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bayesian statistics an introduction
Statistics For Business And Economics 14th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann - Solutions
52. Bed and Breakfast Inns Website. The website for the Bed and Breakfast Inns of North America gets approximately seven visitors per minute. Suppose the number of website visitors per minute follows a Poisson probability distribution.a. What is the mean time between visits to the website?b. Show
51. Mean Time Between Failures. The mean time between failures (MTBF) is a common metric used to measure the performance of manufacturing systems. MTBF is the elapsed time between failures of a system during normal operations. The failures could be caused by broken machines or computer errors,
50. Playing Blackjack. A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average bet of $50. The player’s strategy provides a probability of .49 of winning on any one hand, and the player knows that there are 60 hands per
49. Multiple-Choice Exam. Consider a multiplechoice examination with 50 questions.Each question has four possible answers. Assume that a student who has done the homework and attended lectures has probability .75 of answering any question correctly.a. A student must answer 43 or more questions
48. Filling Weights. A machine fills containers with a particular product. The standard deviation of filling weights is known from past data to be 18 grams. If only 2% of the containers hold less than 540 grams, what is the mean filling weight for the machine?That is, what must m equal? Assume the
47. College Graduates Starting Salaries. According to the National Association of Colleges and Employers, the 2015 mean starting salary for new college graduates in health sciences was $51,541. The mean 2015 starting salary for new college graduates in business was $53,901 (National Association of
46. College Admissions Test Scores. Assume that the test scores from a college admissions test are normally distributed, with a mean of 450 and a standard deviation of 100.a. What percentage of the people taking the test score between 400 and 500?b. Suppose someone receives a score of 630. What
45. Wedding Costs. The XO Group Inc. conducted a 2015 survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is$29,858 (XO Group website). Assume that the cost of a wedding is normally distributed with a mean of $29,858 and a standard deviation
44. Service Contract Offer. Ward Doering Auto Sales is considering offering a special service contract that will cover the total cost of any service work required on leased vehicles.From experience, the company manager estimates that yearly service costs are approximately normally distributed, with
43. Amazon Alexa App Downloads. Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition.It can be used to perform daily tasks such as making todo lists, reporting the news and weather, and interacting with other
42. Bringing Items to a Pawnshop. One indicator of the level of economic hardship is the number of people who bring items to a pawnbroker. Assume that the number of people bringing items to a pawnshop per day in is normally distributed with a mean of 658.a. Suppose you learn that on 3% of the days,
41. Production Defects. Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process.Assume a production process produces items with a mean weight of 300 grams.Calculate the probability of a defect and the expected number
40. NCAA Scholarships. The NCAA estimates that the yearly value of a full athletic scholarship at instate public universities is $19,000. Assume the scholarship value is normally distributed with a standard deviation of $2100.a. For the 10% of athletic scholarships of least value, how much are they
39. Selling a House. A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but
38. Boston 911 Calls. The Boston Fire Department receives 911 calls at a mean rate of 1.6 calls per hour (Mass.gov website). Suppose the number of calls per hour follows a Poisson probability distribution.a. What is the mean time between 911 calls to the Boston Fire Department in minutes?b. Using
37. Patient Length of Stays in ICUs. Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse.Therefore, it is
36. Comcast Service Interruptions. Comcast Corporation is a global telecommunications company headquartered in Philadelphia, PA. Generally known for reliable service, the company periodically experiences unexpected service interruptions. When service interruptions do occur, Comcast customers who
35. Arrival of Vehicles at an Intersection. The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds.a. Sketch this exponential probability distribution.b. What is the probability that the arrival time between
34. Phone Battery Life. Battery life between charges for a certain mobile phone is 20 hours when the primary use is talk time, and drops to 7 hours when the phone is primarily used for Internet applications over a cellular network. Assume that the battery life in both cases follows an exponential
33. Consider the following exponential probability density function.f (x) 5 13 e2x /3 for x $ 0a. Write the formula for P(x ≤ x0).b. Find P(x ≤ 2).c. Find P(x ≥ 3).d. Find P(x ≤ 5).e. Find P(2 ≤ x ≤ 5).
