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Understanding Business Statistics 1st edition Stacey Jones, Tim Bergquist, Ned Freed - Solutions
Two newly hired employees at Gordian Yacht, a luxury boat manufacturer, are beginning their probationary period on the job. Their supervisor assesses a .6 proba-bility that employee A will make it through the probationary period successfully, and a probability of .8 that employee B will make it
As the night Editor for Yahoo! News, you are waiting for two of your reporters—Abbott and Bocelli—to phone in breaking stories before the website’s next scheduled update. You decide that the probability of Abbott beating the deadline is .6. The probability that Bocelli will beat the deadline
In a recent survey of local businessmen and business-women, 40% of the respondents said they were online subscribers to Businessweek magazine, 70% said they were online subscribers to the Wall Street Journal (WSJ ). 30% said that they subscribed to both. What percentage of the respondents subscribe
During its next session, Congress is given a 60% chance of taking serious measures to reduce the federal defcit. Congress is also given a 50% chance of voting a substantial pay raise for its members. If you estimate a 40% probability that it will do both,a. How likely is it that the Congress will
NBC is introducing two new television shows this season. It estimates that “Live,” a reality show in which 12 contestants vie for the affections of Justin Timberlake’s cousin, Russell, has a 60% chance of being a hit. The other show, “Inside,” a look at the seamier side of the wholesale
The table below is from Exercise 4. It shows six stocks traded on either the New York Stock Exchange (NYSE) or the NASDAQ Exchange. Also shown is an indication of whether the stock gained or lost value by the close of a particular trading day.You plan to randomly choose one stock from the group.
Classmates Ken and John have been comparing their past exam performances. On 60% of the exams, Ken received a grade of B or better. John received a grade of B or better on 70% of the exams. They noticed that on 90% of the exams on which Ken scored B or better, John also made B or better.a. What
Following the loss of the Challenger space shuttle, a study was done to fnd better ways to measure and control for risk. One way to reduce the risk of failure is to have redundant (backup) systems. Suppose you have designed a component for the new Mars explorer that, during pre fight tests,
Needing to get to Houston tomorrow, you book a fight on two different airlines, knowing that there’s a chance that the fights will be overbooked and that you could be “bumped” (that is, forced to take a later fight). In fact, an article earlier in the day indicated that, for the two airlines
You have an important document that has to be delivered to your Detroit office tomorrow morning. You call a number of overnight delivery services and fnd that each one claims an 80% probability that it can deliver your document on time. Concerned about your future with the frm, you decide to select
Three solar batteries are installed in each DPC communications satellite placed in orbit. Testing indicates that each of the batteries is 75% likely to remain in good working order for at least 10 years. The satellite will function as designed if at least two of the three batteries remain in good
As a resident of Big City you feel the need to buy two large watchdogs. The dogs’ trainer asserts that each dog is 70% likely to detect and “discourage” any intruder. a. Assuming each dog acts independently, how likely is it that an intruder would go undetected? b. Still insecure, you are
Testing athletes for illegal steroid use is becoming more sophisticated. (For example, see New Designer Steroid Detected A mong Top A thletes , pbs.org/newshour.) Suppose testing Olympic athletes involves three independent laboratories. Each specimen submitted by an athlete is separated into three
As project manager, you estimate that there’s a 50% probability that your current research program will be completed within the next month. You concede that it is 30% likely the program will take two months, and 20% likely it will take a full three months. You also have reason to believe that if
Anson State University will be playing a four-game series in soccer against arch-rival Benton College. Anson coaches are convinced that Anson will be a 3 to 2 favorite in each game (that is, Anson has a 60% probability of winning each individual game). a. How likely is it that Anson will win all 4
The Walton-Draper Company has just received a large shipment of noise canceling headphones from its main supplier. Its quality control people have devised a plan for evaluating the shipment by selecting a few items and subjecting them to rigorous testing. More specifcally, an inspector will select
The table below appeared in Exercise 5. It shows the year-to-year US sales trends or fve auto companies headquartered in the US and Japan.You plan to randomly choose one company from the group. Find the following probabilities: a. The conditional probability that the sales trend
You are at the Screaming Slalom Ski Basin and estimate that you have about a 25% likelihood of successfully navigating a run down the diffcult Yikes! slope without a serious fall. Today you plan to make four trips down the slope. However, if you have a serious fall on any one of these downhill
The Congressional Budget Office estimates that if the economy continues to grow at the current rate, there is a 95% probability that the federal defcit will be eliminated without raising taxes within the next 5 years. If the economy slows, that probability drops to 30%, but if it accelerates, the
Canzano Home Products is trying to assess the likelihood that its proposed new “Royal Family” product line will be successful. The plan is to develop the new line ONLY if its probability of success appears to be more than 60%. The company believes that the new line’s success will be linked to
You want to estimate your chances of getting tickets to next month's State U vs. Acme Tech basketball game on the day of the game. (You don't have the money at the moment to buy the tickets in advance.) You're convinced that the availability of tickets will be affected by such factors as the
