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Data Analysis And Decision Making 4th Edition Christian Albright, Wayne Winston, Christopher Zappe - Solutions

Consumer demand for small, economical automobiles depends somewhat on recent trends in the average price of unleaded gasoline. For example, consider the information given in the file S04_26.xlsx on the distributions of average annual sales of the Honda Civic and the Toyota Prius in relation to the
Upon completing their respective homework assignments, marketing majors and accounting majors at a large state university enjoy hanging out at the local tavern in the evenings. The file S04_27.xlsx contains the distribution of number of hours spent by these students at the tavern in a typical week,
Let X and Y represent the number of Dell and HP laptop computers, respectively, sold per month from online sites. The file S04_28.xlsx contains the probabilities of various combinations of monthly sales volumes of these competitors.a. Find the marginal distributions of X and Y. Interpret your
The joint probability distribution of the weekly demand for two brands of diet soda is provided in the file S04_29.xlsx. In particular, let D1 and D2 represent the weekly demand (in hundreds of two-liter bottles) for brand 1 and brand 2, respectively, in a small town in central Indiana.a. Find the
A local pharmacy has two checkout stations available to its customers: a regular checkout station and an express checkout station. Customers with six or fewer items are assumed to join the express line. Let X and Y be the numbers of customers in the regular checkout line and the express checkout
Suppose that the manufacturer of a particular product assesses the joint distribution of price P per unit and demand D for its product in the coming quarter as provided in the file S04_31.xlsx.a. Find the expected price and the expected demand in the coming quarter.b. What is the probability that
The recent weekly trends of two particular stock prices can best be described by the joint probability distribution shown in the file S04_32.xlsx.a. What is the probability that the price of stock 1 will not increase in the coming week?b. What is the probability that the price of stock 2 will
Two service elevators are used in parallel by employees of a three-story hotel building. At any point in time when both elevators are stationary, let X1 and X2 be the floor numbers at which elevators 1 and 2, respectively, are currently located. The joint probability distribution of X1 and X2 is
The file S04_34.xlsx shows the conditional distribution of the daily number of accidents at a given intersection during the winter months, X2, given the amount of snowfall (in inches) for the day, X1. The marginal distribution of X1 is provided in the bottom row of the table.a. Are X1 and X2
A sporting goods store sells two competing brands of exercise bicycles. Let X1 and X2 be the numbers of the two brands sold on a typical day at this store. Based on available historical data, the conditional probability distribution of X1 given X2 is assessed as shown in the file S04_35.xlsx. The
The file P04_28.xlsx contains the probabilities of various combinations of monthly sales volumes of Dell (X) and HP (Y) laptop computers from online sites. Are the monthly sales of these two competitors independent of each other? Explain your answer.
Let D1 and D2 represent the weekly demand (in hundreds of two-liter bottles) for brand 1 diet soda and brand 2 diet soda, respectively, in a small central Indiana town. The joint probability distribution of the weekly demand for these two brands of diet soda is provided in the file S04_29.xlsx. Are
The file S04_31.xlsx contains the joint probability distribution of price P per unit and demand D for a particular product in the coming quarter.a. Are P and D independent random variables? Explain your answer.b. If P and D are not independent random variables, which joint probabilities result in
You know that in one year you are going to buy a house. The annual interest rate for fixed-rate 30-year mortgages is currently 6.00%, and the price of the type of house you are considering is $120,000. However, things may change. Using your knowledge of the economy (and a crystal ball), you
A typical consumer buys a random number (X) of polo shirts when he shops at a men’s clothing store. The distribution of X is given by the following probability distribution: P(X = 0) = 0.30, P(X = 1) = 0.30, P(X = 2) = 0.20, P(X = 3) = 0.10, and P(X = 4) = 0.10.a. Find the mean and standard
Based on past experience, the number of customers who arrive at a local gasoline station during the noon hour to purchase fuel is best described by the probability distribution given in the file S04_41.xlsx. a. Find the mean, variance, and standard deviation of this random variable.b. Find the
Let X be the number of defective items found by a quality inspector in a random batch of 15 items from a particular manufacturing process. The probability distribution of X is provided in the file S04_18.xlsx. This firm earns $500 profit from the sale of each acceptable item in a given batch. In
The probability distribution for the number of job applications processed at a small employment agency during a typical week is given in the file S04_43.xlsx. a. Assuming that it takes the agency’s administrative assistant two hours to process a submitted job application, on average how many
Consider a financial services salesperson whose annual salary consists of both a fixed portion of $25,000 and a variable portion that is a commission based on her sales performance. In particular, she estimates that her monthly sales commission can be represented by a random variable with mean
A film-processing shop charges its customers 18 cents per print, but customers may refuse to accept one or more of the prints for various reasons. Assume that this shop does not charge its customers for refused prints. The number of prints refused per 24-print roll is a random variable with mean
Suppose the monthly demand for Thomson televisions has a mean of 40,000 and a standard deviation of 20,000. Find the mean and standard deviation of the annual demand for Thomson TVs. Assume that demands in different months are probabilistically independent.
