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Statistics For Business And Economics 8th Edition Paul Newbold, William Carlson, Betty Thorne - Solutions

For each of the following, indicate if a discrete or a continuous random variable provides the best definition: a. The number of cars that arrive each day for repair in a two-person repair shop b. The number of cars produced annually by General Motors c. Total daily e-commerce sales in dollars d.
For a binomial probability distribution with P = 0.5 and n = 12, find the probability that the number of successes is equal to 7 and the probability that the number of successes is fewer than 6.
For a Bernoulli random variable with probability of success P = 0.5, compute the mean and variance.
For a binomial probability distribution with P = 0.3 and n = 14, find the probability that the number of successes is equal to 7 and the probability that the number of successes is fewer than 6.
For a binomial probability distribution with P = 0.4 and n = 20, find the probability that the number of successes is equal to 9 and the probability that the number of successes is fewer than 7.
For a binomial probability distribution with P = 0.7 and n = 18, find the probability that the number of successes is equal to 12 and the probability that the number of successes is fewer than 6.
A production manager knows that 5% of components produced by a particular manufacturing process have some defect. Six of these components, whose characteristics can be assumed to be independent of each other, are examined. a. What is the probability that none of these components has a defect? b.
A state senator believes that 25% of all senators on the Finance Committee will strongly support the tax proposal she wishes to advance. Suppose that this belief is correct and that 5 senators are approached at random.a. What is the probability that at least 1 of the 5 will strongly support the
A public interest group hires students to solicit donations by telephone. After a brief training period students make calls to potential donors and are paid on a commission basis. Experience indicates that early on, these students tend to have only modest success and that 70% of them give up their
Suppose that the probability is 0.2 that the value of the U.S. dollar will rise against the Chinese yuan over any given week and that the outcome in one week is independent of that in any other week. What is the probability that the value of the U.S. dollar will rise against the Chinese yuan at
A company installs new central-heating furnaces and has found that for 15% of all installations, a return visit is needed to make some modifications. Six installations were made in a particular week. Assume independence of outcomes for these installations.a. What is the probability that a return
The Minnesota Twins are to play a series of 5 games in Boston against the Red Sox. For any one game it is estimated that the probability of a Twins' win is 0.5.The outcomes of the 5 games are independent of one another.a. What is the probability that the Twins will win all 5 games?b. What is the
A small commuter airline flies planes that can seat up to 8 passengers. The airline has determined that the probability that a ticketed passenger will not show up for a flight is 0.2. For each flight the airline sells tickets to the first 10 people placing orders. The probability distribution for
Following a touchdown, a college football coach has the option to elect to attempt a two-point conversion; that is, two additional points are scored if the attempt is successful and none, if it is unsuccessful. The coach believes that the probability is 0.35 that his team will be successful in any
A notebook computer dealer mounts a new promotional campaign. Purchasers of new computers may, if dissatisfied for any reason, return them within 2 days of purchase and receive a full refund. The cost to the dealer of such a refund is $100. The dealer estimates that 15% of all purchasers will,
A family of mutual funds maintains a service that allows clients to switch money among accounts through a telephone call. It was estimated that 3.2% of callers either get a busy signal or are kept on hold so long that they may hang up. Fund management assesses any failure of this sort as a $10
We have seen that, for a binomial distribution with n trials, each with probability of success P, the mean is as follows:μX = E[X] = nPVerify this result for the data of Example 4.7 by calculating the mean directly fromμX = ΣxP(x)showing that for the binomial distribution, the two formulas
A campus finance officer finds that, for all parking tickets issued, fines are paid for 78% of the tickets. The fine is $2. In the most recent week, 620 parking tickets have been issued.a. Find the mean and standard deviation of the number of these tickets for which the fines will be paid.b. Find
A company receives a very large shipment of components. A random sample of 16 of these components will be checked, and the shipment will be accepted if fewer than 2 of these components are defective. What is the probability of accepting a shipment containing each number of defectives? a. 5% b.
