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essential statistics
Statistics Data Analysis And Decision Modeling 5th International Edition James R. Evans - Solutions
10. An information system consultant is bidding on a project that involves some uncertainty. Based on past experience, if all went well (probability 0.1), the project would cost $1.2 million to complete. If moderate debugging were required (probability 0.7), the project would probably cost $1.4
9. An investor can invest in three highly speculative opportunities.The returns and standard deviations are given here.Expected Return Standard Deviation Investment A $50,000 $25,000 Investment B $40,000 $24,000 Investment C $30,000 $10,000 Based on the return to risk, which of these is the best
8. Suppose that a car rental agency offers insurance for a week that will cost $10 per day. A minor fender bender will cost $1,500, while a major accident might cost$15,000 in repairs. Without the insurance, you would be personally liable for any damages. What should you do? Clearly, there are two
7. The DoorCo Corporation is a leading manufacturer of garage doors. All doors are manufactured in their plant in Carmel, Indiana, and shipped to distribution centers or major customers. DoorCo recently acquired another manufacturer of garage doors, Wisconsin Door, and is considering moving its
6. Slaggert Systems is considering becoming certified to the ISO 9000 series of quality standards. Becoming certified is expensive, but the company could lose a substantial amount of business if its major customers suddenly demand ISO certification and the company does not have it. At a management
5. Your neighbor’s son or daughter is starting to look at college choices and he has asked you to help make a good choice. You have suggested that a scoring model would be useful in helping to narrow down the choices. Develop a scoring model on a spreadsheet by defining a set of attributes and
4. The cost accountant of a large truck fleet is evaluating options for dealing with a large volume of flat tires.Currently, the company repairs tires on the open market by having the driver take the flat tire to the nearest tire dealer. Last year, this cost an average of $30 per flat tire. The
3. The finance committee at Olson, Inc. has 13 proposed new technology projects under consideration. Estimated initial investments, external revenues, and internal cost reductions are:Project Investment Revenue Impact Cost Reduction A1 $175,600.00 $— $200,358.00 A2 $126,512.00 $422,580.00
2. An e-commerce firm is developing a new application.Financial analysts have estimated the expenses and revenues over the next five years:Month Development Expense Operating Expense Revenue Initial investment $50,000.00 $— $—Year 1 $10,000.00 $10,000.00 $5,000.00 Year 2 $— $10,000.00
1. A company has estimated that a proposed $10,000 investment will generate $3,250 for each of the next four years.a. What is the payback period?b. If the required rate of return is 9%, use internal rate of return to determine whether or not this proposal should be accepted.
14. What is a decision tree? How is Bayes’s rule useful in implementing a decision tree?
13. Explain the concept of utility theory and how utilities can be assessed.
12. What is a risk profile and how can it be used in conjunction with the solution of a decision tree?
11. Discuss the exponential utility function and its characteristics.
10. What are the implications of the “flaw of averages”?
9. Explain the concepts of expected value of sample information and expected value of perfect information.
8. Provide examples of when expected value decision making is appropriate and when it is not.
7. Explain how the standard deviation, coefficient of variation, skewness, and kurtosis of the distribution of outcomes provide information about risk.
