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Applied Statistics In Business And Economics 4th Edition David Doane, Lori Seward - Solutions

Until 2005, the UPC bar code had 12 digits (09). The first six digits represent the manufacturer, the next five represent the product, and the last is a check digit. (a) How many different manufacturers could be encoded? (b) How many different products could be encoded? (c) In 2005, the EAN bar
Bob has to study for four final exams: accounting (A), biology (B), communications (C), and drama (D).(a) If he studies one subject at a time, in how many different ways could he arrange them?(b) List the possible arrangements in the sample space.
Find the following permutations nPr:a. n = 8 and r = 3.b. n = 8 and r = 5.c. n = 8 and r = 1.d. n = 8 and r = 8.
Find the following combinations nCr:a. n = 8 and r = 3.b. n = 8 and r = 5.c. n = 8 and r = 1.d. n = 8 and r = 8.
A real estate office has 10 sales agents. Each of four new customers must be assigned an agent. (a) Find the number of agent arrangements where order is important.(b) Find the number of agent arrangements where order is not important.(c) Why is the number of combinations smaller than the number of
M&Ms are blended in a ratio of 13 percent brown, 14 percent yellow, 13 percent red, 24 per- cent blue, 20 percent orange, and 16 percent green. Suppose you choose a sample of two M&Ms at random from a large bag. (a) Show the sample space. (b) What is the probability that both are brown? (c) Both
Bob owns two stocks. There is an 80 percent probability that stock A will rise in price, while there is a 60 percent chance that stock B will rise in price. There is a 40 percent chance that both stocks will rise in price. Are the stock prices independent?
A study showed that trained police of officers can detect a lie 65 percent of the time, based on controlled studies of videotapes with real-life lies and truths. What are the odds in favor of a lie being detected?
The probability that a 2004 Audi A4 is stolen is 1.2645 percent. Find the odds against the theft of a 2004 Audi A4. Round your answer to the nearest whole number. (www.nhtsa.gov/theft)
The probability of being struck by lightning is .00016. Find the odds against being struck by lightning. Round your answer to the nearest whole number. (www.lightningsafety.noaa.gov)
A certain model of remote-control Stanley garage door opener has nine binary (off/on) switches. The homeowner can set any code sequence. (a) How many separate codes can be programmed? (b) If you try to use your door opener on 1,000 other garages, how many times would you expect to succeed?
(a) In a certain state, license plates consist of three letters (AZ) followed by three digits (09). How many different plates can be issued? (b) If the state allows any six-character mix (in any order) of 26 letters and 10 digits, how many unique plates are possible? (c) Why might some
Bob, Mary, and Jen go to dinner. Each orders a different meal. The waiter forgets who ordered which meal, so he randomly places the meals before the three diners. Let C be the event that a diner gets the correct meal and let N be the event that a diner gets an incorrect meal. Enumerate the sample
An MBA program offers seven concentrations: accounting (A), finance (F), human resources (H), information systems (I), international business (B), marketing (M), and operations management (O). Students in the capstone business policy class are assigned to teams of three. In how many different ways
A poker hand (5 cards) is drawn from an ordinary deck of 52 cards. Find the probability of each event, showing your reasoning carefully.a. The first four cards are the four aces.b. Any four cards are the four aces.
Two cards are drawn from an ordinary deck of 52 cards. Find the probability of each event, showing your reasoning carefully. a. Two aces. b. Two red cards. c. Two red aces. d. Two honor cards (A, K, Q, J, 10).
A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour fight is .02. What is the probability that(a) Both will fail?(b) Neither will fail?(c) One or the other will fail? Show all steps carefully.
A couple has two children. What is the probability that both are boys, given that the first is a boy?
A turboprop aircraft has two attitude gyros, driven from independent electrical sources. On a six-hour fight, assume the probability of failure of each attitude gyroscope is 0.0008. Does this achieve " five-nines" reliability (i.e., a probability of at least 0.99999 that not all gyros will fail)?
Which are likely to be independent events? For those you think are not, suggest reasons why. a. Gender of two babies born consecutively in a hospital. b. Car accident rates and the driver's gender. c. Phone call arrival rates at a university admissions office and time of day.
A web server hosting company advertises 99.999 percent guaranteed network uptime.(a) How many independent network servers would be needed if each has 99 percent reliability?(b) If each has 90 percent reliability?
The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. (b) Why might the assumption of
If there are two riders on a city bus, what is the probability that no two have the same birthday? What if there are 10 riders? 20 riders? 50 riders?