Many investors are prone to listening to “stock pickers” who claim to have beaten the stock market on a consistent basis. Most academics, however, are convinced that the stock market is generally random. Assume that there are only two possible outcomes for the stock market on any given day:
As a writer for DailyObserver.com, you are at a political gathering. Seventy percent o those in attendance are Republicans; the remaining 30% are Democrats. According to best estimates, 90% of all Republicans favor increasing tax credits for companies developing new green technologies, while
Refer to the situation in Exercise 86. Suppose you choose someone randomly and discover that the person is a supporter of expanded tax credits. Use Bayes’ theorem to revise the probability that the person you have chosen is a Democrat.In Exercise 86As a writer for DailyObserver.com, you are at a
Bolton Securities is about to implement a drug-testing procedure for company employees. In a recent anonymous survey, 20% of Bolton’s employees admitted to using illegal drugs. The random drug testing procedure is not infallible. In fact, about 5% of the time it will produce a false positive
Refer to the situation in Exercise 88. Suppose an employee is chosen randomly and that the employee’s test identifes him/her as a drug user. Use Bayes’ theorem to revise the probability that the person chosen is actually a drug user.In Exercise 88Bolton Securities is about to implement a
The table below appeared in Exercise 6. It shows the type of business and the gender of the CEO for your firm€™s five major clients:You plan to randomly choose one company from the group. Find the following probabilities: a. The conditional probability that the company CEO is female,
Forty-five percent of all homes for sale in your local area sell quickly—within 20 days of listing. Thirty-fve percent sell within 21 to 50 days. The remaining homes sell slowly, taking longer than 50 days. Pilot Realty claims that it accounts for 90% of the quick sales (20 days or less), 30% of
ABT Mining is about to perform a detailed geologic analysis at a site that preliminary tests indicate is 60% likely to contain a signifcant vein of silver. The detailed geologic analysis will be used to further assess the chances that a signifcant vein of silver will be found at the site. The
In a survey sponsored by the National Science Foundation, some of the individuals contacted for survey interviews were offered incentives, ranging from $10 to $30, for their cooperation. The table below shows the incentive levels and the fnal status of the interviews for 229 people in the studya.
A government study of personal bankruptcies looked at what the authors called the “trajectory” of two groups of individuals who had declared bankruptcy. One group was classified as “on the way up.” These were individuals whose gross income had risen in each of the three years prior to
Refer to Exercise 65. Construct a joint probability table for the situation described there. Use the table to compute the probability thatIn Exercise 65Two newly hired employees at Gordian Yacht, a luxury boat manufacturer, are beginning their probationary period on the job. Their supervisor
Refer to Exercise 66. Construct a joint probability table to compute the probability that In Exercise 66 As the night Editor for Yahoo! News, you are waiting for two of your reporters—Abbott and Bocelli—to phone in breaking stories before the website’s next scheduled update. You decide that
Refer to Exercise 67. Construct a joint probability table to compute theIn Exercise 67In a recent survey of local businessmen and business-women, 40% of the respondents said they were online subscribers to Businessweek magazine, 70% said they were online subscribers to the Wall Street Journal (WSJ
In a recent survey of 600 top executives (240 CEOs, 210 CFOs, and the remainder COOs), each executive was asked to answer the question, “Is the economic policy of the current Administration generally a help or a hindrance to economic growth?” Overall, 64% of the survey participants said it was
Two key navigation guidance units that will be packaged together for Boeing’s new 1077 have been subjected to repeated testing. Unit Y functioned properly in 96% of the tests. Unit Z functioned properly in 88% of the tests. Curiously, in 90% of the tests in which Unit Y failed, Unit Z also
Local law enforcement authorities are concerned about the growth of violent teenage gangs in the city. They estimate that 65% of juveniles arrested are gang members. If the crime involved is violent, the probability of gang membership jumps to 86%. Crime statistics show that 70% of all juveniles
Unit sales for Harper, Inc. over the last 10 days are as follows: 2, 2, 1, 0, 1, 1, 2, 3, 0, 1.a. If you pick a day at random, how likely is it those two units were sold on that day?b. If we define a random variable that counts the number of daily sales during this 10-day period, what are the
Below is a table showing the probability distribution for the random variable “number of flaws” described in Exercise 3.Flaws Probabilityx
Below is a table showing the probability distribution for the random variable “number of stocks doubling in value” described in Exercise 5.Number of Stocks Doubling ProbabilityX
You have a deck of 10 cards colored on one side—7 red and 3 blue. You plan to blindly select three cards, shuffling the deck after each selection. With the help of a probability tree, produce the full probability distribution or the random variable “number of red cards selected” in this
The table below shows the size distribution for American households in 1970 and 2010Suppose you were to choose one household at random from the 1970 population. a. Show the probability distribution for the random variable €œnumber of people in the household.€ To simplify, let the maximum
In a recent year, the percentage of frst-time California Bar Exam takers that passed the July exam was 68%, while the percentage of repeaters that passed was 22%. Defne x as a random variable representing the number of times a randomly selected individual will take the bar exam until he/she passes.
