colour dye that faded
10.15 As a result of flood damage a supermarket has a very large stock of tins without labels. Forty per cent of the tins contain soup, 30% contain carrots, 25% contain raspberries and 5% contain asparagus. The tins are to be offered for sale at three for 50 pence. If a customer buys three tins
10.14 Every morning Jack makes tea for the other five people in his section. Two of them take sugar. Jack always forgets which teas he has sugared. One of the two senior members of the section, Alicia, takes sugar in her tea; the other, Bashir, does not. If Jack takes tea first to Alicia and then
10.13 Two friends have a favourite compilation CD that contains some of their all-time favourite tracks. There are 20 tracks on the album. Sam likes five tracks and Chris likes six other tracks.If they program their CD player to play three tracks selected at random from the album, and assuming that
10.12* Declan, Emily and Farid each intend to start their own business after leaving college. Declan wants to start a computer software company, Emily intends to open a recruitment agency, and Farid would like to launch a graphic design business. According to available evidence 60% of computer
10.11 A commuter’s journey to work consists of driving her car to her local train station, taking a train to the city, and catching a bus to her place of work. If her car trip is delayed she misses the train and is late for work. If the train is delayed, she misses the bus and is late for work.
10.10 A final year undergraduate applies for a well-paid job with a large and reputable organization in a highly desirable location.Competition for the job is expected to be fierce. The probability that a candidate is selected for first interview is 0.10. The probability that a candidate is then
10.9 The following survey results show the social class and type of main holiday destination of 250 adult holidaymakers.Social class Destination AB C1C2 DE UK 13 25 26 The rest of Europe 29 60 23 Other 55 14 5 Use these figures to estimate:(a) the probability that a holidaymaker belongs to social
10.8 A safety agency analysed road traffic accidents involving injury to pedestrians by private cars and produced the following table:Type of car Degree of injury 4 * 4 Sports Other Fatal 8 5 14 Serious 21 9 38 Non-serious 13 7 95 What is the probability that:(a) an injury to a pedestrian proves
10.7 A soft drinks company has commissioned an investigation of the level of recognition of one of its brands in various countries that are considered important markets. Random samples of respondents in each country were asked to identify the product from the brand image. The results are:Brand
10.6* The 120 employees at a factory were asked which would best improve their working life: better promotion prospects, higher pay or more respect from other staff. The results are tabulated below.Job type Response Manual Clerical Managerial Better promotion prospects 12 12 3 Higher pay 53 19 2
10.5 Last year 12,966 people opened new accounts at a building society. Of these 5314 were branch-based accounts, 4056 were postal accounts and 3596 were Internet accounts. What is the probability that when a customer opens a new account:(a) it is a postal account?(b) it is an Internet account?(c)
10.4* A garage offers a breakdown recovery service for motorists that is available every day of the year. According to their records the number of call-outs they received per day last year were:Number of call-outs 0 1 2 3 4 Number of days 68 103 145 37 12 What is the probability that:(a) they
10.3 A direct marketing company produces leaflets offering membership of a book club. These leaflets are then inserted into the magazine sections of two Sunday newspapers, the Citizen and the Despatch, 360,000 leaflets being put in copies of the Citizen and 2,130,000 put in copies of the Despatch.
10.2 Since it was set up 73,825 people have visited the website of a music and fashion magazine and 6301 of them purchased goods on-line. When someone visits the site what is the probability that:(a) they do not purchase goods on-line?(b) they do purchase goods on-line?
10.1 An electrical goods retailer sold DVD systems to 8200 customers last year and extended warranties to 3500 of these customers.When the retailer sells a DVD system, what is the probability that:(a) the customer will buy an extended warranty?(b) the customer will not buy an extended warranty?
