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Statistics For Business Decision Making And Analysis 2nd Edition Robert Stine, Dean Foster - Solutions

Repeat the calculations of Exercise 33. Rather than treat the random variables X and Y as independent, assume that Cov(X, Y) = 12,500.
Repeat the calculations of Exercise 34. Rather than treat the random variables X and Y as independent, assume that Corr(X, Y) = -0.5.
If the variance of the sum is Var(X + Y) = 8 and Var(X) = Var(Y) = 5, then what is the correlation between X and Y?
A student budgets $60 weekly for gas and a few quick meals off-campus. Let X denote the amount spent for gas and Y the amount spent for quick meals in a typical week. Assume this student is very disciplined and sticks to the budget, spending $60 on these two things each week. (a) Can we model X and
A pharmaceutical company has developed a new drug that helps insomniacs sleep. In tests of the drug, it records the daily number of hours asleep and awake. Let X denote the number of hours awake and let Y denote the number of hours asleep for a typical patient. (a) Explain why the company must
Drivers for a freight company make a varying number of delivery stops. The mean number of stops is 6 with standard deviation 2. Two drivers operate independently of one another. (a) Identify the two random variables and summarize your assumptions. (b) What is the mean and standard deviation of the
Two classmates enjoy playing online poker. They both claim to win $300 on average when they play for an evening, even though they play at different sites on the Web. They do not always win the same amounts, and the SD of the amounts won is $100. (a) Identify the two random variables and summarize
Customers at a fast-food restaurant buy both sandwiches and drinks. The following joint distribution summarizes the numbers of sandwiches (X) and drinks (Y) purchased by customers.(a) Find the expected value and variance of the number of sandwiches. (b) Find the expected value and variance of the
During the 2010-2011 NBA season, LeBron James of the Miami Heat attempted 279 three-point baskets and made 92. He also attempted 1,485 two-point baskets, making 758 of these. Use these counts to determine probabilities for the following questions.(a) Let a random variable X denote the result of a
During the 2010-2011 NBA season, LeBron James of the Miami Heat attempted 279 three-point baskets and made 92. He also attempted 1,485 two-point baskets, making 758 of these. Use these counts to determine probabilities for the following questions. (a) Let a random variable X denote the result of a
During the 2011-2012 NFL regular season, kicker Lawrence Tynes of the Super Bowl winning New York Giants attempted 24 field goals, making 19. Of the kicks, he made 15 out of 16 that were for less than 40 yards, and he made 4 out of 8 longer kicks. Use these counts to form probabilities. (a) Let the
Homes in a community served by a utility company annually use an expected 12,000 kilowatt-hours (kWh) of electricity. The same utility supplies natural gas to these homes, with an annual expected use of 85 thousand cubic feet (85 MCF). The homes vary in size and patterns of use, and so the use of
A direct sales company has a large sales force that visits customers. To improve sales, it designs a new training program. To see if the program works, it puts some new employees through this program and others through the standard training. It then assigns two salespeople to a district, one
A construction firm places bids on various portions of the work in building a new office tower. The key bids it submits are for electrical work and for plumbing. The bid for the electrical work estimates 64 weeks of labor (e.g., 1 electrician for 64 weeks or 8 for 8 weeks). The bid for the plumbing
A retail company operates two types of clothing stores in shopping malls. One type specializes in clothes for men, and the other in clothes for women. The sales from a men’s clothing store average $800,000 annually and those from a women’s clothing store average $675,000 annually. The standard
The relevance of variance and covariance developed for random variables in this chapter carries over to the analysis of returns on real stocks. The data file €œdaily _ stocks€ includes the daily percentage changes in the value of stock in Apple and stock in McDonald€™s in 2010 and 2011.