Five percent of the welds done by the welding robots at Arbitron-Lewisburg Manufacturing are substandard and need to be redone. Suppose you randomly choose fve recent welds. Use the binomial function to compute the probability thata. Exactly three of the five welds are substandard.b. None of the
The Wall Street Journal reports that 42% of the approximately 3500 stocks traded yesterday on the New York Stock Exchange advanced (that is, increased in price) and 58% declined or were unchanged. If you had randomly chosen four stocks at the start of the day, how likely is it thata. all four
In a given year, approximately 1% of all flights scheduled to depart from US airports are canceled. You select 10 flights at random. Use the binomial probability function to compute the probability thata. None of the fights will be canceled.b. Exactly one of the fights will be canceled.c. No more
A study of restaurant failure rates that tracked turnover among 2500 restaurants in Columbus, Ohio, over a three-year period found that one in four restaurants close or change ownership within their first year of business. Over three years, that number rises to three in fve. You select fve new
A technique called 3-D seismic attribute analysis has been used over the past decade to improve the exploration and development of new oil wells in the US. A three-year study done in Kansas reported that the commercial success rate for wells drilled with 3-D seismic data was 70%, compared to a
A psychological exam was given to 50 professional athletes. Scores are given below:Score Number of Athletes20………………………. 830……………………….
The table below shows the probability of drawing various hands in a game of poker (Five Card Stud):Suppose you draw fve hands of poker. (To simplify, assume you start with a new shuffled deck for each hand.) Use the binomial probability function to compute the probability that you will drawa. Three
One of the saddest world statistics is the HIV/AIDS rate in African countries. For example, the HIV/AIDS rate in Sierra Leone among people aged 15 to 45 is reported to be 7%. If doctors were to randomly screen 250 residents of Sierra Leone in this age group, what is thea. Expected number of people
In Exercise 17, it was reported that about 1% of all airline flights scheduled to depart from US airports are canceled. You select 100 flights at random. Assuming all the binomial conditions are met, compute theIn Exercise 17In a given year, approximately 1% of all flights scheduled to depart from
According to a study done by researchers at Georgetown University, recent college graduates who majored in architecture have the highest unemployment rate, at 13.9%. Arts majors are next, with an 11.1% unemployment rate for recent graduates. Recent graduates are defned as eligible workers between
Exercise 18 suggested that one in four new restaurants close or change ownership within their frst year of business, and that over three years, that number rises to three in five. You randomly select 50 new restaurants. Compute theIn Exercise 18A study of restaurant failure rates that tracked
Exercise 19 dealt with a study indicating that the commercial success rate for wells drilled with 3-D seismic data is 70%. You randomly select 30 drilling sites that are using this kind of data. Compute theIn Exercise 19A technique called 3-D seismic attribute analysis has been used over the past
Look again at the poker probabilities in Exercise 20. If you draw 200 hands, with a fresh, shuffled deck for each hand, compute the expected number of hands in which you would havea. Two pair or better.b. A full house.c. Nothing.