32. Consider the following exponential probability density function.f (x) 5 18 e2x /8 for x $ 0a. Find P(x ≤ 6).b. Find P(x ≤ 4).c. Find P(x ≥ 6).d. Find P(4 ≤ x ≤ 6).
31. Visitors to Rocky Mountain National Park. Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance,
30. Playing Video Games. Suppose that of those individuals who play video and computer games, 18% are under 18 years old, 53% are 18–59 years old, and 29% are over 59 years old. Use the normal approximation of the binomial distribution to answer the questions below.a. For a sample of 800 people
29. Americans Who Believe Global Warming Is Occurring. According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening (American Psychological Association website).a. For a sample of 15 Americans, what is the probability that at least 12
28. Adults Who Smoke. Although studies continue to show smoking leads to significant health problems, 20% of adults in the United States smoke. Consider a group of 250 adults, and use the normal approximation of the binomial distribution to answer the questions below.a. What is the expected number
27. Assume a binomial probability distribution has p = .60 and n = 200.a. What are the mean and standard deviation?b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.c. What is the probability of 100 to 110 successes?d. What
26. A binomial probability distribution has p = .20 and n = 100.a. What are the mean and standard deviation?b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.c. What is the probability of exactly 24 successes?d. What is the
25. Household Income in Maryland. According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847 (Time.com website). Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of
24. Labor Day Travel Costs. The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend spend an average of $749.Assume that the amount spent is normally distributed with a standard deviation of $225.a. What is the probability of family expenses
23. Time to Complete Final Exam. The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.a. What is the probability of completing the exam in one hour or
22. Television Viewing. Suppose that the mean daily viewing time of television is 8.35 hours. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household.a. What is the probability that a household views
21. Mensa Membership. A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international highIQ society. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa?
20. Gasoline Prices. Suppose that the average price for a liter of gasoline in the United States is $0.99 and in Russia is $0.90. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $.07 in
19. Automobile Repair Costs. Automobile repair costs continue to rise with an average 2015 cost of $367 per repair (U.S. News & World Report website). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88.Answer the following questions about the cost
16. Given that z is a standard normal random variable, find z for each situation.a. The area to the right of z is .01.b. The area to the right of z is .025.c. The area to the right of z is .05.d. The area to the right of z is .10.b. What is the probability an individual largecap domestic stock fund
15. Given that z is a standard normal random variable, find z for each situation.a. The area to the left of z is .2119.b. The area between −z and z is .9030.c. The area between −z and z is .2052.d. The area to the left of z is .9948.e. The area to the right of z is .6915.
14. Given that z is a standard normal random variable, find z for each situation.a. The area to the left of z is .9750.b. The area between 0 and z is .4750.c. The area to the left of z is .7291.d. The area to the right of z is .1314.e. The area to the left of z is .6700.f. The area to the right of
13. Given that z is a standard normal random variable, compute the following probabilities.a. P(−1.98 ≤ z ≤ .49)b. P(.52 ≤ z ≤ 1.22)c. P(−1.75 ≤ z ≤ −1.04)
12. Given that z is a standard normal random variable, compute the following probabilities.a. P(0 ≤ z ≤ .83)b. P(−1.57 ≤ z ≤ 0)c. P(z > .44)d. P(z ≥ −.23)e. P(z < 1.20)f. P(z ≤ −.71)
11. Given that z is a standard normal random variable, compute the following probabilities.a. P(z ≤ −1.0)b. P(z ≥ −1)c. P(z ≥ −1.5)d. P(−2.5 ≤ z)e. P(−3 < z ≤ 0)
10. Draw a graph for the standard normal distribution. Label the horizontal axis at values of −3, −2, −1, 0, 1, 2, and 3. Then use the table of probabilities for the standard normal distribution inside the front cover of the text to compute the following probabilities.a. P(z ≤ 1.5)b. P(z
9. A random variable is normally distributed with a mean of m = 50 and a standard deviation of s = 5.a. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.6 shows that the normal curve almost touches the
8. Using Figure 6.6 as a guide, sketch a normal curve for a random variable x that has a mean of m = 100 and a standard deviation of s = 10. Label the horizontal axis with values of 70, 80, 90, 100, 110, 120, and 130.