The following two acceptance rules are being considered for determining whether to take delivery of a large shipment of components: • A random sample of 10 components is checked, and the shipment is accepted only if none of them is defective. • A random sample of 20 components is checked, and
List four examples of discrete random variables that could be observed in a new consulting business.
Determine the probability of exactly four successes for a random variable with a Poisson distribution with parameter λ = 2.4.
Determine the probability of more than 7 successes for a random variable with a Poisson distribution with parameter λ = 4.4.
Determine the probability of fewer than 6 successes for a random variable with a Poisson distribution with parameter λ = 3.4.
Determine the probability of fewer than or equal to 9 successes for a random variable with a Poisson distribution with parameter λ = 8.0.
Customers arrive at a busy checkout counter at an average rate of 3 per minute. If the distribution of arrivals is Poisson, find the probability that in any given minute there will be 2 or fewer arrivals.
The number of accidents in a production facility has a Poisson distribution with a mean of 2.6 per month.a. For a given month what is the probability there will be fewer than 2 accidents?b. For a given month what is the probability there will be more than 3 accidents?
A customer service center in India receives, on average, 4.2 telephone calls per minute. If the distribution of calls is Poisson, what is the probability of receiving at least 3 calls during a particular minute?
Records indicate that, on average, 3.2 breakdowns per day occur on an urban highway during the morning rush hour. Assume that the distribution is Poisson.a. Find the probability that on any given day there will be fewer than 2 breakdowns on this highway during the morning rush hour.b. Find the
Blue Cross Health Insurance reported that 4.5% of claims forms submitted for payment after a complex surgical procedure contain errors. If 100 of these forms are chosen at random, what is the probability that fewer than 3 of them contain errors? Use the Poisson approximation to the binomial
A corporation has 250 personal computers. The probability that any 1 of them will require repair in a given week is 0.01. Find the probability that fewer than 4 of the personal computers will require repair in a particular week. Use the Poisson approximation to the binomial distribution.
An insurance company holds fraud insurance policies on 6,000 firms. In any given year the probability that any single policy will result in a claim is 0.001. Find the probability that at least 3 claims are made in a given year. Use the Poisson approximation to the binomial distribution.
A state has a law requiring motorists to carry insurance. It was estimated that, despite this law, 6.0% of all motorists in the state are uninsured. A random sample of 100 motorists was taken. Use the Poisson approximation to the binomial distribution to estimate the probability that at least 3 of
A new warehouse is being designed and a decision concerning the number of loading docks is required. There are two models based on truckarrival assumptions for the use of this warehouse, given that loading a truck requires 1 hour. Using the first model, we assume that the warehouse could be
Compute the probability of 7 successes in a random sample of size n = 14 obtained from a population of size N = 30 that contains 15 successes.
Compute the probability of 9 successes in a random sample of size n = 20 obtained from a population of size N = 80 that contains 42 successes.
Compute the probability of 3 successes in a random sample of size n = 5 obtained from a population of size N = 40 that contains 25 successes.
Compute the probability of 8 successes in a random sample of size n = 15 obtained from a population of size N = 100 that contains 50 successes.
A company receives a shipment of 16 items. A random sample of 4 items is selected, and the shipment is rejected if any of these items proves to be defective. a. What is the probability of accepting a shipment containing 4 defective items? b. What is the probability of accepting a shipment
A committee of 8 members is to be formed from a group of 8 men and 8 women. If the choice of committee members is made randomly, what is the probability that precisely half of these members will be women?
A bond analyst was given a list of 12 corporate bonds. From that list she selected 3 whose ratings she felt were in danger of being downgraded in the next year. In actuality, a total of 4 of the 12 bonds on the list had their ratings downgraded in the next year. Suppose that the analyst had simply
A bank executive is presented with loan applications from 10 people. The profiles of the applicants are similar, except that 5 are minorities and 5 are not minorities.In the end the executive approves 6 of the applications.If these 6 approvals are chosen at random from the 10 applications, what is
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = X + Y.