Use the binomial table to find the following probabilities:a. P ( x = 1), where n = 9, p = .2b. P (x = 4), where n = 20, p = .35c. P (3 < x < 5), where n = 15, p = .5d. P(x > 2), where n = 10, p = .4
Use the binomial table to find the following probabilities:a. P(x = 6), where n = 11, p = .65b. P(x > 5), where n = 7, p = .8c. P(x < 17), where n = 20, p = .7d. P(9 < x < 12), where n = 16, p = .75
A large study done by researchers at the New Jersey School of Medicine reports that 10% of the eyes that undergo LASIK corrective surgery need to be retreated. A nearby clinic performed LASIK surgery on 15 patients (30 eyes) last week. Assuming that all the binomial conditions are met, use the
Seven percent of the units manufactured by Bartlett and Sousa have at least one flaw: 4% are too thick, 5% are too rough, and 2% percent are both too thick and too rough. You randomly select one of the units. Define “number of flaws in the unit” as a random variable anda. show all possible
Marine researchers in the UK recently conducted a study of oil spills from oil tankers that run aground. Using historical data, the study reported that if a tanker goes aground, there is a 30% chance that it will spill oil. Suppose 15 tankers go aground in the next year. Assuming that all the
You plan to randomly select 10 recent sales reports filed by your field representatives to check for accuracy. Historically, 70% of the reports are error free. With .7 as your value for p, use the binomial table to determine the probability that among the 10 reports you select you’ll finda.
In a recent Pew Research survey, 40% of American adults who have taken a college course online said that online courses provide an education value equal to courses taken in a classroom. If the 40% figure is correct for the population of adult online students and you interview 20 students from this
According to the Mortgage Bankers Association, 10% of all home mortgage loans in California were in foreclosure in the fourth quarter of 2011. Assuming this rate holds, if you randomly pick 30 California home mortgage loans, how likely is it thata. At least six of them would be in foreclosure?b. No
In a study of high school graduation rates, Wisconsin had the highest graduation rate among all the states, at 90%. This compares to graduation rates of 75% for Texas high schools and 70% for Alabama high schools. Assume these rates hold and that a random sample of 25 entering high school freshmen
According to a recent study done by the Entertainment Software Association, 55% of all the people who play online games are female. If a sample of 15 online gamers is selected, how likely is it thata. At least 7 of the gamers are female?b. Between 8 and 11 (inclusive) of the gamers are female?c. If
Graph the binomial distribution for the following cases:a. n = 3, p = .3b. n = 9, p = .3
Graph the binomial distribution for the following cases:a. n = 6, p = .2b. n = 10, p = .5
Graph the binomial distribution for the following cases:a. n = 5, p = .75b. n = 9, p = .55
Graph the binomial distribution for the following cases:a. n = 3, p = .65b. n = 2, p = .3
Sam Ruggerio operates a fleet of two fishing trawlers. Based on past frequencies, each trawler is 50% likely to bring back 10 tons of fish on a given day, 20% likely to bring back 20 tons of fish, and 30% likely to return empty. Assume the trawlers perform independently.a. On a randomly selected
Use the Poisson probability function to determine the following probabilities:a. For λ = 2, P(x = 5)b. For λ = 6, P(x = 2)c. For λ = 3.5, P(x = 0)d. For λ = 2, P(2 < x < 4)
Use the Poisson probability function to find the following probabilities:a. For 7, P(x = 3)b. For λ = 1, P(x < 1)c. For λ = 1.3, P(x = 1)d. For λ = 3.2, P(1 < x < 3)
Pedestrian traffic is being monitored at the southeast corner of the intersection of 8th Avenue and 14th Street to determine whether a crossing signal is needed there. The average number of pedestrians arriving at the corner is four per minute. Assume all the Poisson conditions are met. Use the
The metal “skin” of an airplane is inspected carefully at the time of assembly and any flaws that are found are corrected. Suppose the average number of flaws found in these inspections is .1 per square foot. Assume all the Poisson conditions are met. Use the Poisson probability function to
ESRF (European Synchrotron Radiation Facility) reports that its X-ray equipment has an average failure rate of .02 failures per hour. Assume all Poisson conditions are met. Use the Poisson probability function to determine the probability ofa. Exactly one failure in a 10-hour period.b. No more than
Use the Poisson table to find the following probabilities:a. For λ = 2, P(x = 4)b. For λ = 6, P(x = 14)c. For λ = 3.5, P(x < 1)d. For λ = 2, P(3 < x < 5)
Use the Poisson table to find the following probabilities:a. For λ = 7, P(x = 10)b. For λ = 1, P(x = 2)c. For λ = 1.3, P(x = 0)d. For λ = 4.6, P(1 < x < 3)
The US Department of Transportation reports that there were 6,323,000 highways “crashes” (accidents involving one or more vehicles) in the US in a recent year. This means an average of 12 per minute or .2 crashes per second. Assume that these averages are still in effect and that all the
Meteor showers can be a spectacular sight. They are especially intense in late July and early August, when the annual Perseid meteor shower is visible in the early morning sky. As many as 50 to 150 meteors per hour are visible. Suppose you are watching on the morning of August 12. Assuming all the
DuPont produces Kevlar, a high strength (five times stronger than steel) lightweight fiber. Kirby Outfitters uses the fiber in some of its products and occasionally inspectors find a small flaw in the strands of fiber purchased. Assume that inspectors find an average of .3 flaws per 1000 feet of
You have just bought three stocks: Stock A, Stock B, and Stock C. Given the current market, you estimate that each stock has a 60% chance of doubling in value. Assume that stock performances are statistically independent. Defining “number of stocks doubling in value” as your random variable,a.
