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mathematics
statistics
Statistics For Management And Economics Abbreviated 10th Edition Gerald Keller - Solutions
Refer to Exercise.a. Determine P(A1∣B1).b. Determine P(A2∣B1).c. Did your answers to parts (a) and (b) sum to 1? Is this a coincidence? Explain.
Refer to Exercise 6.17. Calculate the following probabilities.a. P(A1∣B2)b. P(B2∣A1)c. Did you expect the answers to parts (a) and (b) to be reciprocals? In other words, did you expect that P(A1∣B2) = 1/P(B2∣A1)? Why is this impossible (unless both probabilities are 1)?
Refer to Exercise 6.17. Compute the following.a. P(A1 or B1)b. P(A1 or B2)c. P(A1 or A2)
Suppose that you have been given the following joint probabilities. Are the events independent?Explain.
Determine whether the events are independent from the following jointprobabilities.
Suppose we have the following joint probabilities.Compute the marginalprobabilities.
Refer to Exercise 6.24.a. Compute P(A2∣B2).b. Compute P(B2∣A2).c. Compute P(B1∣A2).
Refer to Exercise 6.24.a. Compute P(A1 or A2).b. Compute P(A2 or B2).c. Compute P(A3 or B1)
A department store analyzed its most recent sales and determined the relationship between the way the customer paid for the item and the price category of the item. The joint probabilities in the following table were calculated.a. What proportion of purchases was paid by debit card?b. Find the
The method of instruction in college and university applied statistics courses are changing. Historically, most courses were taught with an emphasis on manual calculation. The alternative is to employ a computer and a software package to perform the calculations. An analysis of applied statistics
Many critics of television claim that there is too much violence and that it has a negative effect on society. There may also be a negative effect on advertisers. To examine this issue, researchers developed two versions of a cops-and-robbers made-for-television movie. One version depicted several
Is there a relationship between the male hormone testosterone and criminal behavior? To answer this question, medical researchers measured the testosterone level of penitentiary inmates and recorded whether they were convicted of murder. After analyzing the results, the researchers produced the
Violent crime in many American schools is an unfortunate fact of life. An analysis of schools and violent crime yielded the table of joint probabilities shown next.If one school is randomly selected find the following probabilities.a. Probability of at least one incident of violent crime during the
Refer to Exercise 6.39. A similar analysis produced these joint probabilities.a. What is the probability that a school with an enrollment of less than 300 had at least one violent crime during the year?b. What is the probability that a school that has at least one violent crime had an enrollment of
A retail outlet wanted to know whether its weekly advertisement in the daily newspaper works. To acquire this critical information, the store manager surveyed the people who entered the store and determined whether each individual saw the ad and whether a purchase was made. From
A financial analyst has determined that there is a 22% probability that a mutual fund will outperform the market over a 1-year period provided that it outperformed the market the previous year. If only 15% of mutual funds outperform the market during any year, what is the probability that a mutual
An investor believes that on a day when the Dow Jones Industrial Average (DJIA) increases, the probability that the NASDAQ also increases is 77%. If the investor believes that there is a 60% probability that the DJIA will increase tomorrow, what is the probability that the NASDAQ will increase as
According to TNS Intersearch, 69% of wireless web users use it primarily for receiving and sending e-mail. Suppose that three wireless web users are selected at random. What is the probability that all of them use it primarily for e-mail?
Refer to Exercise 6.47. Determine P(A0B).
The U.S. National Highway Traffic Safety Administration gathers data concerning the causes of highway crashes where at least one fatality has occurred. The following probabilities were determined from the 1998 annual study (BAC is blood-alcohol content).P(BAC = 0 0 Crash with fatality) = .616P(BAC
Refer to Exercise 6.62. A randomly selected candidate who took a CFA exam tells you that he has passed the exam. What is the probability that he took the CFA I exam?
