Question: The random variable is the number of

> A Pew Research Center survey found that social networking is popular in many nations around the world. The file GlobalSocialMedia contains the level of social media networking (measured as the percent of individuals polled who use social networking sites

> The file Protein contains calorie and cholesterol information for popular protein foods (fresh red meats, poultry, and fish) compiled by the U.S. Department of Agriculture. a. Perform a cluster analysis using the complete linkage method on the protein f

> The file Cereals contains the calories, carbohydrates, and sugar, in grams, in one serving of seven breakfast cereals. a. Perform a cluster analysis using the complete linkage method on the cereals based on the calories, carbohydrates, and sugar in gram

> Consider the following payoff table: For this problem, P(E1) = 0.8, P(E2) = 0.1, P(E3) = 0.1, P(F | E1) = 0.2, P(F | E2) = 0.4, and P(F | E3) = 0.4. Suppose you are informed that event F occurs. a. Revise the probabilities P(E1), P(E2), and P(E3) now

> Movie companies need to predict the gross receipts of individual movies once the movie has debuted. The following results, stored in PotterMovies , are the first weekend gross, the U.S. gross, and the worldwide gross (in $millions) of the Harry Potter mo

> Undergraduate students at Miami University in Oxford, Ohio, were surveyed in order to evaluate the effect of price on the purchase of a pizza from Pizza Hut. The students were asked to suppose that they were going to have a large two-topping pizza delive

> An automotive insurance company wants to predict which filed stolen vehicle claims are fraudulent, based on the number of claims submitted per year by the policy holder and whether the policy is a new policy, that is, is one year old or less (coded as 1

> A marketing manager wants to predict customers with risk of churning (switching their service contracts to another company) based on the number of calls the customer makes to the company call center and the number of visits the customer makes to the loca

> A hotel has designed a new system for room service delivery of breakfast that allows the customer to select a specific delivery time. The file Satisfaction contains the difference between the actual and requested delivery times (a negative time means tha

> The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of

> In mining engineering, holes are often drilled through rock using drill bits. As a drill hole gets deeper, additional rods are added to the drill bit to enable additional drilling to take place. It is expected that drilling time increases with depth. Thi

> Starbucks Coffee Co. uses a data-based approach for improving the quality and customer satisfaction of its products. When survey data indicated that Starbucks needed to improve its package sealing process, an experiment was conducted to determine the fac

> The business problem facing a consumer products company is to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of radio advertising and newspa

> Using the bonuses paid to workers on Wall Street data for Problem 16.12 on page 645 and Problem 16.28 on page 655 (stored in Bonuses ), a. perform a residual analysis for each model. b. compute the standard error of the estimate (SYX) for each model. c.

> Consider the following payoff table: For this problem, P(E1) = 0.5, P(E2) = 0.5, P(F | E1) = 0.6, and P(F | E2) = 0.4. Suppose that you are informed that event F occurs. a. Revise the probabilities P(E1) and P(E2) now that you know that event F has occ

> Using the new, single-family house sales data for Problem 16.15 on page 645 and Problem 16.27 on page 654 (stored in HouseSales ), a. perform a residual analysis for each model. b. compute the standard error of the estimate (SYX) for each model. c. compu

> Using the yearly amount of solar power generated by utilities (in millions of kWh) in the United States data for Problem 16.16 on page 645 and Problem 16.31 on page 655 (stored in SolarPower), a. perform a residual analysis. b. compute the standard error

> Refer to Problem 16.32. Suppose the first residual is 12.0 (instead of 2.0) and the last residual is -11.0 (instead of -1.0). a. Compute SYX and interpret your findings Compute the MAD and interpret your findings. Problem 16.32: The following residuals

> The following residuals are from a linear trend model used to forecast sales: 2.0 -0.5 1.5 1.0 0.0 1.0 -3.0 1.5 -4.5 2.0 0.0 -1.0 a. Compute SYX and interpret your findings. b. Compute the MAD and interpret your findings.

> Refer to Problem 16.24. The three most recent values are Y15 = 23 Y16 = 28 Y17 = 34 Forecast the values for the next year and the following year. Problem 16.24: A third-order autoregressive model is fitted to an annual time series with 17 values and h

> A third-order autoregressive model is fitted to an annual time series with 17 values and has the following estimated parameters and standard errors: At the 0.05 level of significance, test the appropriateness of the fitted model.

