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Complete Business Statistics 7th Edition Amir Aczel, Jayavel Sounderpandian - Solutions
In 2003, there were 5,732 deaths from car accidents in France. The population of France is 59,625,919. If I am going to live in France for five years, what is my probability of dying in a car crash?
The probabilities that three drivers will be able to drive home safely after drinking are 0.5, 0.25, and 0.2, respectively. If they set out to drive home after drinking at a party, what is the probability that at least one driver drives home safely?
When one is randomly sampling four items from a population, what is the probability that all four elements will come from the top quartile of the population distribution? What is the probability that at least one of the four elements will come from the bottom quartile of the distribution?
Fifteen locations in a given area are believed likely to have oil. An oil company can only afford to drill at eight sites, sequentially chosen. How many possibilities are there, in order of selection?
In the analysis of variance we compare several population means to see which is largest. After the primary analysis, pair wise comparisons are made. If we want to compare seven populations, each with all the others, how many pairs are there?
In a shipment of 14 computer parts, 3 are faulty and the remaining 11 are in working order. Three elements are randomly chosen out of the shipment. What is the probability that all three faulty elements will be the ones chosen?
Megabucks is a lottery game played in Massachusetts with the following rules. A random drawing of 6 numbers out of all 36 numbers from 1 to 36 is made every Wednesday and every Saturday. The game costs $1 to play, and to win a person must have the correct six numbers drawn, regardless of their
In Megabucks, a player who correctly chooses five out of the six winning numbers gets $400. What is the probability of winning $400?
In a takeover bid for a certain company, management of the raiding firm believes that the takeover has a 0.65 probability of success if a member of the board of the raided firm resigns and a 0.30 chance of success if she does not resign. Management of the raiding firm further believes that the
A drug manufacturer believes there is a 0.95 chance that the Food and Drug Administration (FDA) will approve a new drug the company plans to distribute if the results of current testing show that the drug causes no side effects. The manufacturer further believes there is a 0.50 probability that the
An import-export firm has a 0.45 chance of concluding a deal to export agricultural equipment to a developing nation if a major competitor does not bid for the contract, and a 0.25 probability of concluding the deal if the competitor does bid for it. It is estimated that the competitor will submit
A realtor is trying to sell a large piece of property. She believes there is a 0.90 probability that the property will be sold in the next 6 months if the local economy continues to improve throughout the period, and a 0.50 probability the property will be sold if the local economy does not
Holland America Cruise Lines has three luxury cruise ships that sail to Alaska during the summer months. Since the business is very competitive, the ships must run full during the summer if the company is to turn a profit on this line. A tourism expert hired by Holland America believes there is a
Saflok is an electronic door lock system made in Troy, Michigan, and used in modern hotels and other establishments. To open a door, you must insert the electronic card into the lock slip. Then a green light indicates that you can turn the handle and enter; a yellow light indicates that the door is
A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0.95. When an emergency situation does not exist, the alarm system sounds with probability 0.02. A real emergency situation is a rare event, with probability 0.004. Given that the
When the economic situation is "high," a certain economic indicator rises with probability 0.6. When the economic situation is "medium," the economic indicator rises with probability 0.3. When the economic situation is "low," the indicator rises with probability 0.1. The economy is high 15% of the
An oil explorer orders seismic tests to determine whether oil is likely to be found in a certain drilling area. The seismic tests have a known reliability: When oil does exist in the testing area, the test will indicate so 85% of the time; when oil does not exist in the test area, 10% of the time
Before marketing new products nationally, companies often test them on samples of potential customers. Such tests have a known reliability. For a particular product type, a test will indicate success of the product 75% of the time if the product is indeed successful and 15% of the time when the
A die is tossed twice and the two outcomes are noted. Draw the Venn diagram of the sample space and indicate the event "the second toss is greater than the first." Calculate the probability of the event.