The following table lists the joint probabilities of achieving grades of A and not achieving A’s in two MBA courses.a. What is the probability that a student achieves a grade of A in marketing?b. What is the probability that a student achieves a grade of A in marketing, given that he or she
Laser surgery to fix shortsightedness is becoming more popular. However, for some people, a second procedure is necessary. The following table lists the joint probabilities of needing a second procedure and whether the patient has a corrective lens with a factor (diopter) of minus 8 or less.a. Find
Refer to Exercise 6.89. Suppose that you are told that the drug is effective. What is the probability that the drug taker is a man?
In a four-cylinder engine there are four spark plugs. If any one of them malfunctions, the car will idle roughly and power will be lost. Suppose that for a certain brand of spark plugs the probability that a spark plug will function properly after 5,000 miles is .90. Assuming that the spark plugs
The owner of an appliance store is interested in the relationship between the price at which an item is sold (regular or sale price) and the customer’s decision on whether to purchase an extended warranty. After analyzing her records, she produced the following joint probabilities.a. What is
A union’s executive conducted a survey of its members to determine what the membership felt were the important issues to be resolved during upcoming negotiations with management. The results indicate that 74% of members felt that job security was an important issue, whereas 65% identified pension
In a class on probability, a statistics professor flips two balanced coins. Both fall to the floor and roll under his desk. A student in the first row informs the professor that he can see both coins. He reports that at least one of them shows tails. What is the probability that the other coin is
The sample space of the toss of a fair die is S = {1, 2, 3, 4, 5, 6}If the die is balanced each simple event has the same probability. Find the probability of the following events.a. An even numberb. A number less than or equal to 4c. A number greater than or equal to 5
Refer to Exercise 6.6. Employing the subjective approach a political scientist has assigned the following probabilities:P(Adams wins) = .42P(Brown wins) = .09P(Collins wins) = .27P(Dalton wins) = .22Determine the probabilities of the following events.a. Adams loses.b. Either Brown or Dalton wins.c.
Discrimination in the workplace is illegal, and companies that discriminate are often sued. The female instructors at a large university recently lodged a complaint about the most recent round of promotions from assistant professor to associate professor. An analysis of the relationship between
The following table lists the probabilities of unemployed females and males and their educational attainment.a. If one unemployed person is selected at random, what is the probability that he or she did not finish high school?b. If an unemployed female is selected at random, what is the probability
The costs of medical care in North America are increasing faster than inflation, and with the baby boom generation soon to need health care, it becomes imperative that countries find ways to reduce both costs and demand. The following table lists the joint probabilities associated with smoking and
A restaurant chain routinely surveys its customers. Among other questions, the survey asks each customer whether he or she would return and to rate the quality of food. Summarizing hundreds of thousands of questionnaires produced this table of joint probabilities.a. What proportion of customers say
To determine whether drinking alcoholic beverages has an effect on the bacteria that cause ulcers, researchers developed the following table of joint probabilities.a. What proportion of people have ulcers?b. What is the probability that a teetotaler (no alcoholic beverages) develops an ulcer?c.