> You are given an annual time series with 40 consecutive values and asked to fit a fifth-order autoregressive model. a. How many comparisons are lost in developing the autoregressive model? b. How many parameters do you need to estimate? c. Which of the o

> A time-series plot often helps you determine the appropriate model to use. For this problem, use each of the time series presented in the following table and stored in TSModel2 : a. Plot the observed data Y over time X and plot the logarithm of the obs

> Although you should not expect a perfectly fitting model for any time-series data, you can consider the first differences, second differences, and percentage differences for a given series as guides in choosing an appropriate model. For this problem, u

> The data in CPI-U reflect the annual values of the consumer price index (CPI) in the United States over the 52-year period 1965 through 2016, using 1982 through 1986 as the base period. This index measures the average change in prices over time in a fixe

> In Problem 20.5, you developed a payoff table for whether to purchase 100, 200, 500, or 1,000 Christmas trees. Given the results of that problem, suppose that the probabilities of the demand for the different number of trees are as follows: a. Determin

> The file Silver contains the following prices in London for an ounce of silver (in US$) on the last day of the year from 1999 to 2016: a. Plot the data. b. Compute a linear trend forecasting equation and plot the trend line. c. Compute a quadratic tren

> The average salary of Major League Baseball players on opening day from 2000 to 2017 is stored in BBSalaries and shown below. a. Plot the data. b. Compute a linear trend forecasting equation and plot the trend line. c. Compute a quadratic trend forecas

> The file CarProduction contains the number of passenger cars produced in the U.S. (in thousands) from 1999 to 2016. Source: Data extracted from www.statista.com. a. Plot the data. b. Compute a linear trend forecasting equation and plot the trend line. c.

> The data shown in the following table and stored in Solar Power represent the yearly amount of solar power generated by utilities (in millions of kWh) in the United States from 2002 through 2016: a. Plot the data. b. Compute a linear trend forecasting

> The file HouseSales contains the number of new, single-family houses sold in the U.S. from 1992 through 2016. a. Plot the data. b. Compute a linear trend forecasting equation and plot the trend line. c. Compute a quadratic trend forecasting equation and

> The data in FedReceipt represent federal receipts from 1978 through 2016, in billions of current dollars, from individual and corporate income tax, social insurance, excise tax, estate and gift tax, customs duties, and federal reserve deposits. Source: D

> Gross domestic product (GDP) is a major indicator of a nation’s overall economic activity. It consists of personal consumption expenditures, gross domestic investment, net exports of goods and services, and government consumption expenditures. The file G

> There has been much publicity about bonuses paid to workers on Wall Street. Just how large are these bonuses? The file Bonuses contains the bonuses paid (in $000) from 2000 to 2016. Source: Data extracted from J. Spector, “Wall Street bonuses rise 1% to

> The linear trend forecasting equation for an annual time series containing 42 values (from 1976 to 2017) on net sales (in $billions) is a. Interpret the Y intercept, b0. b. Interpret the slope, b1. c. What is the fitted trend value for the tenth year?

> The linear trend forecasting equation for an annual time series containing 22 values (from 1996 to 2017) on total revenues (in $millions) is a. Interpret the Y intercept, b0. b. Interpret the slope, b1. c. What is the fitted trend value for the fifth y

> In Problem 20.4, you developed a payoff table to assist an author in choosing between signing with company A or with company B. Given the results computed in that problem, suppose that the probabilities of the levels of demand for the novel are as follow

> If you are using the method of least squares for fitting trends in an annual time series containing 25 consecutive yearly values, a. what coded value do you assign to X for the first year in the series? b. what coded value do you assign to X for the fift

> The file IPOs contains the number of initial public offerings (IPOs) issued from 2001 through 2016. Source: Data extracted from K.W. Hanley, “The Economics of Primary Markets,” available at bit.ly/2vWb6hv. a. Plot the data. b. Fit a three-year moving ave

> The data (stored in CoffeeExports ) represent the coffee exports (in thousands of 60 kg bags) by Costa Rica from 2004 to 2016: a. Plot the data. b. Fit a three-year moving average to the data and plot the results. c. Using a smoothing coefficient of W =

> How have stocks performed in the past? The following table presents the data stored in Stock Performance , which show the performance of a broad measure of stock performance (by percentage) for each decade from the 1830s through the 2000s: a. Plot the

> The following data, stored in CoreAppliances provide the total number of shipments of core major household appliances in the U.S. from 2000 to 2016 (in millions). Source: Data extracted from www.statistica.com. a. Plot the time series. b. Fit a three-y