Use values from the Poisson table to sketch the Poisson distribution for λ = .2.
Use values from the Poisson table to sketch the Poisson distribution for λ = 5.
Use values from the Poisson table to sketch the Poisson distribution for λ = 10. Comment on the shape of the distribution as compared to the ones you sketched in Exercises 50 and 51.
Lights used to illuminate a long stretch of Highway 46 burn out at an average rate of 2.3 per day. (Assume that all the Poisson conditions are met.) Letting x represent values of the random variable “number of lights that burn out during any one day,” use the Poisson table toa. Determine the
When he types reports, Tom makes typing errors at an average rate of .7 errors per page. Assume that all the Poisson conditions—independence, etc.—are met. Letting x represent values of the random variable “number of typing errors on a page,” use the Poisson table toa. Determine the
The average number of speeding tickets written per hour by State Troopers patrolling Highway 61 between Oroville and Winnemucca is 3.6. Assume that all the Poisson conditions are met. Let x represent values for the random variable “number of tickets written in an hour.” Determine, in the most
Use the Poisson table to approximate the following binomial probabilities: a. P(x = 2) when n = 50, p = .1 b. P(x = 5) when n = 300, p = .02 c. P(x = 1) when n = 500, p = .005
Use the Poisson table to approximate the following binomial probabilities: a. P(x = 2) when n = 200, p = .03 b. P(x = 4) when n = 1000, p = .001 c. P(x = 2) when n = 800, p = .002
In Exercise 29, results were reported from a study evaluating the effectiveness of LASIK eye surgery. The study found that 10% of eyes that underwent LASIK surgery needed to be retreated. If the Edmonds Eye Clinic performs the operation on 50 eyes this week, what is the probability (using the
Use the binomial and the Poisson tables to compute and compare the binomial probabilities and the approximating Poisson probabilities for the following cases: a. P(x = 5) where n = 20, p = .1 b. P(x < 2) where n = 18, p = .05 c. P(1 < x < 3) where n = 30, p = .01
A recent study commissioned by the City of New York reported that 40% of the 911 calls made in the city were “inadvertent” (source: nydailynews.com). This amounted to nearly 11,000 false calls per day. Most of these inadvertent calls were classified as “pocket calls”—cell phone calls that
On entering a restaurant, three friends wearing similar coats place their coats on a coat rack. When they leave, each selects a coat at random. Using x as the random variable “number of people who get back the correct coat,” show the full probability distribution.
You are at the Devil’s Chasm Ski Basin and estimate that you have a 40% chance of successfully navigating a run down the difficult triple black diamond Yeow! Slope with-out a serious fall. Today you plan to make three runs down Yeow! However, if you have a serious fall on any one of these runs,
The Human Resources Department at Gutierrez and Associates has developed an interviewing procedure for hiring new employees. Prior to the interview, the department head uses the candidate’s resume to assign a probability that the interview will show the candidate to be “excellent”, “good”
Demand for your company’s product is influenced by two factors: economic conditions for the year (good, fair or poor) and the intensity of market competition (intense or moderate). Company analysts estimate a likelihood of 30% that economic conditions will be good, a 50% likelihood that they will
Kimberly Lau plans to make three sales calls today. She estimates that the chance of making a sale on any one call is about 30%. The calls are independent.a. Construct a probability tree to produce the full probability distribution for the random variable “number of sales”. Show distribution
For the situation in Exercise 64,a. Use the binomial function to produce the set of probabilities.b. Compute the expected value and the standard deviation of the distribution using the expressions E(x) = np and σ = √np(1 ─ p).
Peccavi Construction is currently involved in four independent projects. Peccavi estimates that each project is 40% likely to be late.a. Using a tree diagram, produce the full probability distribution for the random variable “number of late projects.” Show distribution results in the x, P(x)
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