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Statistics For Business And Economics 12th Edition James T. McClave, P. George Benson, Terry T Sincich - Solutions

Compute the number of ways you can select n elements from N elements for each of the following: a. n = 2, N = 5 b. n = 3, N = 6 c. n = 5, N = 20
For two events, A and B, P(A) = .4, P(B) = .2, and P(A | B) = .6: a. Find P(A ∩ B). b. Find P(B | A).
For two independent events, A and B, P(A) = .4 and P(B) = .2: a. Find P(A ∩ B) b. Find P(A | B). c. Find P(A ⋃ B)
Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E1 = .20, P(E2) = .30, P(E3) = .30, P(E4) = .10, P(E5) = .10.a. Calculate P(A), P(B), and P(A ˆ© B)b. Suppose we know that
Two fair coins are tossed, and the following events are defined:A: {Observe at least one head}B: {Observe exactly one head}a. Draw a Venn diagram for the experiment, showing events A and B. Assign probabilities to the sample points.b. Find P(A), P(B), and P(A ∩ B)c. Use the formula for
Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd} B: {Sum of the numbers showing is 9, 11, or 12} Are events A and B independent? Why?
Human Performance (Vol. 23, 2010) published the results of a study that found that arrogant workers are more likely to have poor performance ratings. Suppose that 15% of all full-time workers exhibit arrogant behaviors on the job and that 10% of all full-time workers will receive a poor performance
Forbes (Apr. 20, 2011) conducted a survey of the 20 largest public companies in the world. Of these 20 companies, 4 were banking or investment companies based in the United States. A total of 9 U.S. companies were on the top 20 list. Suppose we select one of these 20 companies at random. Given that
Two fair dice are tossed, and the face on each die is observed. a. Use a tree diagram to find the 36 sample points contained in the sample space. b. Assign probabilities to the sample points in part a. c. Find the probability of each of the following events: A = {3 showing on each die} B = {sum of
According to The National Crime Victimization Survey (December 2010), published by the U.S. Department of Justice, about 11.7 million people were victims of identity theft over the past 2 years. This number represents 5% of all persons age 16 or older in the United States. Of these victims, 53%
Refer to the Journal of Allied Health (Fall 2011) study of why emergency medical service (EMS) workers leave the profession, Exercise 3.41. Recall that in a sample of 244 former EMS workers, 127 were fully compensated while on the job, 45 were partially compensated, and 72 had non compensated
Refer to the Adweek/Harris (July 2011) poll of whether U.S. adults work during their summer vacation, Exercise 3.14. Recall that the poll found that 46% of the respondents work during their summer vacation, 35% do not work at all while on vacation, and 19% were unemployed. Also, 35% of those who
The summary table giving the number of the 158,044 Finnish citizens in each IQ score/investment category is reproduced below. Again, suppose one of the citizens is selected at random.For Information: Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the
Survey of the top 40 best-paid CEOs shown in Table 2.1. The data on highest degree obtained are summarized in the SPSS printout below.For Information: Refer to the results of the Forbes (April 13, 2011)Suppose you randomly select five of the CEOs (without replacement) and record the highest degree
Geographical Analysis (Jan. 2010) presented a study of emergency medical service (EMS) ability to meet the demand for an ambulance. In one example, the researchers presented the following scenario. An ambulance station has one vehicle and two demand locations, A and B. The probability that the
The U.S. Census Bureau reports a decline in the percentage of mothers in the workforce who have infant children. The following table gives a breakdown of the marital status and working status of the 1.8 million mothers with infant children in the year 2010. (The numbers in the table are reported in
Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. a. List the sample points for this experiment. b. Assign probabilities to the sample points. c. Determine the probability of observing each of the following events: A: {Two blue
The Journal of Wine Research (Vol. 21, 2010) published a study of the effects of soil and climate on the quality of wine produced in Spain. The soil at two vineyards-Llarga and Solar-was the focus of the analysis. Wine produced from grapes grown in each of the two vineyards was evaluated for each
Red snapper is a rare and expensive reef fish served at upscale restaurants. Federal law prohibits restaurants from serving a cheaper, look-alike variety of fish (e.g., vermillion snapper or lane snapper) to customers who order red snapper. Researchers at the University of North Carolina used DNA
The software for a lie detector based on voice stress levels - called the computerized voice stress analyzer (CVSA) - is available for about $10,000. The manufacturer claims that the CVSA is 98% accurate, and, unlike a polygraph machine, will not be thrown off by drugs and medical factors. However,
Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing patients' awareness of the problem is for physicians to provide patient
In Parade Magazine's (Nov. 26, 2000) column "Ask Marilyn," the following question was posed: "I have just tossed a [balanced] coin 10 times, and I ask you to guess which of the following three sequences was the result. One (and only one) of the sequences is genuine." (1) H H H H H H H H H H (2) H H
Portions of computer software code that may contain undetected defects are called blind spots. The issue of blind spots in software code evaluation was addressed at the 8th IEEE International Symposium on High Assurance Software Engineering (March 2004). The researchers developed guidelines for
Suppose the events B1 and B2 are mutually exclusive and complementary events, such that P(B1) = .75 and P(B2) = .25. Consider another event A such that P(A|B1) = .3 and P(A|B2) = .5. a. Find P(B1 ∩ A). b. Find P(B2 ∩ A). c. Find P(A) using the results in parts a and b. d. Find P(B1|A). e. Find
Suppose the events B1, B2, and B3 are mutually exclusive and complementary events, such that P(B1) = .2, P(B2) = .15, and P(B3) = .65. Consider another event A such that P(A) = .4. If A is independent of B1, B2, and B3, use Bayes's Rule to show that P(B1|A) = P(B1) = .2.