Suppose there are five stocks available for investment and each has an annual mean return of 10% and a standard deviation of 4%. Assume the returns on the stocks are independent random variables.a. If you invest 20% of your money in each stock, find the mean and standard deviation of the annual
An investor puts $10,000 into each of four stocks, labeled A, B, C, and D. The file S04_48.xlsx contains the means and standard deviations of the annual returns of these four stocks. Assuming that the returns of these four stocks are independent, find the mean and standard deviation of the total
Consider again the investment problem described in the previous problem. Now, assume that the returns of the four stocks are no longer independent. Specifically, the correlations between all pairs of stock returns are given in the file S04_49.xlsx.a. Find the mean and standard deviation of the
A supermarket chain operates five stores of varying sizes in Bloomington, Indiana. Profits (represented as a percentage of sales volume) earned by these five stores are 2.75%, 3%, 3.5%, 4.25%, and 5%, respectively. The means and standard deviations of the daily sales volumes at these five stores
A manufacturing company constructs a 1-cm assembly by snapping together four parts that average 0.25 cm in length. The company would like the standard deviation of the length of the assembly to be 0.01 cm. Its engineer, Peter Purdue, believes that the assembly will meet the desired level of
The weekly demand function for one of a given firm’s products can be represented by q = 200 - 5p, where q is the number of units purchased (in hundreds) at price p (in dollars). Assume that the price of the product will be an integer value from $10 to $15, with probabilities 0.10, 0.15, 0.25,
A retailer purchases a batch of 1000 fluorescent light bulbs from a wholesaler at a cost of $2 per bulb. The wholesaler agrees to replace each defective bulb with one that is guaranteed to function properly for a charge of $0.20 per bulb. The retailer sells the bulbs at a price of $2.50 per bulb
A business manager who needs to make many phone calls has estimated that when she calls a client, the probability that she will reach the client right away is 60%. If she does not reach the client on the first call, the probability that she will reach the client with a subsequent call in the next
Suppose that a marketing research firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with probability 0.40.a. What is the probability that both
Based on past sales experience, an appliance store stocks five window air conditioner units for the coming week. No orders for additional air conditioners will be made until next week. The weekly consumer demand for this type of appliance has the probability distribution given in the file
Simulate 1000 weekly consumer demands for window air conditioner units with the probability distribution given in the file S04_56.xlsx. How does your simulated distribution compare to the given probability distribution? Explain any differences between these two distributions.
The probability distribution of the weekly demand for copier paper (in hundreds of reams) used in the duplicating center of a corporation is provided in the file S04_58.xlsx.a. Find the mean and standard deviation of this distribution.b. Find the probability that weekly copier paper demand is at
Consider the probability distribution of the weekly demand for copier paper (in hundreds of reams) used in a corporation’s duplicating center, as shown in the file S04_58.xlsx.a. Use simulation to generate 500 values of this random variable.b. Find the mean and standard deviation of the simulated
The probability distribution of the weekly demand for copier paper (in hundreds of reams) used in the duplicating center of a corporation is provided in the file S04_58.xlsx. Assuming that it costs the duplicating center $5 to purchase a ream of paper, find the mean and standard deviation of the
The instructor of an introductory organizational behavior course believes that there might be a relationship between the number of writing assignments (X) she gives in the course and the final grades (Y) earned by students in this class. She has taught this course with varying numbers of writing
The file S04_62.xlsx contains the joint probability distribution of recent weekly trends of two particular stock prices, P1 and P2.a. Are P1 and P2 independent random variables? Explain why or why not.b. If P1 and P2 are not independent random variables, which joint probabilities result in the same
Consider two service elevators used in parallel by employees of a three-story hotel building. At any point in time when both elevators are stationary, let X1 and X2 be the floor numbers at which elevators 1 and 2, respectively, are currently located. The file S04_33.xlsx contains the joint
A roulette wheel contains the numbers 0, 00, and 1 to 36. If you bet $1 on a single number coming up, you earn $35 if the number comes up and lose $1 otherwise. Find the mean and standard deviation of your winnings on a single bet. Then find the mean and standard deviation of your net winnings if
Assume that there are four equally likely states of the economy: boom, low growth, recession, and depression. Also, assume that the percentage annual return you obtain when you invest a dollar in gold or the stock market is shown in the file S04_65.xlsx. a. Find the covariance and correlation