Management of a chain of retail stores has the opportunity to lock in prices for electricity and natural gas, the two energy sources used in the stores. A typical store in this chain uses electricity for lighting and air conditioning. In the winter, natural gas supplies heat. Managers at a recent
1. Expression for the variance of Y 2. Probability that the first trial B1 fails. 3. Expression for the mean of X 4. Probability that Y is zero 5. Probability that X is 2 6. Covariance between B1 and B2 7. Expression for the expected value of Y 8. The expected value of B1 9. Probability that Y is
1. If the selected 25 transactions are treated as Bernoulli trials, the resulting binomial calculations will be in error because of sampling from a finite population. 2. The binomial model for this problem sets n = 25 and p = 0.10. 3. Assuming Bernoulli trials, there is a 1>1,000 chance for at
1. A Poisson model is well suited to this application so long as the defects come in small clusters of two or three together. 2. To use a Poisson model for the number of defects, we must assume that defects occur at an increasing rate throughout the manufacturing of the fabric. 3. An increase in
Is the binomial model suited to these applications? (a) The next five cars that enter a gasoline filling station get a fill-up. (b) A poll of the 15 members of the board of directors of a company indicates that 6 are in favor of a proposal to change the salary of the CEO. (c) A company realizes
Is the Poisson model suited to these applications? (a) The number of customers who enter a store each hour (b) The number of auto accidents reported to a claims office each day (c) The number of broken items in a shipment of glass vials
If the underlying trials are positively dependent (meaning that a success, say, is more likely followed by another success), would you expect the variance of the total number of successes to be larger or smaller than the binomial expression np(1 – p)?
In the taste test of Exercise 27, are we more likely to find that the four customers prefer the same brand or to find their opinions evenly divided between the two brands?
A manager supervises five experimental projects. Each has a 50-50 chance for producing an innovative, successful new product. The teams that are developing each project work separately, so the success of one project is independent of the success of other projects. A successful project returns 10
A manager randomly selected 25 large cash transactions at a bank that were made in January. The manager then carefully tracked down the details of these transactions to see that the correct procedures for reporting these large transactions were followed. This bank typically makes 1,500 such
A commuter airline deliberately overbooks fights, figuring that only 75% of passengers with reservations show up for its fights. It files small propeller planes that carry 20 passengers. (a) In order to use a binomial model in this problem, what assumptions are necessary? Are these reasonable? (b)
Every now and then even a good diamond cutter has a problem and the diamond breaks. For one cutter, the rate of breaks is 0.1%. (a) What probability model seems well suited to this problem? Why? (b) If this cutter works on 75 stones, what is the probability that he breaks 2 or more?
A manufacturer of LCD panels used in computer displays has decided to ship only panels with at most one defective pixel. Defective pixels are the result of randomly located flaws in the glass used to make the panel. To be profitable, the manufacturer must ship 85% of its panels. If an LCD panel has
An insurance company offers two policies that cover the cost of repairs from driving accidents. A policy costing $1,000 annually has a $1,000 deductible (meaning the driver is responsible for paying the first $1,000 in damages before the insurance kicks in), whereas a policy that costs $3,000
The Food and Drug Administration has veto power over the choice of drug names. In 2004, it used this power regularly, rejecting 36% of the names proposed by companies for reasons such as sounding too much like another product (and causing confusion at the pharmacy). Suppose that a company spends
A dairy farmer accidentally allowed some of his cows to graze in a pasture containing weeds that would contaminate the milk from this herd. The farmer estimates that there’s a 10% chance of a cow grazing on some of the flavorful weeds. (a) Under these conditions, what is the probability that none
Historically a bank expects about 5% of its borrowers to default (not repay). The bank currently has 250 loans outstanding. (a) In order to use a binomial model to compute the probabilities associated with defaults, what must the bank assume about the behavior of these borrowers? (b) Do the
A basketball player attempts 20 shots from the field during a game. This player generally hits about 35% of these shots. (a) In order to use a binomial model for the number of made baskets, what assumptions are needed in this example? Are they reasonable? (b) How many baskets would you expect this
The kicker in a football game scores 3 points for a made field goal. A kicker hits 60% of the attempts taken in a game. (a) What assumptions are needed in order to model the number of made kicks in a game as a binomial random variable? (b) If the kicker tries five attempts during a game, how many
Managers of an office selected a committee of five employees to participate in discussions on how to revise the flow of work in the office. The office has 25 employees, of which 10 are men. If the committee is selected at random from the 25 employees, is it likely to have 4 men? (This question and
Some customers of a retail chain have a store credit card that earns them bonus gifts when they make purchases at the chain. Currently, 40 customers are shopping in a store in this chain. Of these, half already have a store credit card. If employees offer store credit cards to 6 of these, what is
A marketing research firm interviewed visitors at a car show. The show featured new cars with various types of environmentally oriented enhancements, such as hybrid engines, alternative types of fuels (such as bio fuels), and aerodynamic styling. The interviews of 25 visitors who indicated they
Companies that sell food and other consumer products watch for problems. Occasional complaints from dissatisfied customers always occur, but an increase in the level of complaints may signal a serious problem that is better handled sooner than later. With food safety, that’s a particular concern.