Currently, there are three diagnostic tests available for chromosome abnormalities in a developing fetus: triple serum marker screening, ultrasound, and amniocentesis. The safest (to both the mother and fetus) and least expensive of the three is the ultrasound test. Two San Diego State University
Contrary to what is presented on TV shows like CSI, fingerprint identification is not fully automated. Expert examiners are required to identify the person who left the fingerprint. A study published in Psychological Science (August 2011) tested the accuracy of experts and novices in identifying
A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate the costs of 30%, 20%, and 50%, respectively, of all jobs bid by the company. For i = 1, 2, 3, define Ei to be the event that a job is estimated by engineer i. The following probabilities describe the rates at
Due to inaccuracies in drug-testing procedures (e.g., false positives and false negatives) in the medical field, the results of a drug test represent only one factor in a physician's diagnosis. Yet, when Olympic athletes are tested for illegal drug use (i.e., doping), the results of a single
Dolomite is a valuable mineral that is found in sedimentary rock. During mining operations, dolomite is often confused with shale. The radioactivity features of rock can aid miners in distinguishing between dolomite and shale rock zones. For example, if the Gamma ray reading of a rock zone exceeds
An important component of your desktop or laptop personal computer (PC) is a microchip. The table gives the proportions of microchips that a certain PC manufacturer purchases from seven suppliers.a. It is known that the proportions of defective microchips produced by the seven suppliers are .001,
Recall that if there is an intruder, system A sounds an alarm with probability .9, and system B sounds an alarm with probability .95. If there is no intruder, system A sounds an alarm with probability .2, and system B sounds an alarm with probability .1. Now assume that the probability of an
Following the assassination of President John F. Kennedy (JFK) in 1963, the House Select Committee on Assassinations (HSCA) conducted an official government investigation. The HSCA concluded that although there was a probable conspiracy involving at least one shooter in addition to Lee Harvey
In 1940, Forrest E. Mars Sr. formed the Mars Corporation to produce chocolate candies with a sugar shell that could be sold throughout the year and wouldn't melt during the summer. Originally, M&M's Plain Chocolate Candies came in only a brown color. Today, M&M's in standard bags come in six
Which of the following describe continuous random variables? Which describe discrete random variables? a. The number of newspapers sold by the New York Times each month b. The amount of ink used in printing a Sunday edition of the New York Times c. The actual number of ounces in a 1-gallon bottle
Financial analysts who make forecasts of stock prices are categorized as either "buy-side" analysts or "sell-side" analysts. Refer to the Financial Analysts Journal (Jul./Aug. 2008) comparison of earnings forecasts of buy-side and sell-side analysts, Exercise 2.86. The mean and standard deviation
One of the CRASH variables saved in the accompanying file is the severity of a driver's head injury when the car is in a head-on collision with a fixed barrier while traveling at 35 miles per hour. The more points assigned to the head-injury rating, the more severe the injury. The head-injury
In Exercise 4.49 you learned that half of all U.S. adults use the Internet and have paid to download music (Pew Internet & American Life Project Survey, October 2010). In a random sample of 250 U.S. adults, let x be the number who use the Internet and pay to download music. a. Find the mean of x.