An analysis of fired or laid-off workers, their age, and the reasons for their departure produced the following table of joint probabilities.a. What is the probability that a 25- to 54-year-old employee was laid off or fired because of insufficient work?b. What proportion of laid-off or fired
The issue of health care coverage in the United States is becoming a critical issue in American politics. A large-scale study was undertaken to determine who is and is not covered. From this study, the following table of joint probabilities was produced.If one person is selected at random, find the
A firm has classified its customers in two ways: (1) according to whether the account is overdue and (2) whether the account is new (less than 12 months) or old. An analysis of the firm’s records provided the input for the following table of joint probabilities.One account is
How are the size of a firm (measured in terms of the number of employees) and the type of firm related? To help answer the question, an analyst referred to the U.S. Census and developed the following table of joint probabilities.If one firm is selected at random, find the probability of the
Credit scorecards are used by financial institutions to help decide to whom loans should be granted. An analysis of the records of one bank produced the following probabilities.a. What proportion of loans are fully repaid?b. What proportion of loans given to scorers of less than 400 fully
To gauge the relationship between education and unemployment, an economist turned to the U.S. Census from which the following table of joint probabilities was produced:a. What is the probability that a high school graduate is unemployed?b. Determine the probability that a randomly selected
The decision about where to build a new plant is a major one for most companies. One of the factors that is often considered is the education level of the location’s residents. Census information may be useful in this regard. After analyzing a recent census, a company produced the following
Given the following probabilities, compute all joint probabilities.P(A) = .9P(B0A) = .4 P(AC) = .1P(B0AC) = .7
Determine all joint probabilities from the following.P(A) = .8P(B0A) = .4 P(AC) = .2P(B0AC) = .7
Draw a probability tree to compute the joint probabilities from the following probabilities.P(A) = .5P(B0A) = .4 P(AC) = .2P(B0AC) = .7
Given the following probabilities, draw a probability tree to compute the joint probabilities.P(A) = .8P(B0A ) = .3 P(AC) = .2P(B0AC) = .3
Given the following probabilities, find the joint probability P(A and B).P(A) = .7 P(B0A) = .3
Approximately 10% of people are left-handed. If two people are selected at random, what is the probability of the following events?a. Both are right-handed.b. Both are left-handed.c. One is right-handed and the other is left-handed.d. At least one is right-handed.
Refer to Exercise. Suppose that three people are selected at random.a. Draw a probability tree to depict the experiment.b. If we use the notation RRR to describe the selection of three right-handed people, what are the descriptions of the remaining seven events? (Use L for left-hander.)c. How many
Suppose there are 100 students in your accounting class, 10 of whom are left-handed. Two students are selected at random.a. Draw a probability tree and insert the probabilities for each branch. What is the probability of the following events?b. Both are right-handed.c. Both are left-handed.d. One
Refer to Exercise 6.54. Suppose that three people are selected at random.a. Draw a probability tree and insert the probabilities of each branch.b. What is the probability of no right-handers, one right-hander, two right-handers, and three right-handers?
An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 40% probability of winning the first contract. If they win the first contract, the probability of winning the second is 70%. However, if they lose the first
A telemarketer calls people and tries to sell them a subscription to a daily newspaper. On 20% of her calls, there is no answer or the line is busy. She sells subscriptions to 5% of the remaining calls. For what proportion of calls does she make a sale?
A foreman for an injection-molding firm admits that on 10% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability from 2% to 20% that a defective molding will be produced during the early morning run. What proportion
A study undertaken by the Miami-Dade Supervisor of Elections in 2002 revealed that 44% of registered voters are Democrats, 37% are Republicans, and 19% are others. If two registered voters are selected at random, what is the probability that both of them have the same party affiliation?
In early 2001, the U.S. Census Bureau started releasing the results of the 2000 census. Among many other pieces of information, the bureau recorded the race or ethnicity of the residents of every county in every state. From these results, the bureau calculated a “diversity index” that measures
A survey of middle-aged men reveals that 28% of them are balding at the crown of their heads. Moreover, it is known that such men have an 18% probability of suffering a heart attack in the next 10 years. Men who are not balding in this way have an 11% probability of a heart attack. Find the
The chartered financial analyst (CFA) is a designation earned after a candidate has taken three annual exams (CFA I, II, and III). The exams are taken in early June. Candidates who pass an exam are eligible to take the exam for the next level in the following year. The pass rates for levels I, II,
The Nickels restaurant chain regularly conducts surveys of its customers. Respondents are asked to assess food quality, service, and price. The responses areExcellent Good FairSurveyed customers are also asked whether they would come back. After analyzing the responses, an expert in probability
Researchers at the University Of Pennsylvania School Of Medicine have determined that children under 2 years old who sleep with the lights on have a 36% chance of becoming myopic before they are 16. Children who sleep in darkness have a 21% probability of becoming myopic. A survey indicates that
All printed circuit boards (PCBs) that are manufactured at a certain plant are inspected. An analysis of the company’s records indicates that 22% of all PCBs are flawed in some way. Of those that are flawed, 84% are reparable and the rest must be discarded. If a newly produced PCB is randomly
The controls of an airplane have several backup systems or redundancies so that if one fails the plane will continue to operate. Suppose that the mechanism that controls the flaps has two backups. If the probability that the main control fails is .0001 and the probability that each backup will fail
A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 25%. She also believes that if the economy encounters a recession, the probability that her mutual fund will increase in value is 20%. If there is no recession, the probability
Refer to Exercise 6.48. Find the following.a. P(A0B)b. P(AC0B)c. P(A0BC )d. P(AC0BC )
Refer to Example 6.9. An MBA applicant believes that the probability of scoring more than 650 on the GMAT without the preparatory course is .95. What is the probability of attaining that level after taking the preparatory course?
