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mathematics
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Questions and Answers of Statistics

All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and
Refer again to the Lake City Regional Airport described in Problem 18. When the security level is raised to high, the service rate for processing passengers is reduced to 2 passengers per minute at
A Florida coastal community experiences a population increase during the winter months, with seasonal residents arriving from northern states and Canada. Staffing at a local post office is often in a
Refer to the Agan Interior Design situation in Problem 11. Agan’s management would like to evaluate two alternatives:• Use one consultant with an average service time of 8 minutes per
A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per
The following cost information is available for the fast-food franchise in Problem 22:• Customer waiting time is valued at $25 per hour to reflect the fact that waiting time is costly to the
Patients arrive at a dentist’s office with an arrival rate of 2.8 patients per hour. The dentist can treat patients at a service rate of 3 patients per hour. A study of patient waiting times shows
A study of the multiple-channel food-service operation at the Red Birds baseball park shows that the average time between the arrival of a customer at the food-service counter and his or her
Manning Autos operates an automotive service counter. While completing the repair work, Manning mechanics arrive at the company’s parts department counter, with an arrival rate of four per hour.
Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company’s office can be described by a Poisson probability
Jobs arrive randomly at a particular assembly plant; assume that the arrival rate is five jobs per hour. Service times (in minutes per job) do not follow the exponential probability distribution. Two
The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three jobs per 8-hour day. The company’s repair facility is a
A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the
Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies
City Cab, Inc., uses two dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to City Cab use a common telephone number. When both dispatchers are
Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to eight. The president of Kolkmeyer asked for a
Five administrative assistants use an office copier. The average time between arrivals for each assistant is 40 minutes, which is equivalent to an arrival rate of 1/40 = 0.025 arrival per minute. The
Schips Department Store operates a fleet of 10 trucks. The trucks arrive at random times throughout the day at the store’s truck dock to be loaded with new deliveries or to have incoming shipments
Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 A.M. to 11:00 A.M. time period, calls to the reservation agent occur randomly at an average
Office Equipment, Inc. (OEI), leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair
Consider the PortaCom project discussed in Section 16.1.a. An engineer on the product development team believes that first-year sales for the new printer will be 20,000 units. Using estimates of $45
The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is $30,000. The variable cost for the product
a. Use the random numbers 0.3753, 0.9218, 0.0336, 0.5145, and 0.7000 to generate five simulated values for the PortaCom direct labor cost per unit.b. Use the random numbers 0.6221, 0.3418, 0.1402,
To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Attendance is limited to 25 individuals per seminar. Each
The price of a share of a particular stock listed on the New York Stock Exchange is currently $39. The following probability distribution shows how the price per share is expected to change over a
The Statewide Auto Insurance Company developed the following probability distribution for automobile collision claims paid during the past year:Payment ($) Probability0 ............ 0.83500
A variety of routine maintenance checks are made on commercial airplanes prior to each takeoff. A particular maintenance check of an airplane’s landing gear requires an average of 15 minutes of a
Baseballâ€™s World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves are in the World Series and that the first two games
A project has four activities (A, B, C, and D) that must be performed sequentially. The probability distributions for the time required to complete each of the activities are as follows:a. Provide
Blackjack, or 21, is a popular casino game that begins with each player and the dealer being dealt two cards. The value of each hand is determined by the point total of the cards in the hand. Face
Over a five-year period, the quarterly change in the price per share of common stock for a major oil company ranged from 28% to 112%. A financial analyst wants to learn what can be expected for price
The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. Probability distributions for the purchase cost, the labor cost, and the
Develop a worksheet simulation for the following problem. The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of
Use a worksheet to simulate the rolling of dice. Use the VLOOKUP function as described in Appendix 16.1 to select the outcome for each die. Place the number for the first die in column B and the
Strassel Investors buys real estate, develops it, and resells it for a profit. Anew property is available, and Bud Strassel, the president and owner of Strassel Investors, believes it can be sold for
Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is