6. Summarize the decision strategies that model different risk behaviors for making decisions involving uncertainty.
5. Describe how to model decisions involving uncertainty.
4. What are the characteristics of a scoring model?
3. Describe the decisions involving mutually exclusive alternatives.
2. Describe the decisions involving non-mutually exclusive alternatives.
1. Describe the decisions involving single alternatives.
1. J&G Bank receives a large number of credit card applications each month, an average of 30,000 with a standard deviation of 4,000, normally distributed. Approximately 60% of them are approved, but this typically varies between 50% and 70%. Each customer charges a total of$2,000, normally
23. Arbino Mortgage Company obtains business from direct marketing letters signed by a fictitious loan officer named Jackson Smith. The percentages of interested responses from Jackson Smith letters are triangular with parameters 1%, 1.2%, and 2%. Of those responding, the percentage of respondents
22. For the nonprofit ballet company in Problem 17 of Chapter 9 , assume following percentages of donors and gift levels:Gift Level Amount Number of Gifts Benefactor $10,000 1–3 Philanthropist $5,000 3–7 Producer’s Circle $1,000 16–25 Director’s Circle $500 31–40 Principal $100 5–7%
21. For the stock broker problem described in Problem 16 in Chapter 9 , assume that among the qualified clients, half will invest between $2,000 and $10,000, 25% will invest between $10,000 and $25,000, 15% will invest between$25,000 and $50,000, and the remainder will invest between $50,000 and
20. A software development project consists of six activities.The activities and their predecessor relationships are given in the following table. The worksheet Problem 20 in the Excel file Chapter 10 Problem Data provides a sample of times in weeks for activities A, B, E, and F from 40 past
19. Jennifer Bellin (Problem 18 in Chapter 9 ) believes that the activity times for her project are uncertain. The worksheet Problem 19 in the Excel file Chapter 10 Problem Data contains information about the activities, predecessors, and activity times in the worksheet Problem 19 .Assume a
18. A plant manager is considering investing in a new$30,000 machine. Use of the new machine is expected to generate a cash flow of about $8,000 per year for each of the next five years. However, the cash flow is uncertain, and the manager estimates that the actual cash flow will be normally
17. A sporting goods store orders ski jackets in the summer before the winter season. Each jacket costs $80 and sells for $200. Any not sold by March are discounted 75%. Demand depends on the weather. The distribution of demand is triangular (but must be whole numbers)with a minimum of 40, a
16. The data in the Excel file Technical Support Data represent a sample of the number of minutes spent resolving customer support issues for a computer manufacturer.Use the Crystal Ball distribution fitting procedure to find the best-fitting distribution for these data.
15. The data in the Excel file Real Estate Sales represent the annual sales of 100 branch offices of a national real estate company. Use the Crystal Ball distribution fitting procedure to find the best-fitting distribution for these data.
14. Refer back to the college admission director scenario(Problem 20 in Chapter 9 ). Develop a spreadsheet model and apply Crystal Ball tools to make a recommendation on how many scholarships to offer.
13. Review the MBA’s retirement planning situation described in Chapter 9 ( Figure 9.16 ). Modify the spreadsheet to include the assumptions that the annual raise each year is triangular with a minimum of 1%, a most likely value of 3%, and a maximum value of 5%, and that the investment return
12. For the Hyde Park Surgery Center scenario described in Problem 19 in Chapter 9 , suppose that the following assumptions are made: The number of patients served the first year is uniform between 1,300 and 1,700; the growth rate for subsequent years is triangular with parameters (5%, 8%, 9%), and
11. Develop a Crystal Ball model for Koehler Vision Associates (KVA) in Problem 15 of Chapter 9 with the following assumptions: The weekly demand averages 175, but anywhere between 10% and 20% of prospective patients fail to show up or cancel their exam at the last minute. Determine the best level
10. Develop a Crystal Ball model for MasterTech with the fol lowing assumptions (all other data are as described in Problem 13, Chapter 9 ): Net sales are uniformly distributed between $600,000 and $1,200,000. Cost of sales is normally distributed, with a mean of $540,000 and a standard deviation
9. Develop a Crystal Ball model for a three-year financial analysis of total profit based on the following data and information. Sales volume in the first year is estimated to be 100,000 units and is projected to grow at a rate that is normally distributed with a mean of 7% per year and a standard
8. Develop a Crystal Ball model for the garage band in Problem 11 in Chapter 9 with the following assumptions.The expected crowd is normally distributed with a mean of 3,000 and a standard deviation of 400 (minimum of 0). The average expenditure on concessions is also normally distributed with mean
7. The manager of the apartment complex in Problem 9 of Chapter 9 believes that the number of units rented during any given month has a triangular distribution with minimum 30, most likely 34, and maximum 40.Operating costs follow a normal distribution with mean$15,000 and a standard deviation of
6. Using the generic profit model developed in the section Logic and Business Principles in Chapter 9 , develop a financial simulation model for a new product proposal and construct a distribution of profits under the following assumptions: Price is fixed at $1,000. Unit costs are unknown and
5. For the Airline Pricing Model in Chapter 9 , suppose that the fixed cost is triangular with a minimum of $80,000, most likely value of $90,000, and maximum value of$95,000. Also assume that the values of the slope and intercept in the demand function are uniformly distributed plus or minus 5%
4. For the Outsourcing Decision Model , suppose that the demand volume is lognormally distributed with a mean of 1,500 and a standard deviation of 500. What is the distribution of the cost differences between manufacturing in-house and purchasing? What decision would you recommend? Define both the
3. For the Moore Pharmaceuticals model, suppose that analysts have made the following assumptions:R&D costs: Triangular($500, $700, $800) in millions of dollars Clinical trials costs: Triangular($135, $150, $160) in millions of dollars Market size: Normal(2,000,000, 250,000)Market share in year 1:
2. The Miller–Orr model in finance addresses the problem of managing its cash position by purchasing or selling securities at a transaction cost in order to lower or raise its cash position. That is, the firm needs to have enough cash on hand to meet its obligations, but does not want to maintain
1. Financial analysts often use the following model to characterize changes in stock prices:Pt = P0e1m-0.5s22t+sZ2t where P0 = current stock price Pt = price at time t m = mean (logarithmic) change of the stock price per unit time s = (logarithmic) standard deviation of price change Z = standard
6. How can an analyst obtain the sampling distributions of standard descriptive statistical measures such as mean, median, variance, standard deviation, etc. in Crystal Ball ?