How many riders would there have to be on a bus to yield(a) A 50 percent probability that at least two will have the same birthday?(b) A 75 percent probability?
Four students divided the task of surveying the types of vehicles in parking lots of four different shopping malls. Each student examined 100 cars in each of three large suburban Detroit malls and one suburban Jamestown, New York, mall, resulting in the 5 3 4 contingency table shown below.(a)
Refer to the contingency table shown below.(a) Calculate each probability (ivi) and explain in words what it means.(b) Do you see evidence that smoking and race are not independent? Explain.(c) Do the smoking rates shown here correspond to your experience?i. P(S)ii. P(W )iii. P(S | W)iv. P(S |
Analysis of forecasters' interest rate predictions over the period 19821990 was intended to see whether the predictions corresponded to what actually happened. The 2 3 2 contingency table below shows the frequencies of actual and predicted interest rate movements.(a) Calculate each probability
High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. Cockpit noise in a jet aircraft is mostly due to airflow at hundreds of miles per hour. This 3 Ã— 3 contingency table shows 61 observations of data collected by an airline
A test for ovarian cancer has a 5 percent rate of false positives and a 0 percent rate of false negatives. On average, 1 in every 2,500 American women over age 35 actually has ovarian cancer. If a woman over 35 tests positive, what is the probability that she actually has cancer? Hint: Make a
A biometric security device using fingerprints erroneously refuses to admit 1 in 1,000 authorized persons from a facility containing classified information. The device will erroneously admit 1 in 1,000,000 unauthorized persons. Assume that 95 percent of those who seek access are authorized. If the
Dolon Web Security Consultants requires all job applicants to submit to a test for illegal drugs. If the applicant has used illegal drugs, the test has a 90 percent chance of a positive result. If the applicant has not used illegal drugs, the test has an 85 percent chance of a negative result.
Which of the following could not be probability distributions? Explain.
Use Excel to generate 100 random integers from(a) 1 through 2, inclusive;(b) 1 through 5, inclusive; and(c) 0 through 99, inclusive.(d) In each case, write the Excel formula.(e) In each case, calculate the mean and standard deviation of the sample of 100 integers you generated, and compare them
The probability that a bakery customer will order a birthday cake is .04.(a) What is the expected number of customers until the first birthday cake is ordered?(b) What is the probability the first cake order occurs within the first 20 customers?
In a certain city, 8 percent of the cars have a burned-out headlight.(a) What is the expected number that must be inspected before the first one with a burned-out headlight is found?(b) What is the probability of finding the first one within the first five cars?
For patients aged 81 to 90, the probability is .07 that a coronary bypass patient will die soon after the surgery.(a) What is the expected number of operations until the first fatality?(b) What is the probability of conducting 20 or more operations before the first fatality? Hint: Use the CDF.
Historically, 5 percent of a mail-order firm's regular charge-account customers have an incorrect current address in the firm's computer database.(a) What is the expected number of customer orders until the first one with an incorrect current address places an order?(b) What is the probability of
The weight of a Los Angeles Lakers basketball player averages 233.1 pounds with a standard deviation of 34.95 pounds. To express these measurements in terms a European would understand, we could convert from pounds to kilograms by multiplying by .4536.(a) In kilograms, what is the mean?(b) In
The Rejuvo Corp. manufactures granite countertop cleaner and polish. Quarterly sales Q is a random variable with a mean of 25,000 bottles and a standard deviation of 2,000 bottles. Variable cost is $8 per unit and fixed cost is $150,000. (a) Find the mean and standard deviation of Rejuvo's total
A manufacturer fills one-gallon cans (3,785 ml) on an assembly line in two independent steps. First, a high-volume spigot injects most of the paint rapidly. Next, a more precise but slower spigot tops off the can. The ll amount in each step is a normally distributed random variable. For step one,
A manufacturing project has five independent phases whose completion must be sequential. The time to complete each phase is a random variable. The mean and standard deviation of the time for each phase are shown below.(a) Find the expected completion time.(b) Make a 2-sigma interval around the mean
In September, demand for industrial furnace boilers at a large plumbing supply warehouse has a mean of 7 boilers with a standard deviation of 2 boilers. The warehouse pays a unit cost of $2,225 per boiler plus a fee of $500 per month to act as dealer for these boilers. Boilers are sold for $2,850
De ne a Bernoulli variable for (a) Guessing on a true-false exam question; (b) Checking to see whether an ER patient has health insurance; (c) Dialing a talkative friend's cell phone; (d) Going on a 10-day diet.
