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Business Statistics A First Course 7th Global Edition Kathryn A. Szabat, David M. Levine, David F. Stephan - Solutions
The United Auto Courts Reports blog notes that the National Insurance Crime Bureau says that Miami-Dade, Broward, and Palm Beach counties account for a substantial number of questionable insurance claims referred to investigators. Assume that the number of questionable insurance claims referred to
Spurious correlation refers to the apparent relationship between variables that either have no true relationship or are related to other variables that have not been measured. One widely publicized stock market indicator in the United States that is an example of spurious correlation is the
One theory concerning the S&P 500 Index is that if it increases during the first five trading days of the year, it is likely to increase during the entire year. From 1950 through 2013, the S&P 500 Index had these early gains in 41 years (in 2011 there was virtually no change). In 36 of these 41
Refer to Problem 5.42. In the same time period, 25% of the consumers registering a bank account and service compliant cited“deposit and withdrawal” as the type of complaint; these are issues such as transaction holds and unauthorized transactions.a. What is the expected value, or mean, of the
The Consumer Financial Protection Bureau’s consumer response team hears directly from consumers about the challenges they face in the marketplace, brings their concerns to the attention of financial institutions, and assists in addressing their complaints. Consumer response accepts complaints
Social log-ins involve recommending or sharing an article that you read online. According to Janrain, in the fourth quarter of 2013, 35% signed in via Facebook compared with 35% for Google.(Source: “Social Login Trends Across the Web for Q4 2013,” bit.ly/1jmLXRr.) If a sample of 10 social
Refer to Problem 5.39. Suppose that a quality improvement initiative has reduced the percentage of medical bills containing errors to 40%. If a sample of 10 medical bills is selected, what is the probability thata. 0 medical bills will contain errors?b. exactly 5 medical bills will contain
Medical billing errors and fraud are on the rise. According to the MBAA website, 8 out of 10 times, the medical bills that you get are not right. (Source: “Accurate Medical Billing,” bit.ly/1lHKIu3, April 2, 2014.) If a sample of 10 medical bills is selected, what is the probability thata. 0
One theory concerning the Dow Jones Industrial Average is that it is likely to increase during U.S. presidential election years. From 1964 through 2012, the Dow Jones Industrial Average increased in 10 of the 13 U.S. presidential election years.Assuming that this indicator is a random event with no
Smartphone adoption among American teens has increased substantially, and mobile access to the Internet is pervasive. One in four teenagers are “cell mostly” Internet users—that is, they mostly go online using their phone and not using some other device such as a desktop or laptop computer.
Between 1896—when the Dow Jones index was created—and 2013, the index rose in 66% of the years. (Sources: M. Hulbert,“What the Past Can’t Tell Investors,” The New York Times, January 3, 2010, p. BU2 and bit.ly/100zwvT.) Based on this information, and assuming a binomial distribution, what
and that the insurance company charges $4,000.a. Calculate the expected value of the profit made by the insurance company.b. Many call this kind of situation a win–win opportunity for the insurance company and the promoter. Do you agree? explain.
Darwin Head, a 35-year-old sawmill worker, won $1 million and a Chevrolet Malibu Hybrid by scoring 15 goals within 24 seconds at the Vancouver Canucks National Hockey League game(B. Ziemer, “Darwin evolves into an Instant Millionaire,” Vancouver Sun, February 28, 2008, p. 1). Head said he would
What are the four properties that must be present in order to use the Poisson distribution?
What are the four properties that must be present in order to use the binomial distribution?
What are probability density functions? Why are they useful?
calls is received per minute.a. What properties must be true about the situation described here in order to use the Poisson distribution to calculate probabilities concerning the number of phone calls received in a oneminute period?Assuming that this situation matches the properties discussed in
A toll-free phone number is available from 9 a.m. to 9 p.m.for your customers to register complaints about a product purchased from your company. Past history indicates that an average of
(a) and (b).
Refer to Problem 5.29. If you purchased a 2011 Toyota, what is the probability that in the past 12 months, the car hada. zero problems?b. two or fewer problems?c. Compare your answers in (a) and (b) to those for the 2010 model year Toyota in Problem
(b) and (c).
problems per car. (Data extracted from J. B. Healey,“Used Cars Get Less Reliable,” USA Today, February 13, 2014, p. 2B.) If you purchased a 2011 Ford, what is the probability that in the past 12 months the car hada. zero problems?b. two or fewer problems?c. Compare your answers in (a) and (b)
problems per car and Toyota had
Refer to Problem 5.27. Another press release reported that for 2011 model cars, Ford had
(b) and (c).