According to studies, 1 % of all patients who undergo laser surgery (i.e., LASIK) to correct their vision have serious post laser vision problems (All About Vision, 2012). In a sample of 100,000 patients, what is the approximate probability that fewer than 950 will experience serious post laser
Six Sigma is a comprehensive approach to quality goal setting that involves statistics. An article in Aircraft Engineering and Aerospace Technology (Vol. 76, No. 6, 2004) demonstrated the use of the normal distribution in Six Sigma goal setting at Motorola Corporation. Motorola discovered that the
Ambulance response time is measured as the time (in minutes) between the initial call to emergency medical services (EMS) and when the patient is reached by ambulance. Geographical Analysis (Vol. 41, 2009) investigated the characteristics of ambulance response time for EMS calls in Edmonton,
Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. The Wonderlic IQ test is an example of the former; the Purdue Pegboard speed test involving the arrangement of pegs on a peg board is an example of the latter. A particular dexterity test is administered
A discrete random variable x can assume five possible values: 20, 21, 22, 23, and 24. The following Minitab histogram shows the likelihood of each value.a. What is p(22)?b. What is the probability that x equals 20 or 24?c. What is P(x ‰¤ 23)?
Government data indicate that the mean hourly wage for manufacturing workers in the United States is $18.50 (Statistical Abstract of the United States: 2012). Suppose the distribution of manufacturing wage rates nationwide can be approximated by a normal distribution with standard deviation $1.25
During a presidential election, each state is allotted a different number of votes in the Electoral College depending on population. For example, California is allotted 55 votes (the most) while several states (including the District of Columbia) are allotted 3 votes each (the least). When a
The probability of a hotel guest participating in the hotel's "green" conservation program by reusing towels and bed linens is .45. Suppose a large hotel chain randomly samples 200 of its guests. The chain's national director claims that more than 110 of these guests participated in the
The following table reports the U.S. credit card industry's market share data for 2011. A random sample of 100 credit card users is to be questioned regarding their satisfaction with their credit card company. For simplification, assume that each credit card user carries just one credit card and
Poor executive leadership during business meetings can result in counterproductive outcomes (e.g., negative employee attitudes, ambiguous objectives). Can executive coaching help improve business meeting effectiveness? This was the question of interest in an article published in Consulting
What relationship exists between the standard normal distribution and the box-plot methodology (Section 2.8) for describing distributions of data using quartiles? The answer depends on the true underlying probability distribution of the data. Assume for the remainder of this exercise that the
If a population data set is normally distributed, what is the proportion of measurements you would expect to fall within the following intervals? a. μ ± σ b. μ ± 2σ c. μ ± 3σ
Normal probability plots for three data sets are shown below. Which plot indicates that the data are approximately normally distributed?
The random variable x has the following discrete probability distribution:a. List the values x may assume.b. What value of x is most probable?c. Display the probability distribution as a graph.d. Find P(x = 7).e. Find P(x ‰¥ 5).f. Find P(x > 2).g. Find E(x).
Examine the sample data in the accompanying table.a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution.b. Compute 5 for the sample data.c. Find the values of QL and QU and the value of s from part b to assess whether the data come from an
Data on the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) for each of 992 senior managers at CPA firms are saved in the accompanying file. In Exercise 4.98 you assumed that the level of support variable was approximately normally
Software configuration management was used to monitor a software engineering team's performance at Motorola, Inc. (Software Quality Professional, Nov. 2004). One of the variables of interest was the number of updates to a file that was changed because of a problem report. Summary statistics for n =
Wear-out failure time of electronic components is often assumed to have a normal distribution. Can the normal distribution be applied to the wear-out of used manufactured products, such as colored display panels? A lot of 50 used display panels was purchased by an outlet store. Each panel displays
Refer to the NHTSA crash test data for new cars. In Exercise 4.102, you assumed that the driver's head-injury rating is approximately normally distributed. Apply the methods of this chapter to the data saved in the accompanying file to support this assumption.Exercise 4.102Refer to Exercise 4.21
Refer to the data on the Dec. 2008 sanitation scores for 186 cruise ships, first presented in Exercise 2.24. The data are saved in the accompanying file. Assess whether the sanitation scores are approximately normally distributed.Exercise 2.24To minimize the potential for gastrointestinal disease
Recall that the method incorporates a golfer's average driving distance (yards) and driving accuracy (percent of drives that land in the fairway) into a driving performance index. Data on these three variables for the top 40 PGA golfers are saved in the accompanying file. Determine which of these
A discrete random variable x can assume five possible values: 2, 3, 5, 8, and 10. Its probability distribution is shown here:a. What is p(5)?b. What is the probability that x equals 2 or 10?c. What is P(x ‰¤ 8)?