Bad gums may mean a bad heart. Researchers discovered that 85% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums. Only 29% of healthy people have this disease. Suppose that in a certain community heart attacks are quite rare, occurring with only 10%
Refer to Exercise 6.77. If 40% of the people in a community will have a heart attack, what is the probability that a person with periodontal disease will have a heart attack?
Data from the Office on Smoking and Health, Centers for Disease Control and Prevention, indicate that 40% of adults who did not finish high school, 34% of high school graduates, 24% of adults who completed some college, and 14% of college graduates smoke. Suppose that one individual is selected at
Three airlines serve a small town in Ohio. Airline A has 50% of all the scheduled flights, airline B has 30%, and airline C has the remaining 20%. Their on-time rates are 80%, 65%, and 40%, respectively. A plane has just left on time. What is the probability that it was airline A?
Your favorite team is in the final playoffs. You have assigned a probability of 60% that it will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the
Transplant operations have become routine. One common transplant operation is for kidneys. The most dangerous aspect of the procedure is the possibility that the body may reject the new organ. Several new drugs are available for such circum-stances, and the earlier the drug is administered, the
The Rapid Test is used to determine whether someone has HIV (the virus that causes AIDS). The false-positive and false-negative rates are .027 and .080, respectively. A physician has just received the Rapid Test report that his patient tested positive. Before receiving the result, the physician
What are the sensitivity, specificity, positive predictive value, and negative predictive value in the previous exercise?
The Pap smear is the standard test for cervical cancer. The false-positive rate is .636; the false-negative rate is .180. Family history and age are factors that must be considered when assigning a probability of cervical cancer. Suppose that, after obtaining a medical history, a physician
A construction company has bid on two contracts. The probability of winning contract A is .3. If the company wins contract A, then the probability of winning contract B is .4. If the company loses contract A, then the probability of winning contract B decreases to .2. Find the probability of the
The effect of an antidepressant drug varies from person to person. Suppose that the drug is effective on 80% of women and 65% of men. It is known that 66% of the people who take the drug are women. What is the probability that the drug is effective?