Refer to Problem 5.27. If you purchased a Toyota in the 2010 model year, what is the probability that in the past 12 months the car hada. zero problems?b. two or fewer problems?c. Compare your answers in (a) and (b) to those for the Ford in Problem
problems per car. (Data extracted from “2013 U.S. Vehicle Dependability Study,” J.D. Power and Associates, February 13, 2013, bit.ly/101aR9l.) Let X be equal to the number of problems with a three-year-old Ford.a. What assumptions must be made in order for X to be distributed as a Poisson
problems per car and Toyota had
J.D. Power and Associates calculates and publishes various statistics concerning car quality. The dependability score measures problems experienced during the past 12 months by original owners of three-year-old vehicles (those that were introduced for the 2010 model year). For these models of cars,
per day. (Source:Consumer Response: A Snapshot of Complaints Received, 1.usa.gov/WZ9N8Q.) Assume that the number of credit reporting complaints registered by consumers is distributed as a Poisson random variable. What is the probability that on a given daya. no credit reporting complaints will be
The Consumer Financial Protection Bureau’s consumer response team hears directly from consumers about the challenges they face in the marketplace, brings their concerns to the attention of financial institutions, and assists in addressing their complaints. The consumer response team accepts
per 10,000 passengers. What is the probability that in the next 10,000 passengers, there will bea. no one involuntarily denied boarding?b. at least one person involuntarily denied boarding?c. at least two persons involuntarily denied boarding?
The U.S. Department of Transportation maintains statistics for involuntary denial of boarding. In July–September 2013, the American Airlines rate of involuntarily denying boarding was
mishandled bags per 1,000 passengers. What is the probability that in the next 1,000 passengers the airline will havea. no mishandled bags?b. at least one mishandled bag?c. at least two mishandled bags?
One year, airline A had
The quality control manager of a cookie company is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 5.0. How many cookies in a batch of 100 should the manager expect to discard if the company
The quality control manager of Marilyn’s Cookies is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 5.9. What is the probability that in any particular cookie being inspecteda. fewer than
Assume that the number of network errors experienced in a day in a local area network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 1.6. What is the probability that in any given daya. zero network errors will occur?b. exactly one
Assume a Poisson distribution with l = 5.0. What is the probability thata. X = 1?b. X 6 1?c. X 7 1?d. X … 1?
Assume a Poisson distribution.a. If l = 2.0, find P1X Ú 22.b. If l = 8.0, find P1X Ú 32.c. If l = 0.5, find P1X … 12.d. If l = 4.0, find P1X Ú 12.e. If l = 5.0, find P1X … 32.
Assume a Poisson distribution.a. If l = 2.5, find P1X = 52.b. If l = 8.0, find P1X = 32.c. If l = 0.5, find P1X = 12.d. If l = 3.7, find P1X = 92.
on page 208.
and Wendy’s in example
on page 208, you and two friends decided to go to Wendy’s. Now, suppose that instead you go to McDonald’s, which recently filled approximately 88.3% of the orders correctly. What is the probability thata. all three orders will be filled correctly?b. none of the three will be filled correctly?c.
In example
on page 208, you and two friends decided to go to Wendy’s. Now, suppose that instead you go to Burger King, which recently filled approximately 82.3%of orders correctly. What is the probability thata. all three orders will be filled correctly?b. none of the three will be filled correctly?c. at
In example
Past records indicate that the probability of online retail orders that turn out to be fraudulent is 0.08. Suppose that, on a given day, 20 online retail orders are placed. Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable.a.
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.Historically, the failure rate for LeD light bulbs that the company manufactures is 5%. Suppose a random sample of 10 LeD light bulbs is selected. What is the probability thata.