The DoD RAC publishes START sheets for government and industry. These START sheets are designed to improve the reliability, maintainability, supportability, and quality of manufactured components and systems. In Volume 11 (2004), the DoD analyzed the following data set on tensile strength
The variable of interest is the total semester hours of college credit for each candidate. Recall that the mean and median for the data set were 141.31 and 140 hours, respectively, and the standard deviation was 17.77 hours. Demonstrate why the probability distribution for the variable, total
Suppose x is a random variable best described by a uniform probability distribution with c = 3 and d = 7.a. Find f(x).b. Find the mean and standard deviation of x.c. Find P(μ - σ ≤ x ≤ μ + σ).
Suppose x is a random variable best described by a uniform probability distribution with c = 20 and d = 45. a. Find f(x). b. Find the mean and standard deviation of x. c. Graph f(x) and locate μ and the interval μ ± 2σ on the graph. The probability that x assumes a value within the interval μ
Refer to Exercise 4.133. Find the following probabilities:a. P(20 ≤ x ≤ 30)b. P(20 < x ≤ 30)c. P(x ≥ 30)d. P(x ≥ 45)e. P(x ≤ 40)f. P(x < 40)g. P(15 ≤ x ≤ 35)h. P(21.5 ≤ x ≤ 31.5)Exercise 4.133Suppose x is a random variable best described by a uniform probability
Suppose x has an exponential distribution with  = 1. Find the following probabilities:a. P(x > 1)b. P(x ≤ 3)c. P(x > 1.5)d. P(x ≤ 5)
The random variable x is best described by a uniform probability distribution with c = 100 and d = 200. Find the probability that x assumes a valuea. More than 2 standard deviations from μ.b. Less than 3 standard deviations from μ.c. Within 2 standard deviations of μ.
Explain why each of the following is or is not a valid probability distribution for a discrete random variable x:a.b.c.d.
Maintaining a constant pipe wall temperature in some hot-process applications is critical. A technique that utilizes bolt-on trace elements to maintain temperature was presented in the Journal of Heat Transfer (Nov. 2000). Without bolt-on trace elements, the pipe wall temperature of a switch
Researchers at the University of South Florida Center for Biological Defense have developed a safe method for rapidly detecting anthrax spores in powders and on surfaces (USF Magazine, Summer 2002). The method has been found to work well even when there are very few anthrax spores in a powder
On the basis of data collected from metal shredders across the nation, the amount x of extractable lead in metal shredder residue has an approximate exponential distribution with mean θ = 2.5 milligrams per liter (Florida Shredder's Association). a. Find the probability that x is greater than 2
Social networking sites for business professionals are used to promote one's business. Each social network involves interactions (connections) between members of the network. Researchers define network density as the ratio of actual network connections to the number of possible one-to-one
The frequency distribution shown in the next table depicts the property and marine losses incurred by a large oil company over the last 2 years. This distribution can be used by the company to predict future losses and to help determine an appropriate level of insurance coverage. In analyzing the
The manager of a local soft-drink bottling company believes that when a new beverage-dispensing machine is set to dispense 7 ounces, it in fact] dispenses an amount x at random anywhere between 65 and 7.5 ounces inclusive. Suppose x has a uniform probability distribution.a. Is the amount dispensed
Refer to the Chance (Summer 2007) article on phishing attacks at a company, Exercise 2.33. Recall that phishing describes an attempt to extract personal/financial information through fraudulent e-mail. The company set up a publicized e-mail account-called a "fraud box" that enabled employees to
An article in Hotwire (Dec. 2002) discussed the length of time till failure of a product produced at Hewlett-Packard. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with mean 500 thousand hours. In reliability jargon this is known as the
A die is tossed. Let x be the number of spots observed on the upturned face of the die. a. Find the probability distribution of x and display it in tabular form. b. Display the probability distribution of x in graphical form.
In the jargon of system maintenance, cycle availability is defined as the probability that the system is functioning at any point in time. The DoD developed a series of performance measures for assessing system cycle availability (START, Vol. 11, 2004). Under certain assumptions about the failure
A tool-and-die machine shop produces extremely high-tolerance spindles. The spindles are 18-inch slender rods used in a variety of military equipment. A piece of equipment used in the manufacture of the spindles malfunctions on occasion and places a single gouge somewhere on the spindle. However,
For a certain type of halogen light bulb, an old bulb that has been in use for a while tends to have a longer life than a new bulb. Let x represent the life (in hours) of a new halogen light bulb and assume that x has an exponential distribution with mean θ = 250 hours. According to
Toss three fair coins and let x equal the number of heads observed.a. Identify the sample points associated with this experiment and assign a value of x to each sample point.b. Calculate p(x) for each value of x.c. Construct a graph for p(x).d. What is P(x = 2 or x = 3)?