1. Mean of X2. Variance of X3. Probability of X being less than its mean4. Probability of X being less than μ + σ5. Standard deviation of Z6. Probability that a z-score based on X is less than 1 in magnitude7. Proportion of a normal distribution that is more than 20 σ from m8. Difference between
1. More employees at the processing center are older than 44 than between 38 and 44. 2. Most of the employees at this center are older than 25. 3. If the company were to convert these ages from years to days, then the ages in days would also be normally distributed. 4. If none of these employees
1. The total number of packages shipped over five days is normally distributed. 2. The difference between the numbers of packages shipped on any two consecutive days is normally distributed. 3. The difference between the number of packages \shipped today and the number shipped tomorrow is zero. 4.
If X1 ~ N(μ , σ) and X2 ~ N (μ , σ) are iid normal random variables, then what’s the difference between 2X1 and X1 + X2? They both have normal distributions.
If X1 ~ N(μ , σ) and X2 ~ N(μ , σ) are iid, then what is the distribution of (X1 - X2) / (√2σ)?
Which one of the following normal quantile plots indicates that the data c(a) Are nearly normal?(b) Have a bimodal distribution? (One way to recognize a bimodal shape is a gap in the spacing of adjacent data values.)(c) Are skewed?(d) Have outliers to both sides of the center?
Match each histogram to a normal quantile plot.
One of these pairings of histogram with normal quantile plot shows data that have been rounded. The other shows the same data without rounding. The rounding in the example is similar to the rounding in SAT scores.(a) Which is which? How can you tell?(b) Why do the histograms appear so similar if
The normal quantile plot of daily stock returns for General Motors during 1992€“1993 (507 trading days) shows an anomaly, a flat spot at zero.(a) What€™s happened?(b) Why does the anomaly not appear in the histogram?
The amount of electricity supplied by a utility to residences in a community during the summer depends on the local weather as well as the habits of the people in the community. (a) Would a normal model be reasonable to describe the amount of electricity used from one day to the next? Explain your
Dress shoes of a specific style for women come in sizes ranging from 4 to 12. A retailer believes that this range of sizes is adequate for all but 5% of its female customers.(a) What normal model for sizes is consistent with the opinion of the retailer?(b) If the retailer uses a normal model, then
The weekly salary paid to employees of a small company that supplies part-time laborers averages $700 with a standard deviation of $400. (a) If the weekly salaries are normally distributed, estimate the fraction of employees that make more than $300 per week. (b) If every employee receives a
A specialty foods company mails out “gourmet steaks” to customers willing to pay a gourmet price. The steaks vary in size, with a mean uncooked weight of 1.2 pounds and standard deviation of 0.10 pound. Use a normal model for the weight of a steak.(a) Estimate the proportion of steaks that
A contractor built 30 similar homes in a suburban development. The homes have comparable size and amenities, but each has been sold with features that customize the appearance, landscape, and interior. The contractor expects the homes to sell for about $450,000. He expects that one-third of the
An accounting firm assists small businesses file annual tax forms. It assigns each new client to a CPA at the firm who specializes in companies of that type and size. For instance, one CPA specializes in boutique clothing retailers with annual sales of about $2 million. To speed the process, each
Find these probabilities for a standard normal random variable Z. Be sure to draw a picture to check your calculations. Use the normal table in the back of the book or software. (a) P (Z < 1.5) (b) P (Z > -1) (c) P (∣Z∣ < 1.2) (d) P (∣Z∣ > 0.5) (e) P (-1 ≤ Z ≤ 1.5)
Find these probabilities for a standard normal random variable Z. Be sure to draw a picture for each to check your calculations. Use the normal table in the back of the book or software. (a) P (Z ≥ 0.6) (b) P (Z < -2.3) (c) P (–0.8 ≤ Z < 0.8) (d) P (∣Z∣ > 1.5) (e) P (0.3 ≤ Z ≤ 2.2)
Using the normal table in the back of the book or software, find the value of z that makes the following probabilities true. You might find it helpful to draw a picture to check your answers. (a) P (Z < z) = 0.20 (b) P (Z ≤ z) = 0.50 (c) P (-z ≤ Z ≤ z) = 0.50 (d) P (∣Z∣< z) = 0.01 (e) P