A market research field worker needs to interview married couples about use of a certain product. The researcher arrives at a residential building with three apartments. From the names on the mailboxes downstairs, the interviewer infers that a married couple lives in one apartment, two men live in
AT&T was running commercials in 1990 aimed at luring back customers who had switched to one of the other long-distance phone service providers. One such commercial shows a businessman trying to reach Phoenix and mistakenly getting Fiji, where a half-naked native on a beach responds
According to Business Week, 50% of top managers leave their jobs within 5 years. If 25 top managers are followed over 5 years after they assume their positions, what is the probability that none will have left their jobs? All of them will have left their jobs? At least one will have left the
The probability that a graduating senior will pass the certified public accountant (CPA) examination is 0.60. The probability that the graduating senior will both pass the CPA examination and get a job offer is 0.40. Suppose that the student just found out that she passed the CPA examination. What
Two stocks A and B are known to be related in that both are in the same industry. The probability that stock A will go up in price tomorrow is 0.20, and the probability that both stocks A and B will go up tomorrow is 0.12. Suppose that tomorrow you find that stock A did go up in price. What is the
The probability that production will increase if interest rates decline more than 0.5 percentage point for a given period is 0.72. The probability that interest rates will decline by more than 0.5 percentage point in the period in question is 0.25. What is the probability that, for the period in
A large foreign automaker is interested in identifying its target market in the United States. The automaker conducts a survey of potential buyers of its high performance sports car and finds that 35% of the potential buyers consider engineering quality among the car's most desirable features and
Ford Motor Company advertises its cars on radio and on television. The company is interested in assessing the probability that a randomly chosen person is exposed to at least one of these two modes of advertising. If we define event R as the event that a randomly chosen person was exposed to a
Consider the situation in problem 2-79. Three consumers are chosen randomly from among a group of potential buyers of the high-performance automobile. What is the probability that all three of them consider engineering quality to be among the most important features of the car? What is the
A financial service company advertises its services in magazines, runs billboard ads on major highways, and advertises its services on the radio. The company estimates that there is a 0.10 probability that a given individual will see the billboard ad during the week, a 0.15 chance that he or she
An accounting firm carries an advertisement in The Wall Street Journal. The firm estimates that 60% of the people in the potential market read The Wall Street Journal; research further shows that 85% of the people who read the Journal remember seeing the advertisement when questioned about it
A quality control engineer knows that 10% of the microprocessor chips produced by a machine are defective. Out of a large shipment, five chips are chosen at random. What is the probability that none of them is defective? What is the probability that at least one is defective? Explain.
A fashion designer has been working with the colors green, black, and red in preparing for the coming season's fashions. The designer estimates that there is a 0.3 chance that the color green will be "in" during the coming season, a 0.2 chance that black will be among the season's colors, and a
A multinational corporation is considering starting a subsidiary in an Asian country. Management realizes that the success of the new subsidiary depends, in part, on the ensuing political climate in the target country. Management estimates that the probability of success (in terms of resulting
The probability that a shipping company will obtain authorization to include a certain port of call in its shipping route is dependent on whether certain legislation is passed. The company believes there is a 0.5 chance that both the relevant legislation will pass and it will get the required
The probability that a bank customer will default on a loan is 0.04 if the economy is high and 0.13 if the economy is not high. Suppose the probability that the economy will be high is 0.65. What is the probability that the person will default on the loan?
Researchers at Kurume University in Japan surveyed 225 workers aged 41 to 60 years and found that 30% of them were skilled workers and 70% were unskilled. At the time of survey, 15% of skilled workers and 30% of unskilled workers were on an assembly line. A worker is selected at random from the age
Swiss Air maintains a mailing list of people who have taken trips to Europe in the last three years. The airline knows that 8% of the people on the mailing list will make arrangements to fly Swiss Air during the period following their being mailed a brochure. In an experimental mailing, 20 people
At a certain university, 30% of the students who take basic statistics are first year students, 35% are sophomores, 20% are juniors, and 15% are seniors. From records of the statistics department it is found that out of the first-year students who take the basic statistics course 20% get As; out of
The probability that a new product will be successful if a competitor does not come up with a similar product is 0.67. The probability that the new product will be successful in the presence of a competitor's new product is 0.42. The probability that the competing firm will come out with a new
In 2007, Starbucks inaugurated its Dulce de Leche Latte. If 8% of all customers who walk in order the new drink, what is the probability that out of 13 people, at least 1 will order a Dulce de Leche Latte? What assumption are you making?