A certain outpatient medical procedure has five steps that must be performed in sequence.(a) Assuming that the time (in minutes) required for each step is an independent random variable, find the mean and standard deviation for the total time.(b) Why might the assumption of independence be doubtful?
Malaprop Ltd. sells two products. Daily sales of product A have a mean of $70 with a standard deviation of $10, while sales of product B have a mean of $200 with a standard deviation of $30. Sales of the products tend to rise and fall at the same time, having a positive covariance of 400. (a) Find
(a) In the previous exercise, suggest the approximate probability of success in each scenario. (b) Is success a desirable or undesirable thing in each of these scenarios? (a) Guessing on a true-false exam question; (b) Checking to see whether an ER patient has health insurance; (c) Dialing a
List the X values that are included in each italicized event. a. You can miss at most 2 quizzes out of 16 quizzes (X = number of missed quizzes). b. You go to Starbuck's at least 4 days a week (X = number of Starbuck's visits). c. You are penalized if you have more than 3 absences out of 10
Find the mean and standard deviation for each binomial random variable:a. n = 8, π = .10b. n = 10, π = .40c. n = 12, π = .50
Find the mean and standard deviation for each binomial random variable:a. n = 30, π = .90b. n = 80, π = .70c. n = 20, π = .80
Calculate each binomial probability:a. X = 5, n = 9, π = .90b. X = 0, n = 6, π = .20c. X = 9, n = 9, π = .80
Calculate each binomial probability:a. X = 2, n = 8, π = .10b. X = 1, n = 10, π = .40c. X = 3, n = 12, π = .70
Calculate each compound event probability: a. X < 3, n = 8, = .20 b. X < .7, n = 10, = .50 c. X < 3, n = 6, = .70
On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.(a) Calculate the expected value and standard deviation
Calculate each compound event probability: a. X ≤ 10, n = 14, π = .95 b. X > 2, n = 5, π = .45 c. X ≤ 1, n = 10, π = .15
Calculate each binomial probability: a. More than 10 successes in 16 trials with an 80 percent chance of success. b. At least 4 successes in 8 trials with a 40 percent chance of success. c. No more than 2 successes in 6 trials with a 20 percent chance of success.
Calculate each binomial probability: a. Fewer than 4 successes in 12 trials with a 10 percent chance of success. b. At least 3 successes in 7 trials with a 40 percent chance of success. c. At most 9 successes in 14 trials with a 60 percent chance of success.
In the Ardmore Hotel, 20 percent of the customers pay by American Express credit card.(a) Of the next 10 customers, what is the probability that none pay by American Express?(b) At least two?(c) Fewer than three?(d) What is the expected number who pay by American Express?(e) Find the standard
Historically, 5 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database.(a) What is the probability that none of the next 12 repeat customers who call will have an incorrect address?(b) One customer?(c) Two customers?(d) Fewer
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .38. Use Excel to find the probability that in a sample of 5 customers (a) None of the 5 will order a nonalcoholic beverage, (b) At least 2 will, (c) Fewer than 4 will, (d) All 5 will order a
J.D. Power and Associates says that 60 percent of car buyers now use the Internet for re- search and price comparisons.(a) Find the probability that in a sample of 8 car buyers, all 8 will use the Internet;(b) At least 5;(c) More than 4.(d) Find the mean and standard deviation of the probability
There is a 70 percent chance that an airline passenger will check bags. In the next 16 passengers that check in for their fight at Denver International Airport, find the probability that(a) All will check bags;(b) Fewer than 10 will check bags;(c) At least 10 will check bags.