5. Explain the types of charts that Crystal Ball provides for analyzing simulation results and how they may be used to provide useful information to a decision maker.
4. How do we define uncertain model inputs in Crystal Ball ?
3. Explain the terms assumption, forecast , and decision as used in Crystal Ball .
2. What is a Monte Carlo simulation? How is it helpful in the analysis of risk?
1. What is meant by risk? What does risk analysis aim to do?
7. Explain your results and analysis in a memo to the vice president of operations.
6. Conduct what-if analyses to study the sensitivity of total cost to changes in the model parameters.
5. Use Solver to verify your result.
4. Use data tables to find an approximate order quantity that results in the smallest total cost.
3. Implement your model on a spreadsheet.
2. Develop mathematical functions that compute the annual ordering cost and annual holding cost based on average inventory held throughout the year in order to arrive at a model for total cost.
1. Define the data, uncontrollable inputs, and decision variables that influence total inventory cost.
20. The admissions director of an engineering college has$500,000 in scholarships each year from an endowment to offer to high-achieving applicants. The value of each scholarship offered is $25,000 (thus, 20 scholarships are offered). The benefactor who provided the money would like to see all of
19. The Hyde Park Surgery Center specializes in high-risk cardiovascular surgery. The center needs to forecast its profitability over the next three years to plan for capital growth projects. For the first year, the hospital anticipates serving 1,500 patients, which is expected to grow by 8% per
18. Jennifer Bellin has been put in charge planning her company’s annual leadership conference. The dates of the conference have been determined by her company’s execu tive team. The table below contains information about the activities, predecessors, and activity times (in days):Activity
17. The director of a nonprofit ballet company in a mediumsized U.S. city is planning its next fund-raising campaign.In recent years, the program has found the following percentages of donors and gift levels:Develop a spreadsheet model to calculate the total amount donated based on this information
16. A stockbroker calls on potential clients from referrals.For each call, there is a 15% chance that the client will decide to invest with the firm. Sixty percent of those interested are not found to be qualified based on the brokerage firm’s screening criteria. The remaining are qualified. Of
15. Koehler Vision Associates (KVA) specializes in laserassisted corrective eye surgery. Prospective patients make appointments for prescreening exams to determine their candidacy for the surgery, and if they qualify, the $300 charge is applied as a deposit for the actual procedure.The weekly
14. A local pharmacy orders 15 copies of a monthly maga- zine. Depending on the cover story, demand for the magazine varies. The pharmacy purchases the maga- zines for $2.25 and sells them for $5.00. Any magazines left over at the end of the month are donated to hospitals and other health care
13. MasterTech is a new software company that develops and markets productivity software for municipal government applications. In developing their income statement, the following formulas are used:Gross profit = Net sales - Cost of sales Net operating profit = Gross profit - Administrative
12. For a new product, sales volume in the first year is estimated to be 100,000 units and is projected to grow at a rate of 7% per year. The selling price is $10, and will increase by $0.50 each year. Per-unit variable costs are $3, and annual fixed costs are $200,000. Perunit costs are expected
11. A garage band wants to hold a concert. The expected crowd is 3,000. The average expenditure on concessions is $15. Tickets sell for $10 each, and the band’s profit is 80% of the gate, along with concession sales, minus a fixed cost of $10,000. Develop a spreadsheet model to find their
10. Think of any retailer that operates many stores throughout the country, such as Old Navy, Hallmark Cards, or Radio Shack, to name just a few. The retailer is often seeking to open new stores and needs to evaluate the profitability of a proposed location that would be leased for five years. An
9. Monthly rent at an apartment complex is $500. Operating costs average $15,000 per month regardless of the number of units rented. Construct a spreadsheet model to determine the profit if 35 units are rented. The manager has observed that the number of units rented during any given month varies
8. Develop a spreadsheet model to determine how much a person or a couple can afford to spend on a house. 2 Lender guidelines suggest that the allowable monthly housing expenditure should be no more than 28% of monthly gross income. From this, you must subtract total nonmortgage housing expenses,