Blackjack is a popular casino game in which the objective is to reach a card count greater than the dealer's without exceeding 21. One version of the game is referred to as the "hole card" version. Here, the dealer starts by drawing a card for himself or herself and putting it aside, face down,
For the United States, automobile fatality statistics for the most recent year of available data are 40,676 deaths from car crashes, out of a total population of 280 million people. Compare the car fatality probability for one year in the United States and in France. What is the probability of
Recall from Chapter 1 that the median is that number such that one-half the observations lie above it and one-half the observations lie below it. If a random sample of two items is to be drawn from some population, what is the probability that the population median will lie between these two data
Extend your result from the previous problem to a general case as follows. A random sample of n elements is to be drawn from some population and arranged according to their value, from smallest to largest. What is the probability that the population median will lie somewhere between the smallest
A research journal states: "Rejection rate for submitted manuscripts: 86%." A prospective author believes that the editor's statement reflects the probability of acceptance of any author's first submission to the journal. The author further believes that for any subsequent submission, an author's
1. If the graduate applies to all 10 companies, what is the probability that she will get at least one offer?2. If she can apply to only one company, based on cost and success probability criteria alone, should she apply to company 5? Why or why not?3. If she applies to companies 2, 5, 8, and 9,
The number of telephone calls arriving at an exchange during any given minute between noon and 1:00 P.M. on a weekday is a random variable with the following probability distribution. XP(x) 0 ....0.31 ....0.22 ....0.23 ....0.14 ....0.15 ....0.1a. Verify that P(x) is a probability distribution. b.
The daily exchange rate of one dollar in euros during the first three months of 2007 can be inferred to have the following distribution. X P(x) 0.73 ... 0.05 0.74 ... 0.10 0.75 ... 0.25 0.76 ... 0.40 0.77 ... 0.15 0.78 ... 0.05 a. Show that P(x) is a probability distribution. b. What is the
Find the expected value of the random variable. Also find the variance of the random variable and its standard deviation.XP(x)0 ....0.31 ....0.22 ....0.23 ....0.14 ....0.15 ....0.1
Find the mean, variance, and standard deviation of the random variable. x .... P(x) 0 ..... 0.01 1 ..... 0.09 2 ..... 0.30 3 ..... 0.20 4 ..... 0.20 5 ..... 0.10 6 ..... 0.10
Find the mean, variance, and standard deviation of the number of cars sold per day, using the probability distribution.XP(x)0 .....0.11 .....0.12 .....0.23 .....0.24 .....0.35 .....0.1
What is the expected number of dots appearing on two dice?
Use the probability distribution to find the expected number of shipment orders per day. What is the probability that on a given day there will be more orders than the average? X P(x) 0 ..... 0.1 1 ..... 0.2 2 ..... 0.4 3 ..... 0.1 4 ..... 0.1 5 ..... 0.1
Find the mean, variance, and standard deviation of the annual income of a hedge fund manager, using the probability distribution.x ($ millions)P(x)$1,700 ...... 0.21,500 ...... 0.21,200 ...... 0.31,000 ...... 0.1800 ...... 0.1600 ......0.05400 ......0.05
According to Chebyshev's theorem, what is the minimum probability that a random variable will be within 4 standard deviations of its mean?
According to an article in Travel and Leisure, every person in a small study of sleep during vacation was found to sleep longer than average during the first vacation night.1 Suppose that the number of additional hours slept in the first night of a vacation, over the person's average number slept
The average annual return on a certain stock is 8.3%, and the variance of the returns on the stock is 2.3. Another stock has an average return of 8.4% per year and a variance of 6.4. Which stock is riskier? Why?
Returns on a certain business venture, to the nearest $1,000, are known to follow the probability distributionXP(x)-2,000 ......0.1-1,000 ......0.10 ......0.21,000 ......0.22,000 ......0.33,000 ......0.1a. What is the most likely monetary outcome of the business venture?b. Is the venture likely to
Management of an airline knows that 0.5% of the airline's passengers lose their luggage on domestic flights. Management also knows that the average value claimed for a lost piece of luggage on domestic flights is $600. The company is considering increasing fares by an appropriate amount to cover
Refer to problem 3-7. Suppose that hedge funds must withhold $300 million from the income of the manager and an additional 5% of the remaining income. Find the expected net income of a manager in this group. What property of expected values are you using?x ($ millions)P(x)$1,700 ...... 0.21,500
Refer to problem 3-4. Suppose the car dealership's operation costs are well approximated by the square root of the number of cars sold, multiplied by $300. What is the expected daily cost of the operation? Explain.XP(x)0 .....0.11 .....0.12 .....0.23 .....0.24 .....0.35 .....0.1
In problem 3-2, suppose that a cost is imposed of an amount equal to the square of the number of additional hours of sleep. What is the expected cost? Explain. X P(x) 0 ..... 0.01 1 ..... 0.09 2 ..... 0.30 3 ..... 0.20 4 ..... 0.20 5 ..... 0.10 6 ..... 0.10
All voters of Milwaukee County were asked a week before Election Day whether they would vote for a certain presidential candidate. Of these, 48% answered yes, 45% replied no, and the rest were undecided. If a yes answer is coded +1, a no answer is coded -1, and an undecided answer is coded 0, find
Explain the meaning of the variance of a random variable. What are possible uses of the variance?
