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mathematics
statistics

Questions and Answers of Statistics

Consider the situation of Example 17.2. The following data are taken on additional samples of size 5. Plot the X- and S-values on the X- and S-charts that are produced by the data in the preliminary
Samples of size 50 are taken every hour from a process producing a certain type of item that is either considered defective or not defective. Twenty samples are taken.(a) Construct a control chart
For the situation of Review Exercise 17.8, suppose that additional data are collected as follows. Does the process appear to be in control?Explain.
A quality control effort is being attempted for a process where large steel plates are being manufactured and surface defects are of concern. The goal is to set up a quality control chart for the
Estimate the proportion of defectives being produced by the machine! In Example 18.1 if the random sample of size 2 yields 2 defectives.
Let us assume that the prior distribution for the proportion y of drinks from a vending machine that overflow is. If 2 of the next 9 drinks from this machine overflow, find(a) The posterior
Repeat Exercise 18.2 when 1 of the: next 4 drinks overflows and the uniform prior distribution is π (p) = 10, 0.05 < p < 0.15.
The developer of a new condominium complex claims that 3 out of 5 buyers will prefer a two bedroom unit, while his banker claims that it would be more correct to say that 7 out of 10 buyers will
The burn time for the first stage of a rocket is a normal random variable with a standard deviation of 0.8 minute. Assume a normal prior distribution for p with a mean of 8 minutes and a standard
The daily profit, from a juice vending machine placed in an office building is a value of a normal random variable with unknown mean p and variance e r n. Of course, the mean will vary somewhat from
The mathematics department, of a large university is designing a placement test, to be given to the incoming freshman classes. Members of the: department feel that the average grade for this test
Suppose that In Example 18.6 the electrical firm does not have enough prior information regarding the population mean length of life to be able to assume a normal distribution for p. The firm
Suppose that the time to failure T of a certain hinge is an exponential random variable with probability density f (t) = ? c ?? t, t > 0. From prior experience we are led to believe that. 0 is a
Suppose that a sample consisting of 5, 6, 6, 7, 5, 6, 4, 9, 3, and 6 and comes from a Poisson population with mean A. Assume that the parameter A follows a gamma distribution with parameters (3, 2).
A random variable X follows a negative binomial distribution with parameters k = 5 and p (i.e., b*(x; 5, p)). Furthermore, we know that p follows a uniform distribution in the interval (0, 1). Find
Chris Lane, the head professional at Royal Oak Country Club, must develop a schedule of matches for the couples’ golf league that begins its season at 4:00 P.M. tomorrow. Eighteen couples signed up
Define the terms management science and operations research.
List and discuss the steps of the decision-making process.
Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this
Recall the production model from Section 1.3:Max 10xs.t.5x ≤ 40x ≥ 0Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours for each unit
Suppose we modify the production model from Section 1.3 to obtain the following mathematical model: Max 10x s.t.ax ≤ 40x ≥ 0Where a is the number of hours required for each unit produced. With
Aretail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Letx = units of product received from Kansas Cityy = units of product received from
For most products, higher prices result in a decreased demand, whereas lower prices result in an increased demand. Letd = annual demand for a product in unitsp = price per unitAssume that a firm
The O’Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a fixed
Micromedia offers computer training seminars on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting.