Using the normal table in the back of the book or software, find the value of z that makes the following probabilities hold. Again, you might find it helpful to draw a picture to check your answers. (a) P (Z < z) = 0.35 (b) P (Z ≥ z) = 0.60 (c) P (-z ≤ Z ≤ z) = 0.40 (d) P (∣Z∣ > z) =
(a) Find the value at risk (VaR) for an investment of $100,000 at 2%. (That is, find out how low the value of this investment could be if we rule out the worst 2% of outcomes.) The investment is expected to grow during the year by 8% with SD 20%. Assume a normal model for the change in value. (b)
(a) Find the VaR for an investment of $500,000 at 1%. (That is, find out how low the value of this investment could be if we rule out the worst 1% of outcomes.) The investment is expected to grow during the year by 10% with SD 35%. Assume a normal model for the change in value. (b) How much smaller
An insurance company found that 2.5% of male drivers between the ages of 18 and 25 are involved in serious accidents annually. To simplify the analysis, assume that every such accident costs the insurance company $65,000 and that a driver can only have one of these accidents in a year.(a) If the
A tire manufacturer warranties its tires to last at least 20,000 miles or “you get a new set of tires.” In its experience, a set of these tires lasts on average 26,000 miles with SD 5,000 miles. Assume that the wear is normally distributed. The manufacturer profits $200 on each set sold, and
A hurricane bond pays the holder a face amount, say $1 million, if a hurricane causes major damage in the United States. Suppose that the chance for such a storm is 5% per year. (a) If a financial firm sells these bonds for $60,000, what is the chance that the firm loses money if it only sells one
The data are returns of 533 hedge funds. The returns are computed as the change in value of assets managed by the fund during the month divided by the value of the assets at the start of the month. (a) Describe the histogram and boxplot of the returns. Is the histogram symmetric and unimodal? Would
The data give the market share (0 to 100%) of a brand-name pharmaceutical product in 224 metropolitan locations. The market share indicates the percentage of all prescriptions for this type of medication that are written for this brand.(a) Describe the histogram and boxplot of the market shares. Is
Percentage changes (or returns) on the stock market follow a normal distribution—if we don’t reach too far into the tails of the distribution. Are returns on stocks in individual companies also roughly normally distributed? This example uses monthly returns on McDonald’s stock from 1990
We usually do not think of the distribution of income as being normally distributed. Most histograms show the data to be skewed, with a long right tail reaching out toward Bill Gates. This sort of skewness is so common, but normality so useful, that the lognormal model has become popular. The
1. Sample 2. Census 3. Target population 4. Statistic 5. Parameter 6. Sampling frame 7. Simple random sample 8. Stratified sample 9. Bias 10. Nonresponse (a) A complete collection of items desired to be studied (b) A list of all of the items in the population (c) A subset of a larger collection of
True or False?A census offers the most accurate accounting of the characteristics of the target population.
A business magazine mailed a questionnaire to the human resource directors of all of the Fortune 500 companies, and received responses from 23% of them. Among those who responded, 40% reported that they did not find that such surveys intruded significantly on their workday.
Hotels.com asks users to rate hotels that they have visited on a scale from 0 (worst) to 5 (best). Ninety-nine guests gave a hotel at the St. Louis Convention Center a 4.5 out of 5 rating.
A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day’s production. Each case contains 50 bags. An inspector selects and weighs two bags from each case.
Inspectors from the food-safety division of the Department of Agriculture visit dairy farms unannounced and take samples of the milk to test for contamination. If the samples are found to contain dirt, antibiotics unsuited for human consumption, or other foreign matter, the milk will be destroyed.
A vendor opens a small booth at a supermarket to offer customers a taste of a new beverage. The staff at the booth offer the beverage to adults who pass through the soda aisle of the store near a display of the product. Customers who react favorably receive a discount coupon toward future purchases.
The information that comes with a flat-screen television includes a registration card to be returned to the manufacturer. Among questions that identify the purchaser, the registration card asks him or her to identify the cable provider or other source of television programming.