Consider the probability distributions shown here:a. Use your intuition to find the mean for each distribution. How did you arrive at your choice?b. Which distribution appears to be more variable? Why?c. Calculate Î¼ and Ïƒ2 for each distribution. Compare these answers to your answers in parts
Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are discrete and which are continuous random variables? a. The closing price of a particular stock on
According to Nielsen's Television Audience Report, 2010 & 2011, 26% of all U.S. TV house-holds have a size of 1 person, 32% have a household size of 2,17% have a household size of 3, and 25% have a house-hold size of 4 or more. Let x represent the size (number of people) in a randomly selected
A summary of the CRASH driver-side star ratings for the 98 cars in the file is reproduced in the accompanying Minitab printout. Assume that one of the 98 cars is selected at random and let x equal the number of stars in the car's driver-side star rating.For Information: Refer to the NHTSA crash
The age distribution for the employees of a highly successful "dot-com" company headquartered in Atlanta is shown in the next table. An employee is to be randomly selected from this population.a. Can the relative frequency distribution in the table be interpreted as a probability distribution?
According to an August 2011 survey by the Pew Internet & American Life Project, nearly 40% of adult cell phone owners have downloaded an application ("app") to their cell phone. The next table gives the probability distribution for x, the number of "apps" used at least once a week by cell phone
Recall that each of 124 college students selected showroom displays for portable grills. Five different displays (representing five different-sized grills) were available, but the students were instructed to select only three displays in order to maximize purchases of Grill #2 (a smaller-sized
Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Assume the following: Of the 63 robots with legs only, 50
In an effort to minimize the monetary losses that result from a devastating Florida hurricane, part of the researchers' analysis included a graphic showing the sequence number of tropical storms within a season that are most likely to develop into a hurricane. Data for 67 hurricanes are summarized
Consider a random sample of three slaughtered chickens that all pass USDA inspection. Let x equal the number of chickens in the sample that have fecal contamination.a. Find p(x) for x = 0, 1, 2, 3.b. Graph p(x).c. Find P(x ≤ 1).For Information: In Exercise 3.17 you learned that one in every 100
A weapons manufacturer uses a liquid propellant to produce gun cartridges. During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A University of South Florida statistician, hired by the company to investigate the level of
he Journal of Consumer Research (August 2011) published a study demonstrating the "last name" effect-i.e., the tendency for consumers with last names that begin with a later letter of the alphabet to purchase an item before consumers with last names that begin with earlier letters. To facilitate
During autumn 2001, there was a highly publicized outbreak of anthrax cases among U.S. Postal Service workers. In Chance (Spring 2002), research statisticians discussed the problem of sampling mailrooms for the presence of anthrax spores. Let x equal the number of mailrooms contaminated with
The risk of a portfolio of financial assets is sometimes called investment risk. In general, investment risk is typically measured by computing the variance or standard deviation of the probability distribution that describes the decision maker's potential outcomes (gains or losses). The greater
Recall that an IQ score (from a low score of 1 to a high score of 9) was determined for each in a sample of 158,044 Finnish citizens. Also recorded was whether or not the citizen invested in the stock market. The accompanying table gives the number of Finnish citizens in each IQ score/investment
The National Weather Service issues precipitation forecasts that indicate the likelihood of measurable precipitation (≥ .01 inch) at a specific point (the official rain gauge) during a given time period. Suppose that if a measurable amount of rain falls during the next 24 hours, a river will
Most states offer weekly lotteries to generate revenue for the state. Despite the long odds of winning, residents continue to gamble on the lottery each week. In SIA, Chapter 3, you learned that the chance of winning Florida's Pick-6 Lotto game is 1 in approximately 23 million. Suppose you buy a $1
Engineers at Broadcom Corp. and Simon Fraser University collaborated on research involving a robot-sensor system in an unknown environment (International Journal of Robotics Research, Dec. 2004). As an example, the engineers presented the three-point, single-link robotic system shown in the
Odds makers try to predict which professional and college football teams will win and by how much (the spread). If the odds makers do this accurately, adding the spread to the underdog's score should make the final score a tie. Suppose a bookie will give you $6 for every $1 you risk if you pick the

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