A building contractor is preparing a bid on a new construction project. Two other contractors will be submitting bids for the same project. Based on past bidding practices, bids from the other
Develop your own worksheet for the Butler inventory simulation model shown in Figure. Suppose that management prefers not to charge for loss of goodwill. Run the Butler inventory simulation model
In preparing for the upcoming holiday season, Mandrell Toy Company designed a new doll called Freddy. The fixed cost to produce the doll is $100,000. The variable cost, which includes material,
South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 30 passengers, and the airline makes a $100 profit on each passenger on the flight. When South Central
Develop your own waiting line simulation model for the Hammondsport Savings Bank problem. Assume that a new branch is expected to open with interarrival times uniformly distributed between 0 and 4
The Burger Dome waiting line model in Section 16.1 studies the waiting time of customers at its fast-food restaurant. Burger Dome€™s single-channel waiting line system has an arrival rate
Telephone calls come into an airline reservations office randomly at the mean rate of 15 calls per hour. The time between calls follows an exponential distribution with a mean of 4 minutes. When the
What will your portfolio be worth in 10 years? In 20 years? When you stop working? The Human Resources Department at Tri-State Corporation was asked to develop a financial planning model that would
Harbor Dunes Golf Course was recently honored as one of the top public golf courses in South Carolina. The course, situated on land that was once a rice plantation, offers some of the best views of
County Beverage Drive-Thru, Inc., operates a chain of beverage supply stores in Northern Illinois. Each store has a single service lane; cars enter at one end of the store and exit at the other end.
Open the file Nowlin Plastics. Recall that we have modeled total profit for the product CD-50 in this spreadsheet. Suppose we have a second product called a CD-100, with the following
Open the file Foster Rev. Select cells B6:E8 and name these cells Shipping-Cost. Select cells B19:E21 and name these cells Units-Shipped. Use these names in the sum-product function in cell C14 to
Open the file Nowlin Plastics. Recall that we have modeled total profit for the product CD-50 in this spreadsheet. Modify the spreadsheet to take into account production capacity and forecasted
Cox Electric makes electronic components and has estimated the following for a new design of one of its products: Fixed Cost = $10,000 Revenue per unit = $0.65 Material cost
Return to the Cox Electric spreadsheet. Build a table of profits based on different volume levels by doing the following: In cell C15, enter a volume of 20,000. Look at each formula in row 14 and
Open the workbook OM455. Save the file under a new name, OM455COUNTIF.xls. Suppose we wish to automatically count the number of each letter grade.a. Begin by putting the letters A, B, C, D, and F in
Open the workbook OM455. Save the file under a new name, OM4555Revised.xls. Suppose we wish to use a more refined grading system, as shown below:Update the file to use this more refined grading
Newton Manufacturing produces scientific calculators. The models are N350, N450, and the N900. Newton has planned its distribution of these products around eight customer zones: Brazil, China,
Consider the transportation model given in the Excel file Williamson. It is a model that is very similar to the Foster Generators model. Williamson produces a single product and has plants in
A sample of temperature measurements in a furnace yielded a sample average (◦F) of 835.00 and a sample standard deviation of 10.5. Using the results from Exercise 6-90, what are the sample average
Consider the sample x1, x2, . . . , xn with sample x mean and sample standard deviation s. Let zi = (xi – x)/s, i = 1, = 2, . . . , n. What are the values of the sample mean and sample standard
An experiment to investigate the survival time in hours of an electronic component consists of placing the parts in a test cell and running them for 100 hours under elevated temperature conditions.
Suppose that we have a sample x1, x2, . . ., xn and we have calculated xn and sn2 for the sample. Now an (n + 1)st observation becomes available. Let xn + 1 and sn2 + 1 be the sample mean and sample
Suppose that the data are arranged in increasing order, T% of the observations are removed from each end and the sample mean of the remaining numbers is calculated. The resulting quantity is called a
Suppose that the sample size n is such that the quantity nT/100 is not an integer. Develop a procedure for obtaining a trimmed mean in this case
In some data sets, a transformation by some mathematical function applied to the original data, such as √y or log y, can result in data that are simpler to work with statistically than the original
In 1879, A. A. Michelson made 100 determinations of the velocity of light in air using a modification of a method proposed by the French physicist Foucault. He made the measurements in five trials of
In 1789, Henry Cavendish estimated the density of the earth by using a torsion balance. His 29 measurements follow, expressed as a multiple of the density of water.(a) Calculate the sample mean,
Consider the airfoil data in Exercise 6-12. Subtract 30 from each value and then multiply the resulting quantities by 10. Now compute s2 for the new data. How is this quantity related to s2 for the
Consider the quantity.For what value of a is this quantityminimized?
