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Business Statistics A First Course 7th Edition David M. Levine, Kathryn A. Szabat, David F. Stephan - Solutions
Two coins are tossed. a. Give an example of a simple event. b. Give an example of a joint event. c. What is the complement of a head on the first toss? d. What does the sample space consist of?
How will marketers change their social media use in the near future? A survey by Social Media Examiner reported that 78% of B2B marketers (marketers that focus primarily on attracting businesses) plan to increase their use of LinkedIn, as compared to 54% of B2C marketers (marketers that primarily
Referring to the contingency table in Problem 4.10, if a marketer is selected at random, what is the probability that a. He or she plans to increase use of LinkedIn? b. He or she is a B2C marketer? c. He or she plans to increase use of LinkedIn or is a B2C marketer? d. Explain the difference in the
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:If an American is selected at random, what is the probability that he or she a. Prefers Pepsi? b. Is male and prefers Pepsi? c. Is male or prefers Pepsi? d. Explain the
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) indicated that 51% of the females enjoyed shopping for clothing for themselves as compared to 44% of the
Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether a car needs warranty-related repair (yes or no) and the country in which the company manufacturing a car is based (United States
Consider the following contingency table:What is the probability ofa. A ∣ B?b. A ∣ B?c. A ∣ B?d. Are events A and B independent?
Consider the following contingency table:What is the probability of a. A ∣ B? b. A ∣ B? c. A ∣ B? d. Are events A and B independent?
If P(A and B) = 0.4 and P(B) = 0.8, find P(A B).
If P(A) = 0.7, P(B) = 0.6, and A and B are independent, find P( A and B).
An urn contains 12 red balls and 8 white balls. One ball is to be selected from the urn. a. Give an example of a simple event. b. What is the complement of a red ball? c. What does the sample space consist of?
If P(A) = 0.3, P(B) = 0.4, and P(A and B) = 0.2, are A and B independent?
Do males or females feel more tense or stressed out at work? A survey of employed adults conducted online by Harris Interactive on behalf of the American Psychological Association revealed the following:a. Given that the employed adult felt tense or stressed out at work, what is the probability
How will marketers change their social media use in the near future? A survey by Social Media Examiner of B2B marketers (marketers that focus primarily on attracting businesses) and B2C marketers ( marketers that primarily target consumers) was based on 1,331 B2B marketers and 1,694 B2C marketers.
Do Americans prefer Coke or Pepsi? A survey was con-ducted 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
What business and technical skills are critical for todays business intelligence/ analytics and information management professionals? As part of InformationWeeks 2013 U. S. IT Salary Survey, business intelligence/ analytics and information management professionals, both
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.) indicated that 51% of the females enjoyed shopping for clothing for themselves as compared to 44% of the
Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether a car needs warranty-related repair (yes or no) and the country in which the company manufacturing a car is based (United States
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
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
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, with-out replacement (the first cellphone is not returned to the box after it is selected), what is the
Consider the following contingency table:What is the probability of event a. A? b. A ? c. A and B? d. A or B?
If P (B) = 0.05, P(A ∣ B) = 0.80, P(B) = 0.95, and P(A ∣ B) = 0.40, find P(B ∣ A).
If P (B) = 0.30, P (A ∣ B) = 0.60, P (B’) = 0.70, and P (A ∣ B’) = 0.50, find P (B ∣ A)
In Example 4.10 on page 163, 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
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
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
According to a report by The Kauffman Foundation and Legal Zoom, 35% of new businesses in 2013 were started by women and 65% of new businesses in 2013 were started by men. Twenty percent of 2013 new businesses started by women had revenues of $ 50,000 and above, whereas 24% of 2013 new businesses
The editor of a textbook publishing company is trying to decide whether to publish a proposed business statistics text-book. 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
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
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?b. What is the probability that if you randomly select a position
Consider the following contingency table:What is the probability of event a. A ? b. A and B? c. A and B ? d. A or B ?
a. If a coin is tossed seven times, how many different out-comes 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).
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 student has seven books that she would like to place in her backpack. However, there is room for only four books. Regardless of the arrangement, how many ways are there of placing four books into the backpack?
For each of the following, indicate whether the type of probability involved is an example of a priori probability, empirical probability, or subjective probability. a. The next toss of a fair coin will land on heads. b. Italy will win soccer’s World Cup the next time the competition is held. c.
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?
There are 15 exercise bikes in a fitness store showroom. The fitness store owner wishes to select three of them to display at a fitness expo. How many ways can a group of three be selected?
What are the differences between a priori probability, empirical probability, and subjective probability?
How does the multiplication rule differ for events that are and are not independent?
For each of the following, state whether the events created are mutually exclusive and whether they are collectively exhaustive. a. Undergraduate business students were asked whether they were sophomores or juniors. b. Each respondent was classified by the type of car he or she drives: sedan, SUV,
A survey by the Health Research Institute at Pricewater-houseCoopers 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”. Source: Data extracted from “\Social Media
SHL Americas provides a unique, global perspective of how talent is measured in its Global Assessment Trends Report. The re-port presents the results of an online survey conducted in late 2012 with HR professionals from companies headquartered through-out the world. The authors were interested in
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
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 non-profit marketers conducted by the Content Marketing Institute indicated that 26% of nonprofit marketers rated
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
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
Which of the following events occur with a probability of zero? For each, state why or why not. a. A company is listed on the New York Stock Exchange and NASDAQ. b. A consumer owns a smartphone and a tablet. c. A cellphone is a Motorola and a Samsung. d. An automobile is a Toyota and was
Do males or females feel more tense or stressed out at work? A survey of employed adults conducted online by Harris Interactive on behalf of the American Psychological Association revealed the following:a. Give an example of a simple event. b. Give an example of a joint event. c. What is the
Referring to the contingency table in Problem 4.8, if an employed adult is selected at random, what is the probability that a. The employed adult felt tense or stressed out at work? b. The employed adult was a male who felt tense or stressed out at work? c. The employed adult was a male or felt
Given the following probability distributions:a. Compute the expected value for each distribution.b. Compute the standard deviation for each distribution.c. Compare the results of distributions A and B.