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = 2X + Y.
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = 3X + 4Y.
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = 2X - 4Y.
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = 10X - 8Y.
A researcher suspected that the number of between meal snacks eaten by students in a day during final examinations might depend on the number of tests a student had to take on that day. The accompanying table shows joint probabilities, estimated from a survey.a. Find the probability distribution of
A real estate agent is interested in the relationship between the number of lines in a newspaper advertisement for an apartment and the volume of inquiries from potential renters. Let volume of inquiries be denoted by the random variable X, with the value 0 for little interest, 1 for moderate
The accompanying table shows, for credit-card holders with one to three cards, the joint probabilities for number of cards owned (X) and number of credit purchases made in a week (Y).a. For a randomly chosen person from this group, what is the probability distribution for number of purchases made
A market researcher wants to determine whether a new model of a personal computer that had been advertised on a late-night talk show had achieved more brand-name recognition among people who watched the show regularly than among people who did not.After conducting a survey, it was found that 15% of
A college bookseller makes calls at the offices of professors and forms the impression that professors are more likely to be away from their offices on Friday than any other working day. A review of the records of calls, 1/5 of which are on Fridays, indicates that for 16% of Friday calls, the
A restaurant manager receives occasional complaints about the quality of both the food and the service. The marginal probability distributions for the number of weekly complaints in each category are shown in the accompanying table. If complaints about food and service are independent of each
Refer to the information in the previous exercise. Find the mean and standard deviation of the total number of complaints received in a week. Having reached this point, you are concerned that the numbers of food and service complaints may not be independent of each other. However, you have no
A company has 5 representatives covering large territories and 10 representatives covering smaller territories. The probability distributions for the numbers of orders received by each of these types of representatives in a day are shown in the accompanying table. Assuming that the number of orders
As an investment advisor, you tell a client that an investment in a mutual fund has (over the next year) a higher expected return than an investment in the money market. The client then asks the following questions: a. Does that imply that the mutual fund will certainly yield a higher return than
A contractor estimates the probabilities for the number of days required to complete a certain type of construction project as follows:a. What is the probability that a randomly chosen project will take less than 3 days to complete?b. Find the expected time to complete a project.c. Find the
A car salesperson estimates the following probabilities for the number of cars that she will sell in the next week:a. Find the expected number of cars that will be sold in the week.b. Find the standard deviation of the number of cars that will be sold in the week.c. The salesperson receives a
A multiple-choice test has nine questions. For each question there are four possible answers from which to select. One point is awarded for each correct answer, and points are not subtracted for incorrect answers.The instructor awards a bonus point if the students spell their name correctly. A
Develop realistic examples of pairs of random variables for which you would expect to find the following: a. Positive covariance b. Negative covariance c. Zero covariance
What is the probability distribution function of the number of heads when a fair coin is tossed once?
A long-distance taxi service owns four vehicles. These are of different ages and have different repair records. The probabilities that, on any given day, each vehicle will be available for use are 0.95, 0.90, 0.90, and 0.80.Whether one vehicle is available is independent of whether any other
Students in a college were classified according to years in school (X) and number of visits to a museum in the last year (Y = 0 for no visits, 1 for one visit, 2 for more than one visit). The joint probabilities in the accompanying table were estimated for these random variables.a. Find the
A basketball team's star 3-point shooter takes six 3-point shots in a game. Historically, she makes 40% of all 3-point shots taken in a game. State at the outset what assumptions you have made.a. Find the probability that she will make at least two shots.b. Find the probability that she will make
It is estimated that 55% of the freshmen entering a particular college will graduate from that college in four years.a. For a random sample of 5 entering freshmen, what is the probability that exactly 3 will graduate in four years?b. For a random sample of 5 entering freshmen, what is the
The World Series of baseball is to be played by team A and team B. The first team to win four games wins the series. Suppose that team A is the better team, in the sense that the probability is 0.6 that team A will win any specific game. Assume also that the result of any game is independent of
Using detailed cash-flow information, a financial analyst claims to be able to spot companies that are likely candidates for bankruptcy. The analyst is presented with information on the past records of 15 companies and told that, in fact, 5 of these have failed. He selects as candidates for failure
A team of 5 analysts is about to examine the earnings prospects of 20 corporations. Each of the 5 analysts will study 4 of the corporations. These analysts are not equally competent. In fact, one of them is a star, having an excellent record of anticipating changing trends. Ideally, management
On average, 2.4 customers per minute arrive at an airline check-in desk during the peak period. Assume that the distribution of arrivals is Poisson. a. What is the probability that there will be no arrivals in a minute? b. What is the probability that there will be more than three arrivals in a
A company has two assembly lines, each of which stalls an average of 2.4 times per week according to a Poisson distribution. Assume that the performances of these assembly lines are independent of one another.What is the probability that at least one line stalls at least once in any given week?