> The data below (stored in DesktopLaptop ) represent the hours per day spent by American desktop/ laptop users from 2008 to 2016. Source: Data extracted from M. Meeker, Internet Trends 2017-Code Conference, available at bit.ly/2vW8Nej. a. Plot the time

> You are using exponential smoothing on an annual time series concerning total revenues (in $millions). You decide to use a smoothing coefficient of W = 0.20, and the exponentially smoothed value for 2017 is E2017 = (0.20)(12.1) + (0.80)(9.4). a. What is

> Consider a nine-year moving average used to smooth a time series that was first recorded in 1984. a. Which year serves as the first centered value in the smoothed series? b. How many years of values in the series are lost when computing all the nine-year

> If you are using exponential smoothing for forecasting an annual time series of revenues, what is your forecast for next year if the smoothed value for this year is $32.4 million?

> In Problems 15.32–15.36 you developed multiple regression models to predict the fair market value of houses in Glen Cove, Roslyn, and Freeport. Now write a report based on the models you developed. Append all appropriate charts and statistical informatio

> In Problem 20.3, you developed a payoff table for building a small factory or a large factory for manufacturing designer jeans. Given the results of that problem, suppose that the probabilities of the demand are as follows: a. Determine the optimal act

> For the following payoff table, the probability of event 1 is 0.5, and the probability of event 2 is also 0.5: a. Determine the optimal action based on the maximax criterion. b. Determine the optimal action based on the maximin criterion. c. Compute th

> Actual lengths of stay at a hospital’s emergency department in 2009 are shown in the following table (rounded to the nearest hour). Length of stay is the total of wait and service times. Some longer stays are also approximated as 15 hou

> The distribution of the time until a Web site changes is important to Web crawlers that search engines use to maintain current information about Web sites. The distribution of the time until change (in days) of a Web site is approximated in the following

> Consider the visits that result in leave without being seen (LWBS) at an emergency department in Example 2.6. Assume that people independently arrive for service at hospital l. a. What is the probability that the fifth visit is the first one to LWBS? b.

> Suppose that lesions are present at 5 sites among 50 in a patient. A biopsy selects 8 sites randomly (without replacement). a. What is the probability that lesions are present in at least one selected site? b. What is the probability that lesions are pre

> A utility company might offer electrical rates based on time-of-day consumption to decrease the peak demand in a day. Enough customers need to accept the plan for it to be successful. Suppose that among 50 major customers, 15 would accept the plan. The u

> Suppose that a healthcare provider selects 20 patients randomly (without replacement) from among 500 to evaluate adherence to a medication schedule. Suppose that 10% of the 500 patients fail to adhere with the schedule. Determine the following: a. Probab

> a. For Exercise 3.7.1, calculate P(X = 1) and P(X = 4), assuming that X has a binomial distribution, and compare these results to results derived from the hypergeometric distribution. b. Use the binomial approximation to the hypergeometric distribution t

> A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day for sharpness. If any dull blade is found, the assembly is replaced with a newly sharpened set of blades. a. If 10 of the blades in an assembly are dull, wha

> A state runs a lottery in which six numbers are randomly selected from 40 without replacement. A player chooses six numbers before the state’s sample is selected. a. What is the probability that the six numbers chosen by a player match all six numbers in

> The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.05 flaw per square foot of plastic panel. Assume that an automobile interior contains 10 square feet of plastic panel. a. What i

> The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by the type of transformation completed: A naturalist randomly selects three leaves from this set without replacement. Determine the following proba

> Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards, and 20 are selected without replacement for functional testing. a. If 20 cards are defective, what is the probability that at

> A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure. a. If 10 men are selected randomly and tested for the marker, what is the probability that

> Suppose that X has a hypergeometric distribution with N = 10, n = 3, and K = 4. Sketch the probability mass function of X. Determine the cumulative distribution function for X.

> Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. Mean and variance of X

> A Web site randomly selects among 10 products to discount each day. The color printer of interest to you is discounted today. a. What is the expected number of days until this product is again discounted? b. What is the probability that this product is f

> In the process of meiosis, a single parent diploid cell goes through eight different phases. However, only 60% of the processes pass the first six phases and only 40% pass all eight. Assume that the results from each phase are independent. a. If the prob

> A trading company uses eight computers to trade on the New York Stock Exchange (NYSE). The probability of a computer failing in a day is 0.005, and the computers fail independently. Computers are repaired in the evening, and each day is an independent tr

> Assume that 20 parts are checked each hour and that X denotes the number of parts in the sample of 20 that require rework. Parts are assumed to be independent with respect to rework. a. If the percentage of parts that require rework remains at 1%, what i

> Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial blockage, disease, and infection. Assume that causes of he

> The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. a. What is the probability of no views in a minute? b. What is the probability of two or fewer views in 10 minutes? c. Does the answer to the previo

> A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Successwith any opponent is independent of previous encounters. Until defeated, the player continues to contest opponents. a. What is the

> Assume that each of your calls to a popular radio station has a probability of 0.02 of connecting, that is, of not obtaining a busy signal. Assume that your calls are independent. a. What is the probability that your first call that connects is your 10th

> In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1. People are assumed to be independent with respect to the gene. a. What is the probability

> Consider a sequence of independent Bernoulli trials with p = 0.2. a. What is the expected number of trials to obtain the first success? b. After the eighth success occurs, what is the expected number of trials to obtain the ninth success?

> Suppose that X is a negative binomial random variable with p = 0.2 and r = 4. Determine the following: a. E(X) b. P(X = 20) c. P(X = 19) d. P(X = 21) e. The most likely value for X

> Suppose that the random variable X has a geometric distribution with p = 0.5. Determine the following probabilities: a. P(X = 1) b. P(X = 4) c. P(X = 8) d. P(X ≤ 2) e. P(X > 2)

> Consider the lengths of stay at a hospital’s emergency department in Exercise 3.1.19. Assume that five persons independently arrive for service. a. What is the probability that the length of stay of exactly one person is less than or equal to 4 hours? b.

> This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 100 customer orders to fill. Each order requires one component part that is purchased from a supplier. However, typically, 2% of the components are id

> Because all airline passengers do not show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. a. What i

> Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 20 that require rework. A process problem is suspected if X exceeds its mean by more t

> In 1898, L. J. Bortkiewicz published a book titled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution wi

> A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replacement) 100,000 p

> Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial blockage, disease, and infection. Suppose that 20 patients

> Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose that 15 samples are studied and can be considered to be independent for mutation. Determine the following probabilities. a. No samples are mutated. b. At most one sample

> Amultiple-choice test contains 25 questions, each with four answers. Assume that a student just guesses on each question. a. What is the probability that the student answers more than 20 questions correctly? b. What is the probability that the student an

> An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the pro

> Determine the cumulative distribution function of a binomial random variable with n = 3 and p = 1/4.

> The random variable X has a binomial distribution with n = 10 and p = 0.5. Sketch the probability mass function of X. a. What value of X is most likely? b. What value(s) of X is(are) least likely? c. Repeat the previous parts with p = 0.01.

> The random variable X has a binomial distribution with n = 10 and p = 0.01. Determine the following probabilities. a. P(X = 5) b. P(X ≤ 2) c. P(X ≥ 9) d. P(3 ≤ X < 5)

> Let X be a binomial random variable with p = 0.1 and n = 10. Calculate the following probabilities. a. P(X ≤ 2) b. P(X > 8) c. P(X = 4) d. P(5 ≤ X ≤ 7)

> The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile. a. What is the probability that there are no cracks that require repair

> For each scenario (a)–(j), state whether or not the binomial distribution is a reasonable model for the random variable and why. State any assumptions you make. a. A production process produces thousands of temperature transducers. Let X denote the numbe

> Trees are subjected to different levels of carbon dioxide atmosphere with 6% of them in a minimal growth condition at 350 parts per million (ppm), 10% at 450 ppm (slow growth), 47% at 550 ppm (moderate growth), and 37% at 650 ppm (rapid growth). What are

> The range of the random variable X is [0, 1, 2, 3, x] where x is unknown. If each value is equally likely and the mean of X is 6, determine x.

> Each multiple-choice question on an examhas four choices. Suppose that there are 10 questions and the choice is selected randomly and independently for each question. Let X denote the number of questions answered correctly. Does X have a discrete uniform

> Suppose that 1000 seven-digit telephone numbers within your area code are dialed randomly. What is the probability that your number is called?

> Thickness measurements of a coating process are made to the nearest hundredth of amillimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for

> Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard deviation of the random variable Y = 5X and compare to the corresponding results for X.

> Let the random variable X have a discrete uniform distribution on the integers 0 ≤ x ≤ 99. Determine the mean and variance of X.

> Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 675 to 700 nm. a. What are the mean and variance of the wavelength distribution for this radiation? b. If t