A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one
A recent Pew Research survey reported that 48% of 18- to 29-year-olds in the United States own tablets. (Data extracted from “Tablet and e-Reader Ownership,” bit.ly/1gEwogC). Using the binomial distribution, what is the probability that in the next six 18- to 29-year-olds surveyed,a. four will
The increase or decrease in the price of a stock between the beginning and the end of a trading day is assumed to be an equally likely random event. What is the probability that a stock will show an increase in its closing price on five consecutive days?
Determine the mean and standard deviation of the variable X in each of the following binomial distributions:a. n = 4 and p = 0.10b. n = 4 and p = 0.40c. n = 5 and p = 0.80d. n = 3 and p = 0.50
Determine the following:a. For n = 4 and p = 0.12, what is P1X = 02?b. For n = 10 and p = 0.40, what is P1X = 92?c. For n = 10 and p = 0.50, what is P1X = 82?d. For n = 6 and p = 0.83, what is P1X = 52?
You plan to invest $1,000 in a corporate bond fund or in a common stock fund. The following table presents the annual return (per $1,000) of each of these investments under various economic conditions and the probability that each of those economic conditions will occur. Compute thea. expected
You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the following probability distribution:Compute thea. expected return for stock X and for stock Y.b. standard
The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years (104 weeks) are as follows:a. Compute the expected number of mortgages approved per
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes with the following results:a. Compute the expected number of arrivals per minute.b. Compute the standard deviation.
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet$1 that the sum will be under 7—that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result
Recently, a regional automobile dealership sent out fliers to perspective customers indicating that they had already won one of three different prizes: an automobile valued at $25,000, a $100 gas card, or a $5 Walmart shopping card. To claim his or her prize, a prospective customer needed to
The following table contains the probability distribution for the number of traffic accidents daily in aa. Compute the mean number of accidents per day.b. Compute the standard deviation.
Given the following probability distributions:
Are there any probability calculations that would be appropriate for rating an investment service? Why or why not?
Using the table found under the “Show Me the Winning Probabilities” subhead, compute the proper probabilities for the group of investors. What mistake was made in reporting the 7% probability claim?
How accurate is the claim of the probability of success for EndRun’s GIP? In what ways is the claim misleading? How would you calculate and state the probability of having an annual rate of return not less than 15%?
A 2013 Sage North America survey examined the “financial literacy” of small business owners. The study found that 23%of small business owners indicated concern about income tax compliance for their business; 41% of small business owners use accounting software, given that the small business
The CMO Council and SAS set out to better understand the key challenges, opportunities, and requirements that both chief marketing officers (CMOs) and chief information officers (CIOs)were facing in their journey to develop a more customer-centric enterprise. The following findings are from an
Content Marketing Institute provides insights on the content marketing habits of nonprofit professionals representing a broad range of nonprofit agencies and organizations. A survey of nonprofit marketers conducted by the Content Marketing Institute indicated that 26% of nonprofit marketers rated
The 2012 Restaurant Industry Forecast takes a closer look at today’s consumers. Based on a 2011 National Restaurant Association survey, consumers are divided into three segments (optimistic, cautious, and hunkered-down) based on their financial situation, current spending behavior, and economic
SHL Americas provides a unique, global perspective of how talent is measured in its Global Assessment Trends Report. The report presents the results of an online survey conducted in late 2012 with HR professionals from companies headquartered throughout the world. The authors were interested in
A survey by the Health Research Institute at PricewaterhouseCoopers LLP indicated that 80% of “young invincibles”(those aged 18 to 24) are likely to share health information through social media, as compared to 45% of “baby boomers” (those aged 45 to 64).Source: Data extracted from
A reading list for a course contains 19 articles. How many ways are there to choose four articles from this list?
A daily lottery is conducted in which 2 winning numbers are selected out of 100 numbers. How many different combinations of winning numbers are possible?
A student has 20 books that he would like to place in his backpack. However, there is only room for 18 books. Regardless of the arrangement, how many ways are there of placing 18 books into his backpack?
Four members of a group of 10 people are to be selected to a team. How many ways are there to select these four members?
How many different ways can a senior project manager and an associate project manager be selected for an analytics project if there are eight data scientists available?
A gardener has ten rows available in his vegetable garden to place ten different vegetables. Each vegetable will be allowed one and only one row. How many ways are there to position these vegetables in his garden?
Referring to Problem 4.44, how many different orders of finish are possible for the first four positions?