Suppose there are three states of the economy: boom, moderate growth, and recession. The annual return on Honda and Toyota stock in each state of the economy is shown in the file S04_66.xlsx.a. Calculate the mean and standard deviation of the annual return on each stock, assuming the probability of
Each year the employees at Zipco receive a $0, $2000, or $4500 salary increase. They also receive a merit rating of 0, 1, 2, or 3, with 3 indicating outstanding performance and 0 indicating poor performance. The joint probability distribution of salary increase and merit rating is listed in the
The return on a portfolio during a period is defined by PVend – Pvbeg / PVbegWhere PVbeg is the portfolio value at the beginning of a period and PVend is the portfolio value at the end of the period. Suppose there are two stocks in which you can invest, stock 1 and stock 2. During each year there
You are involved in a risky business venture where three outcomes are possible: (1) You will lose not only your initial investment ($5000) but an additional $3000; (2) You will just make back your initial investment (for a net gain of $0); or (3) You will make back your initial investment plus an
Suppose X and Y are independent random variables. The possible values of X are -1, 0, and 1; the possible values of Y are 10, 20, and 30. You are given that P(X = -1 and Y = 10) = 0.05, P(X = 0 and Y = 30) = 0.20, P(Y = 10) = 0.20, and P(X = 0) = 0.50. Determine the joint probability distribution
Equation (4.7) for variance indicates exactly what variance is: the weighted average of squared deviations from the mean, weighted by the probabilities. However, the computing formula for variance, Equation (4.9), is more convenient for spreadsheet calculations. Show algebraically that the two
Equation (4.10) for covariance indicates exactly what covariance is: the weighted average of products of deviations from the means, weighted by the joint probabilities. However, the computing formula for covariance, Equation (4.12), is more convenient for spreadsheet calculations. Show
The basic game of craps works as follows. You throw two dice. If the sum of the two faces showing up is 7 or 11, you win and the game is over. If the sum is 2, 3, or 12, you lose and the game is over. If the sum is anything else (4, 5, 6, 8, 9, or 10), that value becomes your “point.” You then
Imagine that you are trying to predict the price of gasoline (regular unleaded) and the price of natural gas for home heating during the next month. Assume you believe that the price of either will stay the same, go up by 5%, or go down by 5%. Assess the joint probabilities of these possibilities,
Consider an individual selected at random from a sample of 750 married women in answering each of the following questions.a. What is the probability that this woman does not work outside the home, given that she has at least one child?b. What is the probability that this woman has no children,
Suppose that 8% of all managers in a given company are African American, 13% are women, and 17% have earned an MBA degree from a top-10 graduate business school. Let A, B, and C is, respectively, the events that a randomly selected individual from this population is African American, is a woman,
Consider again the supermarket chain described in Problem 50. Now, assume that the daily sales of the five stores are no longer independent of one another. In particular, the file S04_77.xlsx contains the correlations between all pairs of daily sales volumes. a. Find the mean and standard deviation
A manufacturing plant produces two distinct products, A and B. The cost of producing one unit of A is $18 and that of B is $22. Assume that this plant incurs a weekly setup cost of $24,000 regardless of the number of units of A or B produced. The means and standard deviations of the weekly
The typical standard deviation of the annual return on a stock is 20% and the typical mean return is about 12%. The typical correlation between the annual returns of two stocks is about 0.25. Mutual funds often put an equal percentage of their money in a given number of stocks. By choosing a large
You are ordering milk for Mr. D’s supermarket, and you are determined to please. Milk is delivered once a week (at midnight Sunday). The mean and standard deviation of the number of gallons of milk demanded each day are given in the file S04_80.xlsx. Find the mean and standard deviation of the
Two gamblers play a version of roulette with a wheel as shown in the file S04_81.xlsx. Each gambler places four bets, but their strategies are different, as explained below. For each gambler, use the rules of probability to find the distribution of their net winnings after four bets. Then find the
Suppose the New York Yankees and Philadelphia Phillies are playing a best-of-three series. The first team to win two games is the winner of the series, and the series ends as soon as one team has won two games. The first game is played in New York, the second game is in Philadelphia, and if
The application at the beginning of this chapter describes the campaign McDonald’s used several years ago, where customers could win various prizes.a. Verify the figures that are given in the description. That is, argue why there are 10 winning outcomes and 120 total outcomes.b. Suppose