Using the results of Exercise 6-87, which of the two quantities will be smaller, provided that ?
Let Yi = a + bxi, i = 1, 2, .. , n, where a and b are nonzero constants. Find the relationship between x and y, and between sx and sy.
What is the difference between quantitative and qualitative analysis? Give several examples.
Define quantitative analysis. What are some of the organizations that support the use of the scientific approach?
What is the quantitative analysis process? Give several examples of this process.
Briefly trace the history of quantitative analysis. What happened to the development of quantitative analysis during World War II?
Give some examples of various types of models. What is a mathematical model? Develop two examples of mathematical models.
List some sources of input data.
What is implementation, and why is it important?
Describe the use of sensitivity analysis and post optimality analysis in analyzing the results.
Why do you think many quantitative analysts don't like to participate in the implementation process? What could be done to change this attitude?
Should people who will be using the results of a new quantitative model become involved in the technical aspects of the problem-solving procedure?
C. W. Churchman once said that "mathematics ...tends to lull the unsuspecting into believing that he who thinks elaborately thinks well." Do you think that the best QA models are the ones that are
What is the break-even point? What parameters are necessary to find it?
Gina Fox has started her own company, Foxy Shirts, which manufactures imprinted shirts for special occasions.Since she has just begun this operation, she rents the equipment from a local printing
Ray Bond sells handcrafted yard decorations at county fairs. The variable cost to make these is $20 each, and he sells them for $50. The cost to rent a booth at the fair is $150. How many of these
Ray Bond, from Problem 1-15, is trying to find a new supplier that will reduce his variable cost of production to $15 per unit. If he was able to succeed in reducing this cost, what would the
Katherine D'Ann is planning to finance her college education by selling programs at the football games for State University. There is a fixed cost of $400 for printing these programs, and the
Katherine D'Ann, from Problem 1-17, has become concerned that sales may fall, as the team is on a terrible losing streak, and attendance has fallen off.In fact, Katherine believes that she will sell
Farris Billiard Supply sells all types of billiard equipment, and is considering manufacturing their own brand of pool cues. Mysti Farris, the production manager, is currently investigating the
Mysti Farris (see Problem 1-19) is considering raising the selling price of each cue to $50 instead of $40. If this is done while the costs remain the same, what would the new break-even point be?
Mysti Farris (see Problem 1-19) believes that there is a high probability that 120 pool cues can be sold if the selling price is appropriately set. What selling price would cause the break-even point
Golden Age Retirement Planners specializes in providing financial advice for people planning for a comfortable retirement. The company offers seminars on the important topic of retirement
A couple of entrepreneurial business students at State University decided to put their education into practice by developing a tutoring company for business students. While private tutoring was
Southwestern University (SWU), a large state college in Stephenville, Texas, 30 miles southwest of the Dallas/Fort Worth metroplex, enrolls close to 20,000 students. The school is the dominant force
Give an example of a good decision that you made that resulted in a bad outcome. Also give an example of a bad decision that you made that had a good outcome. Why was each decision good or bad?
Describe what is involved in the decision process.
What is an alternative? What is a state of nature?
Discuss the differences among decision making under certainty, decision making under risk, and decision making under uncertainty.
What techniques are used to solve decision-making problems under uncertainty? Which technique results in an optimistic decision? Which technique results in a pessimistic decision?
Define opportunity loss. What decision-making criteria are used with an opportunity loss table?
What information should be placed on a decision tree?
Describe how you would determine the best decision using the EMV criterion with a decision tree.
What is the difference between prior and posterior probabilities?

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