In Major League Baseball, there are five teams in the Eastern Division of the National League: Atlanta, Florida, New York, Philadelphia, and Washington. How many different orders of finish are there for these five teams? (Assume that there are no ties in the standings.) Do you believe that all
A team that includes eight different people is being formed. There are eight different positions on the team. How many different ways are there to assign the eight people to the eight positions?
You would like to “build-your-own-burger” at a fast-food restaurant. There are five different breads, seven different cheeses, four different cold toppings, and five different sauces on the menu.If you want to include one choice from each of these ingredient categories, how many different
A particular brand of women’s jeans is available in seven different sizes, three different colors, and three different styles.How many different women’s jeans does the store manager need to order to have one pair of each type?
a. If a coin is tossed seven times, how many different outcomes are possible?b. If a die is tossed seven times, how many different outcomes are possible?c. Discuss the differences in your answers to (a) and (b).
A lock on a bank vault consists of three dials, each with 30 positions. In order for the vault to open, each of the three dials must be in the correct position.a. How many different possible dial combinations are there for this lock?
If there are 10 multiple-choice questions on an exam, each having three possible answers, how many different sequences of answers are there?
A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued throughout the United States, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 50%were issued by cities, 40% by suburbs, and 10%
The editor of a textbook publishing company is trying to decide whether to publish a proposed business statistics textbook. Information on previous textbooks published indicates that 10% are huge successes, 20% are modest successes, 40% break-even, and 30% are losers. However, before a publishing
Laid-off workers who become entrepreneurs because they cannot find meaningful employment with another company are known as entrepreneurs by necessity. A major national newspaper reports that these entrepreneurs by necessity are less likely to grow into large businesses than are entrepreneurs by
Olive Construction Company is determining whether it should submit a bid for a new shopping center.In the past, Olive’s main competitor, Base Construction Company, has submitted bids 70% of the time. If Base Construction Company does not bid on a job, the probability that Olive Construction
A banking executive is studying the role of trust in creating customer advocates, and how valuable trust is to the overall banking relationship. Based on study results, the executive has determined that 44% of banking customers have complete trust in their primary financial institution, 49% of
In Example 4.10 on page 185, suppose that the probability that a medical diagnostic test will give a positive result if the disease is not present is reduced from 0.02 to 0.01.a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the
If P1B2 = 0.30, P1A B2 = 0.60, P1B′2 = 0.70, and and P1A B′2 = 0.50, find P1B A2.
If P1B2 = 0.15, P1A B2 = 0.50, P1B′2 = 0.85, and P1A B′2 = 0.60, find P1B A2.
A box of nine iPhone 5C cellphones (the iPhone “for the colorful”) contains two yellow cellphones and seven green cellphones.a. If two cellphones are randomly selected from the box, without replacement (the first cellphone is not returned to the box after it is selected), what is the
A standard deck of cards is being used to play a game. There are four suits (hearts, diamonds, clubs, and spades), each having 13 faces (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king), making a total of 52 cards. This complete deck is thoroughly mixed, and you will receive the first 2
In 41 of the 63 years from 1950 through 2013 (in 2011 there was virtually no change), the S&P 500 finished higher after the first five days of trading. In 36 out of 41 years, the S&P 500 finished higher for the year. Is a good first week a good omen for the upcoming year? The following table gives
Each year, ratings are compiled concerning the performance of new cars during the first 100 days of use. Suppose that the cars have been categorized according to whether a car needs warrantyrelated repair (yes or no) and the country in which the company manufacturing a car is based (in country X or
A survey of 1,085 adults asked, “Do you enjoy shopping for clothing for yourself?” The results (data extracted from “Split Decision on Clothes Shopping,” USA Today, January 28, 2011, p. 1B) indicated that 51% of the females enjoyed shopping for clothing for themselves as compared to 44% of
What business and technical skills are critical for today’s business intelligence/analytics and information management professionals? As part of InformationWeek’s 2013 U.S. IT Salary Survey, business intelligence/analytics and information management professionals, both staff and managers, were
Do Americans prefer Coke or Pepsi? A survey was conducted by Public Policy Polling (PPP) in 2013; the results were as follows:a. Given that an American is a male, what is the probability that he prefers Pepsi?b. Given that an American is a female, what is the probability that she prefers Pepsi?c.
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