Eastman Publishing Company is considering publishing a paperback textbook on spreadsheet applications for business. The fixed cost of manuscript preparation, textbook design, and production setup is
Preliminary plans are underway for the construction of a new stadium for a major league baseball team. City officials question the number and profitability of the luxury corporate boxes planned for
Financial Analysts, Inc., is an investment firm that manages stock portfolios for a number of clients. Anew client requested that the firm handle an $80,000 portfolio. As an initial investment
Models of inventory systems frequently consider the relationships among a beginning inventory, a production quantity, a demand or sales, and an ending inventory. For a given production period j,
A firm has three investment alternatives. Payoffs are in thousands of dollars.a. Using the expected value approach, which decision is preferred?b. For the lottery having a payoff of $100,000 with
Alexander Industries is considering purchasing an insurance policy for its new office building in St. Louis, Missouri. The policy has an annual cost of $10,000. If Alexander Industries doesn't
In a certain state lottery, a lottery ticket costs $2. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies:a. A realistic
Two different routes accommodate travel between two cities. Route A normally takes 60 minutes and route B normally takes 45 minutes. If traffic problems are encountered on route A, the travel time
Three decision makers have assessed utilities for the following decision problem (payoff test in dollars):The indifference probabilities are as follows:a. Plot the utility function for money for each
In Problem 5, if P(s1) = 0.25, P(s2) = 0.50, and P(s3) = 0.25, find a recommended decision for each of the three decision makers. (For the same decision problem, different utilities can lead to
Suppose that the point spread for a particular sporting event is 10 points and that with this spread you are convinced you would have a 0.60 probability of winning a bet on your team. However, the
ALas Vegas roulette wheel has 38 different numerical values. If an individual bets on one number and wins, the payoff is 35 to 1.a. Show a payoff table for a $10 bet on one number for decision
A new product has the following profit projections and associated probabilities:Profit Probability$150,000 ....... 0.10$100,000 ........ 0.25$ 50,000 ....... 0.200 ....... 0.15-$ 50,000
A television network has been receiving low ratings for its programs. Currently, management is considering two alternatives for the Monday night 8:00 P.M.â€“9:00 P.M. time slot: a western with a
Consider the following two-person, zero-sum game. Identify the pure strategy. What is the value of thegame?
Two television stations in a market compete with each other for viewing audience. Local programming options for the 5:00 P.M. weekday time slot include a sitcom rerun, an early news program, or a
Two Indiana state senate candidates must decide which city to visit the day before the November election. The same four citiesâ€”Indianapolis, Evansville, Fort Wayne, and South Bendâ€”are
In Section 5.5, we showed the following two-person, zero-sum game had a mixed strategy:a. Use dominance to reduce the game to a 2 Ã— 2 game. Which strategies are dominated?b. Determine the optimal
In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the
Two companies compete for a share of the soft drink market. Each worked with an advertising agency in order to develop alternative advertising strategies for the coming year. A variety of television
Glenn Foreman, president of Oceanview Development Corporation, is considering submitting a bid to purchase property that will be sold by sealed bid at a county tax foreclosure. Glennâ€™s initial
John Campbell, an employee of Manhattan Construction Company, claims to have injured his back as a result of a fall while repairing the roof at one of the Eastview apartment buildings. He filed a
The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:a. Construct a decision tree for this problem.b. If the decision
Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table:a. If the decision maker knows nothing about the probabilities
Southland Corporation's decision to produce a new line of recreational products resulted in the need to construct either a small plant or a large plant. The best selection of plant size depends on
Amy Lloyd is interested in leasing a new Saab and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36-month lease with no down payment due at the
The following profit payoff table was presented in Problem 1. Suppose that the decision maker obtained the probability assessments P(s1) - 0.65, P(s2) - 0.15, and P(s3) = 0.20. SELF test Use the
Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the
Hudson Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or
The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives:a. Use graphical sensitivity analysis to determine the range of
Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the companyâ€™s new fleet of jet aircraft and a
Video Tech is considering marketing one of two new video games for the coming holiday season: Battle Pacific or Space Pirates. Battle Pacific is a unique game and appears to have no competition.