7. Bidding on Land. Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.1 The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor’s bid x is a random variable that is uniformly distributed between
6. Daily Discretionary Spending. A Gallup Daily Tracking Survey found that the mean daily discretionary spending by Americans earning over $90,000 per year was $136 per day. The discretionary spending excluded home purchases, vehicle purchases, and regular monthly bills. Let x 5 the discretionary
5. Tesla Battery Recharge Time. The electricvehicle manufacturing company Tesla estimates that a driver who commutes 80 kilometers per day in a Model S will require a nightly charge time of around 1 hour and 45 minutes (105 minutes) to recharge the vehicle’s battery (Tesla company website).
4. Excel RAND Function. Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with
3. Cincinnati to Tampa Flight Time. Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.a. Show the graph of the probability density function
2. The random variable x is known to be uniformly distributed between 10 and 20.a. Show the graph of the probability density function.b. Compute P(x < 15).c. Compute P(12 ≤ x ≤ 18).d. Compute E(x).e. Compute Var(x).
1. The random variable x is known to be uniformly distributed between 1.0 and 1.5.a. Show the graph of the probability density function.b. Compute P(x = 1.25).c. Compute P(1.0 ≤ x ≤ 1.25).d. Compute P(1.20 < x < 1.5).
74. Business School Student GPAs. According to U.S. News & World Reports, 7 of the top 10 graduate schools of business have students with an average undergraduate grade point average (GPA) of 3.50 or higher. Suppose that we randomly select 2 of the top 10 graduate schools of business.a. What is the
73. Poker Hands. A deck of playing cards contains 52 cards, four of which are aces.What is the probability that the deal of a fivecard poker hand providesa. A pair of aces?b. Exactly one ace?c. No aces?d. At least one ace?
72. Bank Customer Arrivals. Customer arrivals at a bank are random and independent;the probability of an arrival in any oneminute period is the same as the probability of an arrival in any other oneminute period. Answer the following questions, assuming a mean arrival rate of three customers per
71. Small Business Failures. A regional director responsible for business development in the state of Pennsylvania is concerned about the number of small business failures. If the mean number of small business failures per month is 10, what is the probability that exactly 4 small businesses will
70. Production Process Breakdowns. A new automated production process averages 1.5 breakdowns per day. Because of the cost associated with a breakdown, management is concerned about the possibility of having three or more breakdowns during a day. Assume that breakdowns occur randomly, that the
69. Arrivals to a Car Wash. Cars arrive at a car wash randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 15 cars per hour. What is the probability that 20 or more cars will arrive during any given hour of
68. Choosing a Home Builder. Mahoney Custom Home Builders, Inc. of Canyon Lake, Texas, asked visitors to their website what is most important when choosing a home builder. Possible responses were quality, price, customer referral, years in business, and special features. Results showed that 23.5%
67. Americans with at Least a Two-Year Degree. PBS News Hour reported in 2014 that 39.4% of Americans between the ages of 25 and 64 have at least a twoyear college degree (PBS website). Assume that 50 Americans between the ages of 25 and 64 are selected randomly.a. What is the expected number of
66. Acceptance Sampling. Many companies use a quality control technique called acceptance sampling to monitor in com ing shipments of parts, raw materials, and so on. In the electronics industry, component parts are commonly shipped from suppliers in large lots. Inspection of a sample of n
65. Investing in the Stock Market. According to a 2017 Gallup survey, the percentage of individuals in the United States who are invested in the stock market by age is as shown in the following table (Gallup website).Age Range Percent of Individuals Invested in Stock Market 18 to 29 31 30 to 49 62
64. Giving up Technology. A Pew Research Survey asked adults in the United States which technologies would be “very hard” to give up. The following responses were obtained: Internet 53%, smartphone 49%, email 36%, and landline phone 28%(USA Today website).a. If 20 adult Internet users are