A telemarketer sells magazine subscriptions over the telephone. The probability of a busy signal or no answer is 65%. If the telemarketer does make contact, the probability of 0, 1, 2, or 3 magazine subscriptions is .5, .25, .20, and .05, respectively. Find the probability that in one call she
A statistics professor believes that there is a relationship between the number of missed classes and the grade on his midterm test. After examining his records, he produced the following table of joint probabilities.a. What is the pass rate on the midterm test?b. What proportion of students who
In Canada, criminals are entitled to parole after serving only one-third of their sentence. Virtually all prisoners, with several exceptions including murderers, are released after serving two-thirds of their sentence. The government has proposed a new law that would create a special category of
Casino Windsor conducts surveys to determine the opinions of its customers. Among other questions, respondents are asked to give their opinion about “Your overall impression of Casino Windsor.†The responses areExcellent Good Average PoorIn addition, the gender of the respondent is
A customer-service supervisor regularly conducts a survey of customer satisfaction. The results of the latest survey indicate that 8% of customers were not satisfied with the service they received at their last visit to the store. Of those who are not satisfied, only 22% return to the store within
How does level of affluence affect health care? To address one dimension of the problem, a group of heart attack victims was selected. Each was categorized as a low-, medium-, or high-income earner. Each was also categorized as having survived or died. A demographer notes that in our society 21%
A statistics professor and his wife are planning to take a 2-week vacation in Hawaii, but they can’t decide whether to spend 1 week on each of the islands of Maui and Oahu, 2 weeks on Maui, or 2 weeks on Oahu. Placing their faith in random chance, they insert two Maui brochures in one envelope,
Researchers have developed statistical models based on financial ratios that predict whether a company will go bankrupt over the next 12 months. In a test of one such model, the model correctly predicted the bankruptcy of 85% of firms that did in fact fail, and it correctly predicted nonbankruptcy
A number of years ago, there was a popular television game show called Let’s Make a Deal. The host, Monty Hall, would randomly select contestants from the audience and, as the title suggests, he would make deals for prizes. Contestants would be given relatively modest prizes and would then be
Suppose that there are two people in a room. The probability that they share the same birthday (date, not necessarily year) is 1/365, and the probability that they have different birthdays is 364/365. To illustrate, suppose that you’re in a room with one other person and that your birthday is
No sport generates as many statistics as baseball. Reporters, managers, and fans argue and discuss strategies on the basis of these statistics. An article in Chance (“A Statistician Reads the Sports Page,” Hal S. Stern, Vol. 1, winter 1997) offers baseball lovers another opportunity to
Refer to Case 6.2. Another baseball strategy is to attempt to steal second base. Historically the probability of a successful steal of second base is approximately 68%. The probability of being thrown out is 32%. (We’ll ignore the relatively rare event wherein the catcher throws the ball into
Pregnant women are screened for a birth defect called Down syndrome. Down syndrome babies are mentally and physically challenged. Some mothers choose to abort the fetus when they are certain that their baby will be born with the syndrome. The most common screening is maternal serum screening, a
The number of accidents that occur on a busy stretch of highway is a random variable.a. What are the possible values of this random variable?b. Are the values countable? Explain.c. Is there a finite number of values? Explain.d. Is the random variable discrete or continuous? Explain.
The distance a car travels on a tank of gasoline is a random variable.a. What are the possible values of this random variable?b. Are the values countable? Explain.c. Is there a finite number of values? Explain.d. Is the random variable discrete or continuous? Explain.
The amount of money students earn on their summer jobs is a random variable.a. What are the possible values of this random variable?b. Are the values countable? Explain.c. Is there a finite number of values? Explain.d. Is the random variable discrete or continuous? Explain.
The mark on a statistics exam that consists of 100 multiple-choice questions is a random variable.a. What are the possible values of this random variable?b. Are the values countable? Explain.c. Is there a finite number of values? Explain.d. Is the random variable discrete or continuous? Explain.
Determine whether each of the following is a valid probabilitydistribution.
The random variable X has the following probability distribution.Find the following probabilities.a. P(X > 0)b. P(X ≥ 1)c. P(X ≥ 2)d. P(2 ≤ X ≤5)
An Internet pharmacy advertises that it will deliver the over-the-counter products that customers purchase in 3 to 6 days. The manager of the company wanted to be more precise in its advertising. Accordingly, she recorded the number of days it took to deliver to customers. From the data, the
The probability that a university graduate will be offered no jobs within a month of graduation is estimated to be 5%. The probability of receiving one, two, and three job offers has similarly been estimated to be 43%, 31%, and 21%, respectively. Determine the following probabilities.a. A graduate
Refer to Exercise 7.14. Find the following probabilities.a. No headsb. One headc. Two headsd. At least one head
The number of pizzas delivered to university students each month is a random variable with the following probability distribution.a. Find the probability that a student has received delivery of two or more pizzas this month.b. Determine the mean and variance of the number of pizzas delivered to
Refer to Exercise 7.20. If the pizzeria makes a profit of $3 per pizza, determine the mean and variance of the profits per student.
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