The profit for a production process is equal to $1,000 minus two times the number of units produced. The mean and variance for the number of units produced are 50 and 90, respectively. Find the mean and variance of the profit.
Flybynite Airlines has a regularly scheduled flight from Minneapolis to Frankfurt every weekday evening at 6:30. Based on a complex relationship between Flybynite and Bigrain Airlines, a local line that flys to a number of small towns, 100 seats are reserved for passengers from two of Bigrain's
Shirley Johnson is developing a new mutual fund portfolio and in the process has asked you to develop the mean and variance for the stock price that consists of 10 shares of stocks from each of the following firms: Alcoa Inc., Reliant Energy, and Sea Container.Using the data file Stock Price File,
Zafer Toprak is a developing a new mutual fund portfolio and in the process has asked you to develop the mean and variance for the stock price that consists of 10 shares of stocks from Alcoa Inc., 20 shares from AB Volvo, 10 shares from TCF Financial, and 20 shares from Pentair Inc. Using the data
Charles Thorson has asked you to determine the mean and variance for a portfolio that consists of 100 shares of stock from each of the following firms: 3M Company, Alcoa, Inc., Intel Corporation, Potlatch Corp., General Motors, and Sea Containers. Using the data file Stock Price File, compute the
You have been asked to evaluate the monthly stock price growth for a portfolio which contains the following firms: 3M Company, Alcoa, Inc., Intel Corporation, Potlatch Corp., General Motors, and Sea Containers. The fraction of the portfolio dollar value for each firm will be the same. Using the
Deep Water Financial of Duluth, Minnesota, has asked you to evaluate the stock price growth for a portfolio containing the following firms: General Motors, International Business Machines, Potlatch, Inc., Sea Containers, Ltd., and Tata Communications. Compute the means, variances, and
Consider a portfolio that contains stocks from the following firms: AB Volvo, Pentair, Inc., Reliant Energy, Inc., TCF Financial, 3M Company, and Restoration Hardware. Data for these stocks for a 60-month period (May 2003-April 2008) are contained in the data file Return on Stock Price 60 month.
The profit for a production process is equal to $2,000 minus two times the number of units produced. The mean and variance for the number of units produced are 500 and 900, respectively. Find the mean and variance of the profit.
The profit for a production process is equal to $6,000 minus three times the number of units produced. The mean and variance for the number of units produced are 1,000 and 900, respectively. Find the mean and variance of the profit.
An author receives a contract from a publisher, according to which she is to be paid a fixed sum of $10,000 plus $1.50 for each copy of her book sold. Her uncertainty about total sales of the book can be represented by a random variable with a mean of 30,000 and a standard deviation of 8,000. Find
A contractor submits a bid on a project for which more research and development work needs to be done. It is estimated that the total cost of satisfying the project specifications will be $20 million plus the cost of the further research and development work. The contractor views the cost of this
A charitable organization solicits donations by telephone. Employees are paid $60 plus 20% of the money their calls generate each week. The amount of money generated in a week can be viewed as a random variable with a mean of $700 and a standard deviation of $130. Find the mean and standard
A salesperson receives an annual salary of $6,000 plus 8% of the value of the orders she takes. The annual value of these orders can be represented by a random variable with a mean of $600,000 and a standard deviation of $180,000. Find the mean and standard deviation of the salesperson's annual
Let the random variable Z follow a standard normal distribution. a. Find P(Z < 1.202. b. Find P(Z > 1.332. c. Find P(Z > – 1.702. d. Find P(Z > – 1.002. e. Find P(1.20 < Z < 1.332. f. Find P(–1.70 < Z < 1.202. g. Find P(–1.70 < Z < –1.002.