9.20 Select the appropriate definition for each term on the lefthand side from the list on the right-hand side.(i) a trend component (a) an actual value minus a predicted value(ii) an additive model (b) an underlying movement in a time series(iii) a moving average (c) a long-term repeating effect
9.19 To minimize the risk of accidents from their activities pigeons nesting in the tunnels of an underground railway system are culled every night. The numbers of birds shot over recent weeks has been:Week 1 2 3 4 5 6 7 8 9 Birds shot 260 340 190 410 370 280 330 400 450(a) Generate predictions for
9.18 The bookings taken by an airline on the first eight days after a well-publicized aviation accident were:Day 1 2 3 4 5 6 7 8 Bookings 78 33 41 86 102 133 150 210(a) Produce predictions up to and including day 9 using the exponential smoothing model with a smoothing constant of 0.3 and calculate
9.17 In the nine months since new parking regulations were introduced the numbers of vehicles impounded by a city highways department were:Month 1 2 3 4 5 6 7 8 9 Vehicles 207 246 195 233 218 289 248 292 276(a) Apply the exponential smoothing model with an alpha value of 0.5 to predict values of
9.16* A new security system was installed at the Platia Clothing Store eight weeks ago. The numbers of items stolen from the store in the period since are:Week 1 2 3 4 5 6 7 8 Items stolen 63 56 49 45 51 36 42 37(a) Use the exponential smoothing model with a smoothing constant of 0.8 to predict
9.12, develop forecasts for the sales of travel packs in the four quarters of the fourth year using the more appropriate decomposition model.
9.15 Making use of your answers to Review Questions 9.5, 9.9 and
9.14 Referring to your answers to Review Questions 9.4, 9.8 and 9.11, generate forecasts for the gas consumption in the quarters of year 4 using the more appropriate decomposition model.
9.13* Basing your work on the answers you obtained to Review Questions 9.1, 9.7 and 9.10, use the more appropriate decomposition model to produce forecasts for the newspaper sales in the morning, afternoon and evening of day 4.
9.12 Building on your answers to Review Question 9.5, use the multiplicative decomposition model to:(a) Establish the seasonal factors for each quarter.(b) Work out the mean squared deviation (MSD) for the model.(c) Refer to your answers to part (b) and the MSD for the additive model you obtained
9.11 Building on your answers to Review Question 9.4, use the multiplicative decomposition model to:(a) Find the seasonal factors for each quarter.(b) Calculate the mean squared deviation (MSD) for the model.(c) By contrasting your answer to part (b) with the MSD for the additive model you obtained
9.10* Using the multiplicative model and your answers to Review Question 9.1:(a) Evaluate the recurring factors for the parts of the day.(b) Calculate the mean squared deviation (MSD) for the model.(c) Compare the MSD for this model with your answer to Review Question 9.7 part (b) and say which
9.9 Use the additive decomposition model and your answers to Review Question 9.5 to:(a) Ascertain the seasonal components for each quarter.(b) Compute the mean squared deviation (MSD) for the model.
9.8 Draw on your answers to Review Question 9.4 and apply the additive decomposition model to:(a) Identify the seasonal components for each quarter.(b) Work out the mean squared deviation (MSD) for the model.
9.7* Using the results from Review Question 9.1 and applying the additive decomposition model:(a) Determine the recurring components for each part of the day.(b) Calculate the mean squared deviation (MSD) for the model.
9.6 The quarterly sales (in £000) of greeting cards in a supermarket were:Quarter 1 2 3 4 Year 1 12.0 14.8 9.6 19.2 Year 2 13.1 16.3 8.2 22.8 Year 3 14.8 18.9 6.9 25.1(a) Produce a time series plot to show these figures.(b) Work out centred four-point moving averages for this series and plot them
9.5 A High Street chemist sells travel first aid packs. The numbers of these sold over three years were:Quarter Winter Spring Summer Autumn Year 1 11 37 61 18 Year 2 13 49 58 16 Year 3 16 53 66 18(a) Plot a graph to portray the data.(b) Calculate centred four-point moving averages for the time
9.4 The amounts of gas (in thousands of gigawatt hours) sold to domestic consumers by a regional energy company over three years were:Quarter Winter Spring Summer Autumn Year 1 28 12 7 23 Year 2 27 14 7 24 Year 3 28 13 6 24(a) Produce a graph to represent these data.(b) Determine centred four-point
9.3 A body-piercing and tattoo studio is open each day of the week except Sundays and Mondays. The number of customers visiting the studio per day over a period of three weeks is:Tuesday Wednesday Thursday Friday Saturday Week 1 5 8 9 18 34 Week 2 4 8 11 22 39 Week 3 7 9 14 21 42(a) Plot this time
9.2 Sales of alcoholic beverages (in £) at an off-licence during the course of three days were:Morning Afternoon Evening Day 1 204 450 939 Day 2 261 459 1056 Day 3 315 522 1114(a) Plot a graph to display the time series.(b) Calculate three-point moving averages for the series and plot them on the
9.1* The revenue (in £) from newspaper sales at a new service station for the morning, afternoon and evening periods of the first three days of operation are:Morning Afternoon Evening Day 1 320 92 218 Day 2 341 101 224 Day 3 359 116 272(a) Construct a time series chart and examine it for evidence
8.20 Lovekey Home Service is new firm set up to provide on-line emergency domestic assistance from plumbers, locksmiths,electricians etc. They need to invest in a website to operate their business. They have been offered three website designs, with different layouts and interactive features, and
8.19 Serebro Screen Films is an independent company specializing in the speedy production of low-budget films. Currently they have three film proposals and need to select which, if any, to make.The first is an occult thriller, the second a romantic comedy and the third a science fiction feature.