A manufacturing company is trying to decide whether to sign a contract with the government to deliver an instrument to the government no later than eight weeks from now. Due to various uncertainties, the company isn’t sure when it will be able to deliver the instrument. Also, when the instrument
Have you ever watched the odds at a horse race? You might hear that the odds against a given horse winning are 9 to 1, meaning that the horse has a probability 1/(1 + 9) = 1/10 of winning. However, these odds, after being converted to probabilities, typically add to something greater than one. Why
The results we obtain with conditional probabilities can be quite counterintuitive, even paradoxical. This case is similar to one described in an article by Blyth (1972), and is usually referred to as Simpson’s paradox. Essentially, Simpson’s paradox says that even if one treatment has a better
The grades on the midterm examination given in a large managerial statistics class are normally distributed with mean 75 and standard deviation 9. The instructor of this class wants to assign an A grade to the top 10% of the scores, a B grade to the next 10% of the scores, a C grade to the next 10%
Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.a. What is the probability that a randomly selected customer spends less than $35 at this store?b. What is the probability that
A machine used to regulate the amount of a certain chemical dispensed in the production of a particular type of cough syrup can be set so that it discharges an average of µ milliliters (ml) of the chemical in each bottle of cough syrup. The amount of chemical placed into each bottle of cough syrup
Assume that the weekly demand for Ford car sales follows a normal distribution with mean 50,000 cars and standard deviation 14,000 cars. a. There is a 1% chance that Ford will sell more than what number of cars during the next year?b. What is the probability that Ford will sell between 2.4 and 2.7
An investor has invested in nine different investments. The dollar returns on the different investments are probabilistically independent, and each return follows a normal distribution with mean $50,000 and standard deviation $10,000. a. There is a 1% chance that the total return on the nine
Scores on an exam appear to follow a normal distribution with µ = 60 and σ = 20. The instructor wishes to give a grade of D to students scoring between the 10th and 30th percentiles on the exam. For what range of scores should a D be given? What percentage of the students will get a D?
Suppose that the weight of a typical American male follows a normal distribution with µ = 180 lb and σ = 30 lb. Also, suppose 91.92% of all American males weigh more than I weigh.a. What fraction of American males weigh more than 225 pounds?b. How much do I weigh? c. If I weighed 20 pounds more
Assume that the length of a typical televised baseball game, including all the commercial timeouts, is normally distributed with mean 2.45 hours and standard deviation 0.37 hour. Consider a televised baseball game that begins at 2:00 in the afternoon. The next regularly scheduled broadcast is at
The amount of a soft drink that goes into a typical 12-ounce can varies from can to can. It is normally distributed with an adjustable mean µ and a fixed standard deviation of 0.05 ounce. a. If regulations require that cans have at least 11.9 ounces, what is the smallest mean _ that can be used so
Suppose that the demands for a company’s product in weeks 1, 2, and 3 are each normally distributed. The means are 50, 45, and 65. The standard deviations are 10, 5, and 15. Assume that these three demands are probabilistically independent. This means that if you observe one of them, it doesn’t
Matthew’s Bakery prepares peanut butter cookies for sale every morning. It costs the bakery $0.50 to bake each peanut butter cookie, and each cookie is sold for $1.25. At the end of the day, leftover cookies are discounted and sold the following day at $0.40 per cookie. The daily demand (in
The manufacturer of a particular bicycle model has the following costs associated with the management of this product’s inventory. In particular, the company currently maintains an inventory of 1000 units of this bicycle model at the beginning of each year. If X units are demanded each year and X
Suppose that a particular production process fills detergent in boxes of a given size. Specifically, this process fills the boxes with an amount of detergent (in ounces) that is adequately described by a normal distribution with mean 50 and standard deviation 0.5.a. Simulate this production process
It is widely known that many drivers on interstate highways in the United States do not observe the posted speed limit. Assume that the actual rates of speed driven by U.S. motorists are normally distributed with mean _ mph and standard deviation 5 mph. Given this information, answer each of the
The lifetime of a certain manufacturer’s washing machine is normally distributed with mean 4 years. Only 15% of all these washing machines last at least 5 years. What is the standard deviation of the lifetime of a washing machine made by this manufacturer?