63. Creating a Diversified Investment Portfolio. The Knowles/Armitage (KA) group at Merrill Lynch advises clients on how to create a diversified investment portfolio. One of the investment alternatives they make available to clients is the All World Fund composed of global stocks with good dividend
62. Bookstore Customer Purchases. A bookstore at the HartsfieldJackson Airport in Atlanta sells reading materials (paperback books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.). A pointofsale terminal collects a variety of information about customer purchases. Shown
61. Expense Forecasts. The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13.Because the actual expenses are unknown, the following respective probabilities are assigned: .3, .2, .25, .05, and .2.a. Show the
60. Wait Times at Car Repair Garages. The Car Repair Ratings website provides consumer reviews and ratings for garages in the United States and Canada. The time customers wait for service to be completed is one of the categories rated. The following table provides a summary of the waittime ratings
59. Wind Conditions and Boating Accidents. The U.S. Coast Guard (USCG) provides a wide variety of information on boating accidents including the wind condition at the time of the accident. The following table shows the results obtained for 4401 accidents(USCG website,
58. TARP Funds. The Troubled Asset Relief Program (TARP), passed by the U.S.Congress in October 2008, provided $700 billion in assistance for the struggling U.S.economy. Over $200 billion was given to troubled financial institutions with the hope that there would be an increase in lending to help
57. Business Meal Reimbursement. The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a
56. Computer Company Benefits Questionnaire. Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 40 employees; the Hawaii plant has 20. A random sample of 10 employees is to be asked to fill out a benefits questionnaire.a. What
55. Playing Blackjack. Blackjack, or twentyone as it is frequently called, is a popular gambling game played in casinos. A player is dealt two cards. Face cards (jacks, queens, and kings) and tens have a point value of 10. Aces have a point value of 1 or 11. A 52card deck contains 16 cards with a
54. Online Holiday Shopping. More and more shoppers prefer to do their holiday shopping online from companies such as Amazon. Suppose we have a group of 10 shoppers; 7 prefer to do their holiday shopping online and 3 prefer to do their holiday shopping in stores. A random sample of 3 of these 10
51. Emails Received. According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day (Entrepreneur magazine website). Assume the number of emails received per hour follows a Poisson distribution and that
50. Tornadoes in Colorado. According to the National Oceanic and Atmospheric Administration(NOAA), the state of Colorado averages 18 tornadoes every June (NOAA website).(Note: There are 30 days in June.)a. Compute the mean number of tornadoes per day.b. Compute the probability of no tornadoes
49. Airport Passenger-Screening Facility. Airline passengers arrive randomly and independently at the passengerscreening facility at a major international airport. The mean arrival rate is 10 passengers per minute.a. Compute the probability of no arrivals in a oneminute period.b. Compute the
48. Motor Vehicle Accidents in New York City. In a oneyear period, New York City had a total of 11,232 motor vehicle accidents that occurred on Monday through Friday between the hours of 3 p.m. and 6 p.m. (New York State Department of Motor Vehicles website). This corresponds to mean of 14.4
47. 911 Calls. Emergency 911 calls to a small municipality in Idaho come in at the rate of one every 2 minutes.a. What is the expected number of 911 calls in one hour?b. What is the probability of three 911 calls in five minutes?c. What is the probability of no 911 calls in a fiveminute period?
46. Regional Airways Calls. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.a. Compute the probability of receiving three calls in a 5minute interval of time.b. Compute the probability of receiving exactly 10 calls in 15 minutes.c. Suppose no calls are
45. Consider a Poisson distribution with a mean of two occurrences per time period.a. Write the appropriate Poisson probability function.b. What is the expected number of occurrences in three time periods?c. Write the appropriate Poisson probability function to determine the probability of x
44. Consider a Poisson distribution with m = 3.a. Write the appropriate Poisson probability function.b. Compute f (2).c. Compute f (1).d. Compute P(x ≥ 2).