Let the random variable Z follow a standard normal distribution. a. The probability is 0.70 that Z is less than what number? b. The probability is 0.25 that Z is less than what number? c. The probability is 0.2 that Z is greater than what number? d. The probability is 0.6 that Z is greater than
Let the random variable X follow a normal distribution with m = 50 and s2 = 64.a. Find the probability that X is greater than 60.b. Find the probability that X is greater than 35 and less than 62.c. Find the probability that X is less than 55.d. The probability is 0.2 that X is greater than what
Let the random variable X follow a normal distribution with μ = 80 and σ2 = 100.a. Find the probability that X is greater than 60.b. Find the probability that X is greater than 72 and less than 82.c. Find the probability that X is less than 55.d. The probability is 0.1 that X is greater than what
Let the random variable X follow a normal distribution with μ = 0.2 and σ2 = 0.0025.a. Find the probability that X is greater than 0.4.b. Find the probability that X is greater than 0.15 and less than 0.28.c. Find the probability that X is less than 0.10.d. The probability is 0.2 that X is
It is known that amounts of money spent on clothing in a year by students on a particular campus follow a normal distribution with a mean of $380 and a standard deviation of $50.a. What is the probability that a randomly chosen student will spend less than $400 on clothing in a year?b. What is the
Anticipated consumer demand in a restaurant for free-range steaks next month can be modeled by a normal random variable with mean 1,200 pounds and standard deviation 100 pounds.a. What is the probability that demand will exceed 1,000 pounds?b. What is the probability that demand will be between
The tread life of Road Stone tires has a normal distribution with a mean of 35,000 miles and a standard deviation of 4,000 miles.a. What proportion of these tires has a tread life of more than 38,000 miles?b. What proportion of these tires has a tread life of less than 32,000 miles?c. What
An investment portfolio contains stocks of a large number of corporations. Over the last year the rates of return on these corporate stocks followed a normal distribution with mean 12.2% and standard deviation 7.2%.a. For what proportion of these corporations was the rate of return higher than
Southwest Co-op produces bags of fertilizer, and it is concerned about impurity content. It is believed that the weights of impurities per bag are normally distributed with a mean of 12.2 grams and a standard deviation of 2.8 grams. A bag is chosen at random.a. What is the probability that it
A contractor has concluded from his experience that the cost of building a luxury home is a normally distributed random variable with a mean of $500,000 and a standard deviation of $50,000.a. What is the probability that the cost of building a home will be between $460,000 and $540,000?b. The
A broadcasting executive is reviewing the prospects for a new television series. According to his judgment, the probability is 0.25 that the show will achieve a rating higher than 17.8, and the probability is 0.15 that it will achieve a rating higher than 19.2. If the executive's uncertainty about
The number of hits per day on the Web site of Professional Tool, Inc., is normally distributed with a mean of 700 and a standard deviation of 120.a. What proportion of days has more than 820 hits per day?b. What proportion of days has between 730 and 820 hits?c. Find the number of hits such that
I am considering two alternative investments. In both cases I am unsure about the percentage return but believe that my uncertainty can be represented by normal distributions with the means and standard deviations shown in the accompanying table. I want to make the investment that is more likely to
Tata Motors, Ltd., purchases computer process chips from two suppliers, and the company is concerned about the percentage of defective chips. A review of the records for each supplier indicates that the percentage defectives in consignments of chips follow normal distributions with the means and

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