8.18 Otto Carr owns a chain of car parks in small towns. He wants to expand his business by leasing a suitable site in a city centre.There are two sites that would be appropriate. There is a six-year lease available on the Markets site for £200,000 and a sevenyear lease available on the Riverside
8.17 A pub management company acquired a derelict public house when they took over a rival business. They want to renovate it as either a cafe bar offering a wide range of drinks or a family pub concentrating on food. The cost of fitting it out as a cafe bar is£200,000, the cost of making it into
8.16 A Russian businessman offers a major Japanese car manufacturer an eight-year lease on a disused tank factory in Southern Russia. The company could refit the factory and use it to manufacture low-cost recreational off-road vehicles for the holiday car-hire market in Southern Europe. The total
8.15 Ricky Sadovnik, a geologist, discovered a deposit of decorative stone during a holiday in Scotland. He wants to establish a quarry to extract the stone and sell it to gardeners. The owner of the land is prepared to allow him to open and operate a quarry on the site for five years for a fee of
8.14 After a bad accident Anton receives a large sum in compensation.He is thinking about using it to invest in a stretch limousine to hire out for special occasions. The cost of the limousine is £100,000. Anton is due to retire in six years, at which stage he thinks he will be able to sell the
8.13* An advertisement offers a time share investment in a luxury apartment in the Algarve region of Portugal. Investors can purchase the use of the apartment for an eight-week period each year to rent out to tourists. The cost of the time share is £15,000 for five years and it is claimed that the
8.12 A young aspiring DJ has saved up £4000 to buy the equipment she needs. She anticipates that the equipment will last for five years, after which it will be obsolete and have no disposal value.During these five years she believes she can use it to earn the following amounts, after allowing for
8.11 Select the appropriate definition for each term on the lefthand side from the list on the right-hand side.(i) a simple price index (a) uses current period weights(ii) a Laspeyre price index (b) an un-weighted index of prices of several items(iii) the base period (c) using an index to adjust
8.10 A media and entertainments company operates two theme parks in two different countries: Dorrogoy and Stoymost. The annual profits of each theme park over the first five years of operations, in millions of units of local currency (the Lukar in Dorrogoy and the Diyengi in Stoymost) were:1998
8.9 An enthusiast paid £5000 for a classic car in 1993. Since that time the car has been kept carefully and been valued every two years. The valuations were:Year 1995 1997 1999 2001 2003 Valuation (£) £5800 £5200 £5500 £6200 £6000 The values of the Retail Price Index (RPI) for these years
8.8* The turnover figures provided in the annual accounts of a large retail grocer over the six years from 1998 to 2003 were:Year 1998 1999 2000 2001 2002 2003 Turnover (£m) 7022 7101 7350 7844 8249 8598 The values of the Retail Price Index (RPI) for this period were:Year 1998 1999 2000 2001 2002
8.7 A confectioner buys cocoa, cocoa butter, sugar and milk solids.The prices per kilogram of these ingredients in 1997, 2000 and 2003 were:1997 2000 2003 Cocoa £1.50 £1.45 £1.70 Cocoa butter £1.30 £1.95 £2.05 Sugar £0.45 £0.50 £0.55 Milk solids £0.35 £0.62 £0.68 The quantities that
8.6 A textile manufacturer makes casual jackets. The company buys lining fabric, interfacing fabric and outer fabric. These fabrics are cut and machined to make the garments. The prices per metre of these materials in 2001, 2002 and 2003 were:2001 2002 2003 Lining £2.20 £2.30 £2.35 Interfacing

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Quantitative Methods For Business 1st Edition John Buglear - Solutions

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