Determine the mean and standard deviation of the variable X in each of the following binomial distributions:a. n = 4 and π = 0.10b. n = 4 and π = 0.40c. n = 5 and π = 0.80d. n = 3 and π = 0.50
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
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 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 that a.
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.
In Example 5.4 on page 186, 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
In Example 5.4 on page 186, 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
Assume a Poisson distribution.a. If λ = 2.5, find P(X = 2).b. If λ = 8.0, find P(X = 8).c. If λ = 0.5, find P(X = 1).d. If λ = 3.7, find P(X = 0).
Assume a Poisson distribution.a. If λ = 2.0, find P(X ≥ 2).b. If λ = 8.0, find P(X ≥ 3).c. If λ = 0.5, find P(X ≤ 1).d. If λ = 4.0, find P(X ≥ 1).e. If λ = 5.0, find P(X ≤ 3).
The following table contains the probability distribution for the number of traffic accidents daily in a small town:a. Compute the mean number of accidents per day.b. Compute the standard deviation.
Assume a Poisson distribution with l = 5.0. What is the probability thata. X = 1?b. X < 1?c. X > 1?d. X ≤ 1?
Assume that the number of new visitors to a website in one hour is distributed as a Poisson variable. The mean number of new visitors to the website is 4.0 per hour. What is the probability that in any given houra. Zero new visitors will arrive at the website?b. Exactly one new visitor will arrive
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 chocolate- chip parts per cookie is 6.0. What is the probability that in any particular cookie being inspecteda.
Refer to Problem 5.22. How many cookies in a batch of 100 should the manager expect to discard if company policy requires that all chocolate- chip cookies sold have at least four chocolate-chip parts?DataAverage/Expected number of successes:6Poisson Probabilities
The U. S. Department of Transportation maintains statistics for mishandled bags per 1,000 airline passengers. In October 2013, Delta mishandled 1.55 bags per 1,000 passengers. What is the probability that in the next 1,000 passengers, Delta will have a. No mishandled bags?b. At least one
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 0.45 per 10,000 passengers. What is the probability that in the next 10,000 passengers, there will be a. No one
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 com-plaints. The consumer response team accepts
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
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 had a. Zero problems? b. Two or fewer problems? c. Compare your answers in (a) and (b) to those for the Ford in Problem 5.27 (b) and (c).
Refer to Problem 5.27. Another press release reported that for 2011 model cars, Ford had 1.40 problems per car and Toyota had 1.14 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
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
Refer to Problem 5.29. If you purchased a 2011 Toyota, what is the probability that in the past 12 months, the car had a. 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 5.28 (a) and (b).
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 0.8 calls is received per minute.a. What properties must be true about the situation described here in order
What are the four properties that must be present in order to use the binomial distribution?
What are the four properties that must be present in order to use the Poisson distribution?
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
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 de-vice such as a desktop or laptop computer.
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 Aver-age increased in 10 of the 13 U. S. presidential election years. Assuming that this indicator is a random event
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 that a. 0
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
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
Social log- ins involve recommending or sharing an article that you read online. According to Jan rain, 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
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
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
One theory concerning the S& P 500 Index is that if it in-creases 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
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
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
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.
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
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
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
Determine the following:a. For n = 4 and π = 0.12, what is P(X = 0)?b. For n = 10 and π = 0.40, what is P(X = 9)?c. For n = 10 and π = 0.50, what is P(X = 8)?d. For n = 6 and π = 0.83, what is P(X = 5)?
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E. 2), what is the probability thata. Z is less than 1.57?b. Z is greater than 1.84?c. Z is between 1.57 and 1.84? d. Z is less than 1.57 or greater than 1.84?
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8.a. What is the probability that a student scored below 91 on this exam?b. What is the probability that a student scored between 65 and 89?c. The
A Nielsen study indicates that 18 to 24 year old spend a mean of 135 minutes watching video on their smartphones per month. (Data extracted bit. ly/1hF3BP2.) Assume that the amount of time watching video on a smartphone per month is normally distributed and that the standard deviation is 15
According to a special issue of Beverage Digest (bit.ly/1e9ORS3), the U. S. per capita consumption of soft drinks in 2013 was 42.2 gallons. Assume that the per capita consumption of soft drinks in the United States is approximately normally distributed with a mean of 42.2 gallons and a standard
Many manufacturing problems involve the matching of machine parts, such as shafts that fit into a valve hole. A particular design requires a shaft with a diameter of 22.000 mm, but shafts with diameters between 21.990 mm and 22.010 mm are accept-able. Suppose that the manufacturing process yields
Show that for a sample of n = 39, the smallest and largest Z values are - 1.96 and + 1.96, and the middle (i. e., 20th) Z value is 0.00.
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