Refer to problem 3-23. Find the variance and the standard deviation of hedge fund managers' income. x ($ millions) P(x) $1,700 ...... 0.2 1,500 ...... 0.2 1,200 ...... 0.3 1,000 ...... 0.1 800 ...... 0.1 600 ...... 0.05 400 ...... 0.05
The percentage of people (to the nearest 10) responding to an advertisement is a random variable with the following probability distribution: x(%) ...P(x)0 ......0.1010 ......0.2020 ......0.3530 ......0.2040 ......0.1050 ......0.05a. Show that P(x) is a probability distribution. b. Find the
The daily exchange rate of one dollar in euros during the first three months of 2007 can be inferred to have the following distribution.XP(x)0.73 ...0.050.74 ...0.100.75 ...0.250.76 ...0.400.77 ...0.150.78 ...0.05Find the mean and the standard deviation of the dollar to euros exchange rate.
Lobsters vary in sizes. The bigger the size, the more valuable the lobster per pound (a 6-pound lobster is more valuable than two 3-pound ones). Lobster merchants will sell entire boatloads for a certain price. The boatload has a mixture of sizes. Suppose the distribution is as follows:What is a
A large shipment of computer chips is known to contain 10% defective chips. If 100 chips are randomly selected, what is the expected number of defective ones? What is the standard deviation of the number of defective chips? Use Chebyshev's theorem to give bounds such that there is at least a 0.75
Look at the histogram of probabilities in the binomial distribution template for the case n = 5 and p = 0.6.a. Is this distribution symmetric or skewed? Now, increase the value of n to 10, 15, 20, . .. Is the distribution becoming more symmetric or more skewed? Make a formal statement about what
A salesperson goes door-to-door in a residential area to demonstrate the use of a new household appliance to potential customers. At the end of a demonstration, the probability that the potential customer would place an order for the product is a constant 0.2107. To perform satisfactorily on the
An MBA graduate is applying for nine jobs, and believes that she has in each of the nine cases a constant and independent 0.48 probability of getting an offer. a. What is the probability that she will have at least three offers? b. If she wants to be 95% confident of having at least three offers,
An automobile dealership records the number of cars sold each day. The data are used in calculating the following probability distribution of daily sales:XP(x)0 .....0.11 .....0.12 .....0.23 .....0.24 .....0.35 .....0.1a. Find the probability that the number of cars sold tomorrow will be between
A computer laboratory in a school has 33 computers. Each of the 33 computers has 90% reliability. Allowing for 10% of the computers to be down, an instructor specifies an enrollment ceiling of 30 for his class. Assume that a class of 30 students is taken into the lab. a. What is the probability
A commercial jet aircraft has four engines. For an aircraft in flight to land safely, at least two engines should be in working condition. Each engine has an independent reliability of p = 92%. a. What is the probability that an aircraft in flight can land safely? b. If the probability of landing
An investment portfolio has equal proportions invested in five stocks. The expected returns and standard deviations (both in percent per year) are (8, 3), (5, 2), (12, 8), (7, 9), (14, 15). What are average return and standard deviation for this portfolio?
A graduating student keeps applying for jobs until she has three offers. The probability of getting an offer at any trial is 0.48.a. What is the expected number of applications? What is the variance?b. If she has enough time to complete only six applications, how confident can she be of getting
A real estate agent has four houses to sell before the end of the month by contacting prospective customers one by one. Each customer has an independent 0.24 probability of buying a house on being contacted by the agent.a. If the agent has enough time to contact only 15 customers, how confident can
A graduating student keeps applying for jobs until she gets an offer. The probability of getting an offer at any trial is 0.35.a. What is the expected number of applications? What is the variance?b. If she has enough time to complete at most four applications, how confident can she be of getting an
A shipment of pins contains 25 good ones and 2 defective ones. At the receiving department, an inspector picks three pins at random and tests them. If any defective pin is found among the three that are tested, the shipment would be rejected.a. What is the probability that the shipment would be
A committee of 7 members is to be formed by selecting members at random from a pool of 14 candidates consisting of 5 women and 9 men.a. What is the probability that there will be at least three women in the committee?b. It is desired to increase the chance that there are at least three women in the
A mainframe computer in a university crashes on the average 0.71 time in a semester.a. What is the probability that it will crash at least two times in a given semester?b. What is the probability that it will not crash at all in a given semester?c. The MIS administrator wants to increase the
The number of rescue calls received by a rescue squad in a city follows a Poisson distribution with ยต = 2.83 per day. The squad can handle at most four calls a day.a. What is the probability that the squad will be able to handle all the calls on a particular day?b. The squad wants to have at least
Consider the roll of a pair of dice, and let X denote the sum of the two numbers appearing on the dice. Find the probability distribution of X, and find the cumulative distribution function. What is the most likely sum?