You have been told that the distribution of regular unleaded gasoline prices over all gas stations in Indiana is normally distributed with mean $2.95 and standard deviation $0.075, and you have been asked to find two dollar values such that 95% of all gas stations charge somewhere between these two
A fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday the demand for hamburgers is normally distributed with mean 313 and standard deviation 57; the demand for chicken sandwiches is normally distributed with mean 93 and standard deviation 22.a. How many hamburgers
Referring to the box plots introduced in Chapter 2, the sides of the “box” are at the first and third quartiles and the difference between these (the length of the box) is called the inter-quartile range (IQR). A mild outlier is an observation that is between 1.5 and 3 IQRs from the box, and an
In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant binomial distribution, answer the following questions: a. What is the probability that
Continuing the previous exercise, use the normal approximation to the binomial to answer each of the questions posed in parts a through f. How well does the normal approximation perform in this case? Explain. a. What is the probability that exactly five customers will buy life insurance from this
Many vehicles used in space travel are constructed with redundant systems to protect flight crews and their valuable equipment. In other words, backup systems are included within many vehicle components so that if one or more systems fail, backup systems will assure the safe operation of the given
Suppose that a popular hotel for vacationers in Orlando, Florida, has a total of 300 identical rooms. As many major airline companies do, this hotel has adopted an overbooking policy in an effort to maximize the usage of its available lodging capacity. Assume that each potential hotel customer
A production process manufactures items with weights that are normally distributed with mean 15 pounds and standard deviation 0.1 pound. An item is considered to be defective if its weight is less than 14.8 pounds or greater than 15.2 pounds. Suppose that these items are currently produced in
Past experience indicates that 30% of all individuals entering a certain store decide to make a purchase. Using (a) the binomial distribution and (b) the normal approximation to the binomial, find that probability that 10 or more of the 30 individuals entering the store in a given hour will decide
Suppose that the number of ounces of soda put into a soft-drink can is normally distributed with µ = 12.05 ounces and σ = 0.03 ounce.a. Legally, a can must contain at least 12 ounces of soda. What fraction of cans will contain at least 12 ounces of soda?b. What fraction of cans will contain less
Suppose that 53% of all registered voters prefer Barack Obama to John McCain. a. In a random sample of 100 voters, what is the probability that the sample will indicate that Obama will win the election (that is, there will be more votes in the sample for Obama)?b. In a random sample of 100 voters,
Assume that, on average, 95% of all ticket holders’ show up for a flight. If a plane seats 200 people, how many tickets should be sold to make the chance of an overbooked flight as close as possible to 5%?
Suppose that 55% of all people prefer Coke to Pepsi. We randomly choose 500 people and ask them if they prefer Coke to Pepsi. What is the probability that our survey will (erroneously) indicate that Pepsi is preferred by more people than Coke? Does this probability increase or decrease as we take
A firm’s office contains 150 PCs. The probability that a given PC will not work on a given day is 0.05. a. On a given day what is the probability that exactly one computer will not be working?b. On a given day what is the probability that at least two computers will not be working?c. What
Suppose that 4% of all tax returns are audited. In a group of n tax returns, consider the probability that at most two returns are audited. How large must n be before this probability is less than 0.01?
Suppose that the height of a typical American female is normally distributed with µ = 64 inches and σ = 4 inches. We observe the height of 500 American females.a. What is the probability that fewer than 35 of the 500 women will be less than 58 inches tall?b. Let X be the number of the 500 women
Consider a large population of shoppers, each of whom spends a certain amount during his or her current shopping trip; the distribution of these amounts is normally distributed with mean $55 and standard deviation $15. We randomly choose 25 of these shoppers. What is the probability that at least
Many firms utilize sampling plans to control the quality of manufactured items ready for shipment. To illustrate the use of a sampling plan, suppose that a particular company produces and ships electronic computer chips in lots, each lot consisting of 1000 chips. This company’s sampling plan
Suppose you play a game at a casino where your probability of winning each game is 0.49. On each game, you bet $10, which you either win or lose. Let P(n) be the probability that you are ahead by at least $50 after n games. Graph this probability versus n for n equal to multiples of 50 up to 1000.
Comdell Computer receives computer chips from Chipco. Each batch sent by Chipco is inspected as follows: 35 chips are tested and the batch passes inspection if at most one defective chip is found in the set of 35 tested chips. Past history indicates an average of 1% of all chips produced by Chipco
A standardized test consists entirely of multiple-choice questions, each with five possible choices. You want to ensure that a student who randomly guesses on each question will obtain an expected score of zero. How can you accomplish this?
In the current tax year, suppose that 5% of the millions of individual tax returns are fraudulent. That is, they contain errors that were purposely made to cheat the government.a. Although these errors are often well concealed, let’s suppose that a thorough IRS audit will uncover them. If a
Suppose you work for a survey research company. In a typical survey, you mail questionnaires to 150 companies. Of course, some of these companies might decide not to respond. Assume that the non-response rate is 45%; that is, each company’s probability of not responding, independently of the
Suppose you are sampling from a large population, and you ask the respondents whether they believe men should be allowed to take paid paternity leave from their jobs when they have a new child. Each person you sample is equally likely to be male or female. The population proportion of females who

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