For the Pittsburgh Development Corporation problem in Section 4.3, the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. In
The distance from Potsdam to larger markets and limited air service have hindered the town in attracting new industry. Air Express, a major overnight delivery service, is considering establishing a
Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The
The following profit payoff table was presented in Problem 1:The probabilities for the states of nature are P(s1) = 0.65, P(s2) = 0.15, and P(s3) = 0.20.a. What is the optimal decision strategy if
The Lake Placid Town Council decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the appropriate size. Many
Consider a variation of the PDC decision tree shown in Figure. The company must first decide whether to undertake the market research study. If the market research study is conducted, the outcome
Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingwayâ€™s president is concerned because the probability that
Dante Development Corporation is considering bidding on a contract for a new office building complex. Figure shows the decision tree prepared by one of Danteâ€™s analysts. At node 1, the company
Hale€™s TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may
Embassy Publishing Company received a six-chapter manuscript for a new college textbook. The editor of the college division is familiar with the manuscript and estimated a 0.65 probability that the
A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor
Lawson€™s Department Store faces a buying decision for a seasonal product for which demand can be high, medium, or low. The purchaser for Lawson€™s can order 1, 2, or 3 lots of
Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. The prior probabilities are P(s1) = 0.2, P(s2) = 0.5, and P(s3) = 0.3. With sample information I,
To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. Rona preferred to use the somewhat longer but more consistent Queen City Avenue. Although Jerry preferred
The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent
Hamilton County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed,
A study examined waiting times in the X-ray department for a hospital in Jacksonville, Florida. A clerk recorded the number of patients waiting for service at 9:00 A.M. on 20 consecutive days and
A company that franchises coffee houses conducted taste tests for a new coffee product. The company prepared four blends and randomly chose individuals to do a taste test and state which of the four
A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection
The availability of venture capital provided a big boost in funds available to companies in recent years. According to Venture Economics (Investor’s Business Daily, April 28, 2000), 2374 venture
Strom Construction made a bid on two contracts. The owner identified the possible outcomes and subjectively assigned the following probabilities.a. Are these valid probability assignments? Why or why
A sample of 100 customers of Montana Gas and Electric resulted in the following frequency distribution of monthly charges. Amount ($) Number0–49 ......... 1350–99
Suppose that a sample space has five equally likely experimental outcomes: E1, E2, E3, E4, E5. LetA = {E1, E2}B = {E3, C4}C = {E2, E3, E5}a. Find P(A), P(B), and P(C).b. Find P(A ( B). Are A and B
Data on the 30 largest bond funds provided one-year and five-year percentage returns for the period ending March 31, 2000 (The Wall Street Journal, April 10, 2000). Suppose we consider a one-year
A pharmaceutical company conducted a study to evaluate the effect of an allergy relief medicine; 250 patients with symptoms that included itchy eyes and a skin rash received the new drug. The results
A quality control specialist has sampled 25 widgets from the production line. A widget can have minor or major defects. Of the 25 sampled widgets, 4 have minor defects and 2 have major defects. What
Let A be an event that a person’s primary method of transportation to and from work is an automobile and B be an event that a person’s primary method of transportation to and from work is a bus.
For two events A and B, P(A) = 0.5, P(B) = 0.60, and P(A ( B) = 0.40.a. Find P(A | B).b. Find P(B | A).c. Are A and B independent? Why or why not?
A survey of MBA students obtained the following data on â€œStudentsâ€™ first reason for application to the school in which they matriculated.â€a. Develop a joint probability table using
The checking accounts of Sun Bank are categorized by the age of account and the account balance. Auditors will select accounts at random from the following 1000 accounts (numbers in the table are the
Due to rising health insurance costs, 43 million people in the United States go without health insurance (Time, December 1, 2003). Sample data representative of the national health insurance coverage
A purchasing agent placed a rush order for a particular raw material with two different suppliers, A and B. If neither order arrives in four days the production process must be shut down until at
A study of job satisfaction was conducted for four occupations: cabinetmaker, lawyer, physical therapist, and systems analyst. Job satisfaction was measured on a scale of 0â€“ 00. The data
In the evaluation of a sales training program, a firm discovered that of 50 salespeople receiving a bonus last year, 20 had attended a special sales training program. The firm employs 200
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 6% of the employees had lost-time accidents last year. Management believes
The prior probabilities for events A1, A2, and A3 are P(A1) = 0.20, P(A2) = 0.50, and P(A3) = 0.30. The conditional probabilities of event B given A1, A2, and A3 are P(B | A1) = 0.50, P(B | A2) =
A consulting firm submitted a bid for a large research project. The firm’s management initially felt there was a 50/50 chance of getting the bid. However, the agency to which the bid was submitted
Companies that do business over the Internet can often obtain probability information about Web site visitors from previous Web sites visited. For instance, the Q.M. in Action, Internet Marketing,
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.P(high-quality oil) = 0.50P(medium-quality oil) = 0.20P(no oil) = 0.30a.
Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars accounted for 18% of the vehicles on the road, but accidents involving small cars led to 11,898 fatalities
The Wayne Manufacturing Company purchases a certain part from suppliers A, B, and C. Supplier A supplies 60% of the parts, B 30%, and C 10%. The quality of parts varies among the suppliers, with A,
Bayesâ€™ theorem and conditional probability can be used in medical diagnosis. Prior probabilities of diseases are based on the physicianâ€™s assessment of factors such as geographic
Specialty Toys, Inc., sells a variety of new and innovative children’s toys and believes that the preholiday season is the best time to introduce a new toy. Many families use this time to look for

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