A bank with branches in a large metropolitan area is considering opening its offices on Saturday, but it is uncertain whether customers will prefer (1) having walk-in hours on Saturday or (2) having extended branch hours during the week. Listed below are some of the ideas proposed for gathering
Four new sampling strategies have been proposed to help the bank in Exercise 27 determine whether customers favor opening on Saturdays versus keeping branches open longer during the week. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. (a)
Between quarterly audits, a company checks its accounting procedures to detect problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day a supervisor checks 10 of the transactions to be sure they were processed properly. (a) Propose a
A car manufacturer is concerned that dealers conceal unhappy customers by keeping them out of surveys conducted by the manufacturer. The manufacturer suspects that certain dealers enter incorrect ad-dresses for dissatisfied customers so that they do not receive the satisfaction survey that is
Print a blank 50 × 15 spreadsheet on construction paper, and then cut the printed cells into 25 rectangles of varying size, some with just a few cells and some with many. Ask a few friends to pick a sample of 5 pieces from these. (One at a time, and don’t let them see what the others do, so that
Companies in the competitive hotel industry need to keep up with the tastes of their visitors. If the rooms seem dated and the service is slow, travelers will choose a different destination for their next visit. One means of monitoring customer satisfaction is to put cards in guest rooms, asking
The Internal Revenue Service collects personal income and corporate taxes. Most of the job involves processing the paperwork that accompanies taxes. The IRS verifies, for example, the reported Social Security numbers and compares reported earnings from W-2 and 1099 forms to the earnings reported by
1. A histogram of the average withdrawal amounts made daily over the span of a month should cluster around $50.2. A histogram of the daily standard deviations of the withdrawal amounts over the span of a month should cluster around $40.3. It would be surprising to discover a transaction for more
Which of the following X-bar charts show that a process went out of control?
Rather than stop the production when a mean crosses the control limits in the X-bar chart, a manager has decided to wait until two consecutive means lie outside the control limits before stopping the process. The control limits are at μ ± 2σ / √n.(a) By waiting for two consecutive sample means
Suppose that a manager monitors both the X-bar and S-charts. The manager will stop the process if either a sample mean lies outside the control limits or a sample standard deviation lies outside the control limits. The control limits are set at ± 3 standard error bounds.(a) By tracking both X-bar
Which of the following processes would you expect to be under control, and which would you expect not to be under control? Explain briefly why or why not. (a) Daily sales at each checkout line in a supermarket (b) Number of weekday calls to a telephone help line (c) Monthly volume of shipments of
Do you think the following data would represent processes that were under control or out of control? Explain your thinking. (a) Monthly shipments of snow skis to retail stores (b) Number of daily transactions at the service counter in a local bank (c) Attendance at NFL games during the 16-week
A monitoring system records the production of an assembly line each hour. The design calls for output to be four units per hour. Current policy calls for stopping the line to check for flaws if fewer than two items are produced in an hour. Use what you learned about counting random variables in
A bottler carefully weighs bottles coming off its production line to check that the system is filling the bottles with the correct amount of beverage. By design, the system is set to slightly overfill the bottles to allow for random variation in the packaging. The content weight is designed to be
Auto manufacturers buy car components from suppliers who deliver them to the assembly line. A manufacturer can schedule staff time to check a sample of 5 parts a day for defects or a sample of 25 parts over the weekend when the assembly line is slowed. (a) If the manufacturer is interested in
The Web site of a photo processor allows customers to send digital files of pictures to be printed on high-quality paper with durable inks. When the inks used by the processor start to run out, the color mix in the pictures gradually degrades. (a) How could the facility use a quality control
Which, if any, of these combinations of an X-bar chart and an S-chart suggest a problem? If there€™s a problem, did you find it in the X-bar chart, the S-chart, or both?
Using X-bar and S-charts that set control limits at ± 3 standard errors, (a) What is the probability that one or more of the first 10 sample averages from a process that is under control lands outside the control limits? (b) What is the probability that both the sample average and the sample
These data give the diameter (in thousandths of an inch) of motor shafts that will be used in automobile engines. Each day for 80 weekdays, five shafts were sampled from the production line and carefully measured. For these shafts to work properly, the diameter must be about 815 thousandths of an
A truck manufacturer monitors the width of the door seam as vehicles come off its assembly line. The seam width is the distance between the edge of the door and the truck body, in inches. These data are 62 days of measurements of a passenger door seam, with 10 trucks measured each day. It has been
One stage in the manufacture of semiconductor chips applies an insulator on the chips. This process must coat the chip evenly to the desired thickness of 250 microns or the chip will not be able to run at the desired speed. If the coating is too thin, the chip will leak voltage and not function
Most commercial Internet sites monitor site traffic so that they can recognize attacks by hackers, such as a distributed denial of service attack (DDoS). In this attack, the hacker hijacks a collection of the computers connected to the Internet and has them all attempt to access the commercial
A firm monitors the use of its email system. A sudden change in activity might indicate a virus spreading in the system, and a lull in activity might indicate problems on the network. When the system and office are operating normally, about 16.5 messages move through the system on average every
Control charts are also useful when you look at financial data. These charts help you recognize that some processes are not very simple: Their features change over time. X-bar and S-charts are convenient to plot means and standard deviations, and the control limits supply a point of reference for

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