A student takes the campus shuttle bus to reach the classroom building. The shuttle bus arrives at his stop every 15 minutes but the actual arrival time at the stop is random. The student allows 10 minutes waiting time for the shuttle in his plan to make it in time to the class.a. What is the
A hydraulic press breaks down at the rate of 0.1742 times per day.a. What is the MTBF?b. On a given day, what is the probability that it will break down?c. If four days have passed without a breakdown, what is the probability that it will break down on the fifth day?d. What is the probability that
Laptop computers produced by a company have an average life of 38.36 months. Assume that the life of a computer is exponentially distributed (which is a good assumption).a. What is the probability that a computer will fail within 12 months?b. If the company gives a warranty period of 12 months,
In most statistics textbooks, you will find cumulative binomial probability tables in the format shown below. These can be created using spreadsheets using the Binomial template and Data | Table commands.a. Create the above table.b. Create a similar table for n = 7.
Look at the shape of the binomial distribution for various combinations of n and p. Specifically let n = 5 and try p = 0.2, 0.5, and 0.8. Repeat the same for other values of n. Can you say something about how the skewness of the distribution is affected by p and n?
An MBA graduate keeps interviewing for jobs, one by one, and will stop interviewing on receiving an offer. In each interview he has an independent probability 0.2166 of getting the job.a. What is the expected number of interviews? What is the variance?b. If there is enough time for only six
A shipment of thousands of pins contains some percentage of defectives. To decide whether to accept the shipment, the consumer follows a sampling plan where 80 items are chosen at random from the sample and tested. If the number of defectives in the sample is at most three, the shipment is
A shipment of 100 pins contains some defectives. To decide whether to accept the shipment, the consumer follows a sampling plan where 15 items are chosen at random from the sample and tested. If the number of defectives in the sample is at most one, the shipment is accepted.a. Assuming that the
A recent study published in the Toronto Globe and Mail reveals that 25% of mathematics degrees from Canadian universities and colleges are awarded to women. If five recent graduates from Canadian universities and colleges are selected at random, what is the probability thata. At least one would be
The number of intercity shipment orders arriving daily at a transportation company is a random variable X with the following probability distribution:XP(x)0 .....0.11 .....0.22 .....0.43 .....0.14 .....0.15 .....0.1a. Verify that P(x) is a probability distribution.b. Find the cumulative probability
An article published in Access magazine states that according to a survey conducted by the American Management Association, 78% of major U.S. companies electronically monitor their employees. If five such companies are selected at random, find the probability thata. At most one company monitors its
An article published in Business Week says that according to a survey by a leading organization 45% of managers change jobs for intellectual challenge, 35% for pay, and 20% for long-term impact on career. If nine managers who recently changed jobs are randomly chosen, what is the probability thata.
Estimates published by the World Health Organization state that one out of every three workers may be toiling away in workplaces that make them sick. If seven workers are selected at random, what is the probability that a majority of them are made sick by their workplace?
Based on the survey conducted by a municipal administration in the Netherlands, Monday appeared to be managements' preferred day for laying off workers. Of the total number of workers laid off in a given period, 30% were on Monday, 25% on Tuesday, 20% on Wednesday, 13% on Thursday, and 12% on
A recent survey published in Business Week concludes that Gatorade commands an 83% share of the sports drink market versus 11% for Coca-Cola's PowerAde and 3% for Pepsi's All Sport. A market research firm wants to conduct a new taste test for which it needs Gatorade drinkers. Potential participants
The time between customer arrivals at a bank has an exponential distribution with a mean time between arrivals of three minutes. If a customer just arrived, what is the probability that another customer will not arrive for at least two minutes?
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