43. Tracked Emails. According to a 2017 Wired magazine article, 40% of emails that are received are tracked using software that can tell the email sender when, where, and on what type of device the email was opened (Wired magazine website). Suppose we randomly select 50 received emails.a. What is
42. State of the Nation Survey. Suppose a sample of 20 Americans is selected as part of a study of the state of the nation. The Americans in the sample are asked whether or not they are satisfied with the way things are going in the United States.a. Compute the probability that exactly 4 of the 20
41. Introductory Statistics Course Withdrawals. A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.a. Compute the probability that 2 or fewer will withdraw.b. Compute the probability that
40. Contributing to Household Income. Suppose that a random sample of fifteen 18to 34yearolds living with their parents is selected and asked if they contribute to household expenses.a. Is the selection of the fifteen 18to 34yearolds living with their parents a binomial experiment? Explain.b. If
39. Web Browser Market Share. Marketshareanalysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of 2014, Google’s Chrome browser exceeded a 20% market share for the first time, with a 20.37% share of the browser market
38. Detecting Missile Attacks. Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a .90 probability
37. Americans Saving for Retirement. According to a 2018 survey by Bankrate.com, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose that 15 adults in the United States are selected randomly.a. Is the selection of the 15 adults a binomial experiment? Explain.b.
36. Number of Defective Parts. When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.a. Describe the conditions under which this
35. Appeals for Medicare Service. The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medicare service.For this group, 40% of firstround appeals were successful (The Wall Street Journal).Suppose 10 firstround appeals have just
34. How Teenagers Listen to Music. For its Music 360 survey, Nielsen Co. asked teenagers and adults how each group has listened to music in the past 12 months. Nearly twothirds of U.S. teenagers under the age of 18 say they use Google Inc.’s videosharing site to listen to music and 35% of the
33. Consider a binomial experiment with n = 20 and p = .70.a. Compute f (12).b. Compute f (16).c. Compute P(x ≥ 16).d. Compute P(x ≤ 15).e. Compute E(x).f. Compute Var (x) and s.
32. Consider a binomial experiment with n = 10 and p = .10.a. Compute f (0).b. Compute f (2).c. Compute P(x ≤ 2).d. Compute P(x ≥ 1).e. Compute E(x).f. Compute Var(x) and s.
31. Consider a binomial experiment with two trials and p = .4.a. Draw a tree diagram for this experiment (see Figure 5.3).b. Compute the probability of one success, f (1).c. Compute f (0).d. Compute f (2).e. Compute the probability of at least one success.f. Compute the expected value, variance,
30. Investment Fund Including REITs. In addition to the information in exercise 29 on the S&P 500 and core bonds, J.P. Morgan Asset Management reported that the expected return for real estate investment trusts (REITs) during the same time period was 13.07% with a standard deviation of 23.17% (J.P.
29. Investment Portfolio of Index Fund and Core Bonds Fund. J.P. Morgan Asset Management publishes information about financial investments. Between 2002 and 2011, the expected return for the S&P 500 was 5.04% with a standard deviation of 19.45% and the expected return over that same period for a
28. Printer Manufacturing Costs. PortaCom has developed a design for a highquality portable printer. The two key components of manufacturing cost are direct labor and parts. During a testing period, the company has developed prototypes and conducted extensive product tests with the new printer.
27. Canadian Restaurant Ratings. The Chamber of Commerce in a Canadian city has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received a rating on a 3point scale on typical meal price (1 least expensive to 3 most expensive) and quality (1 lowest quality to 3
26. A person is interested in constructing a portfolio. Two stocks are being considered. Let x = percent return for an investment in stock 1, and y = percent return for an investment in stock 2. The expected return and variance for stock 1 are E(x) = 8.45% and Var(x) = 25.The expected return and
25. Given below is a bivariate distribution for the random variables x and y.f (x, y) x y.2 50 80.5 30 50.3 40 60a. Compute the expected value and the variance for x and y.b. Develop a probability distribution for x + y.c. Using the result of part (b), compute E(x + y) and Var (x + y).d. Compute
24. Computer Company Plant Expansion. The J. R. Ryland Computer Company is considering a plant expansion to enable the company to begin production of a new computer product. The company’s president must determine whether to make the expansion a mediumor largescale project. Demand for the new
23. Coffee Consumption. In Gallup’s Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was, “How many cups of coffee, if any, do you drink on an average day?” The following table shows the results
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