7. Each worksheet in the Excel file LineFit Data contains a set of data that describes a functional relationship between the dependent variable y and the independent variable x . Construct a line chart of each data set, and use the Add Trendline tool to determine the best-fitting functions to model
6. A forest fire is burning down a narrow valley three miles wide at a speed of 40 feet per minute. The fire can be contained by cutting a firebreak through the forest across the valley. It takes 30 seconds for one person to clear one foot of the firebreak. The value of lost timber is $4,000 per
5. The Radio Shop sells two popular models of portable sport radios: model A and model B . The sales of these products are not independent of each other (in economics, we call these substitutable products, because if the price of one increases, sales of the other will increase).The store wishes to
4. A manufacturer is preparing to set the price on a new action game. Demand is thought to depend on the price and is represented by the model:D = 2,000 - 3.5P The accounting department estimates that the total costs can be represented by:C = 5,000 + 4.1Da. Develop a model for the total profit and
3. Total marketing effort is a term used to describe the critical decision factors that affect demand: price, advertising, distribution, and product quality. Define the variable x to represent total marketing effort. A typical model that is used to predict demand as a function of total marketing
2. Four key marketing decision variables are price ( P ), advertising ( A ), transportation ( T ), and product quality( Q ). Consumer demand ( D ) is influenced by these variables. The simplest model for describing demand in terms of these variables is:D = k - pP + aA + tT + qQ where k, p,a, t, and
1. A supermarket has been experiencing long lines during peak periods of the day. The problem is noticeably worse on certain days of the week, and the peak periods are sometimes different according to the day of the week. There are usually enough workers on the job to open all cash registers. The
9. Discuss the inherent conflict between the realism and complexity of a model. Explain the meaning of the term validity in this connection.
8. What is meant by What-if Analysis and Sensitivity Analysis ?
7. What is meant by verification? What is spreadsheet engineering?
6. Summarize the important knowledge that you need to successfully build good decision models.
5. How does model analysis help managers make a decision?
4. Explain the purpose of Solver and what type of decision model it is used for.
3. Describe how to use Excel data tables, Scenario Manager , and goal seek tools to analyze decision models.
2. What are optimization models?
1. What is a model? When is a model called a decision model?
14. Refer to the data in the worksheet Problem 9. Suppose that the specification limits for the process are 25 (lower)and 40 (upper). Compute the process capability index and interpret. Eliminate any out-of-control points first, if any are found.
13. Refer to the data in the worksheet Problem 8. Suppose that the specification limits for the process are 90 (lower)and 110 (upper). Compute the process capability index and interpret. Eliminate any out-of-control points first, if any are found.
12. A warehouse double-checks the accuracy of its order fulfillment process each day. The data in the worksheet Problem 12 shows the number of orders processed each day and the number of inaccurate orders found. Construct a p -chart for these data and interpret the results.
11. A manufacturer of high-quality medicinal soap advertises its product as 99 and 44/100% free of medically offensive pollutants. Twenty-five samples of 100 bars of soap were gathered at the beginning of each hour of production;the numbers of bars not meeting this requirement are given in the
10. Hunter Nut Company produces cans of mixed nuts, advertised as containing no more than 20% peanuts.Hunter Nut Company wants to establish control limits for their process to ensure meeting this requirement.They have taken 30 samples of 144 cans of nuts from the production process at periodic
9. Compute control limits for x - and R -charts for the data in the worksheet Problem 9. Construct and interpret the charts.
8. Compute control limits for x - and R -charts for the data in the worksheet Problem 8. Construct and interpret the charts.
7. Suppose that the standard deviation of a machine manufacturing process is 0.24 inch, and while the upper and lower specification limits are 4.2 and 2.6 inches. What is the process capability index?
6. Suppose that an operation produces output with a standard deviation of 0.5 pounds, with an upper specification limit of 9 pounds and a lower specification limit of 4 pounds. Compute the process capability index.
5. If 30 samples of 100 items are run through a battery of tests, and 120 of the 3000 items are defective, calculate the upper and lower control limits for a p -chart.
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