Police records in the town of Saratoga show that 15 percent of the drivers stopped for speeding have invalid licenses. If 12 drivers are stopped for speeding, find the probability that(a) None will have an invalid license;(b) Exactly one will have an invalid license;(c) at least 2 will have invalid
Find the mean and standard deviation for each Poisson:a. λ = 1.0b. λ = 2.0c. λ = 4.0
On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below.(a) Calculate the mean and standard deviation.(b) Describe the shape of this
Find the mean and standard deviation for each passion:a. λ = 9.0b. λ = 12.0c. λ = 7.0
Calculate each passion probability:a. P(X = 6), λ = 4.0b. P(X = 10), λ = 12.0c. P(X = 4), λ = 7.0
Calculate each passion probability:a. P(X = 2), λ = .01b. P(X = 1), λ = 2.2c. P(X = 3), λ = 1.6
Calculate each compound event probability:a. P (X ≤ 3), λ = 4.3b. P (X > 7), λ = 5.2c. P (X < 3), λ = 2.7
Calculate each poisson probability:a. P (X ≤ 3), λ = 4.3b. P (X > 7), λ = 5.2c. P (X < 2), λ = 3.7
Calculate each Poisson probability:a. More than 10 arrivals with λ = 8.0.b. No more than 5 arrivals with λ = 4.0.c. At least 2 arrivals with λ = 5.0
Calculate each Poisson probability: a. Fewer than 4 arrivals with λ = 5.8. b. At least 3 arrivals with λ = 4.8. c. At most 9 arrivals with λ = 7.0.
According to J.D. Power and Associates' 2006 Initial Quality Study, consumers reported on average 1.7 problems per vehicle with new 2006 Volkswagens. In a randomly selected new Volkswagen, find the probability of(a) At least one problem;(b) No problems;(c) More than three problems.(d) Construct the
At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 1.5 per day on a typical Wednesday. Let X be the number of cancellations on a particular Wednesday. (a) Justify the use of the Poisson model.(b) What is the probability that no cancellations will occur on a
The average number of items (such as a drink or dessert) ordered by a Noodles & Company customer in addition to the meal is 1.4. These items are called add-ons. De ne X to be the number of add-ons ordered by a randomly selected customer.(a) Justify the use of the Poisson model.(b) What is the
Pepsi and Mountain Dew products sponsored a contest giving away a Lamborghini sports car worth $215,000. The probability of winning from a single bottle purchase was .00000884. Find the expected value. Show your calculations clearly. (Data are from J. Paul Peter and Jerry C. Olson, Consumer
(a) Why might the number of yawns per minute by students in a warm classroom not be a Poisson event? (b) Give two additional examples of events per unit of time that might violate the assumptions of the Poisson model, and explain why.
An experienced order taker at the L.L. Bean call center has a .003 chance of error on each keystroke (i.e., 5 .003). In 500 keystrokes, find the approximate probability of (a) At least two errors and (b) Fewer than four errors. (c) Is the Poisson approximation justified?
The probability of a manufacturing defect in an aluminum beverage can is .00002. If 100,000 cans are produced, find the approximate probability of (a) At least one defective can and (b) Two or more defective cans. (c) Is the Poisson approximation justified?
Three percent of the letters placed in a certain postal drop box have incorrect postage. Suppose 200 letters are mailed.(a) For this binomial, what is the expected number with incorrect postage?(b) For this binomial, what is the standard deviation?(c) What is the approximate probability that at
In a string of 100 Christmas lights, there is a .01 chance that a given bulb will fail within the first year of use (if one bulb fails, it does not affect the others). Find the approximate probability that two or more bulbs will fail within the first year.
The probability that a passenger's bag will be mishandled on a U.S. airline is .0046. During spring break, suppose that 500 students y from Minnesota to various southern destinations. (a) What is the expected number of mishandled bags? (b) What is the approximate probability of no mishandled bags?
(a) State the values that X can assume in each hypergeometric scenario.(b) Use the hypergeometric PDF formula to find the probability requested.(c) Check your answer by using Excel.i. N = 10, n = 3, s = 4, P(X = 3)ii. N = 20, n = 5, s = 3, P(X = 2)iii. N = 36, n = 4, s = 9, P(X = 1)iv. N = 50, n =
ABC Warehouse has eight refrigerators in stock. Two are side-by-side models and six are top-freezer models.(a) Using Excel, calculate the entire hypergeometric probability distribution for the number of top-freezer models in a sample of four refrigerators chosen at ran- dom.(b) Make an Excel graph
A statistics textbook chapter contains 60 exercises, 6 of which are essay questions. A student is assigned 10 problems. De ne X to be the number of essay questions the student receives.(a) Use Excel to calculate the entire hypergeometric probability distribution for X.(b) What is the probability
Fifty employee travel expense reimbursement vouchers were led last quarter in the finance department at Ramjac Corporation. Of these, 20 contained errors. A corporate auditor inspects five vouchers at random. Let X be the number of incorrect vouchers in the sample.(a) Use Excel to calculate the
Student Life Insurance Company wants to offer an insurance plan with a maximum claim amount of $5,000 for dorm students to cover theft of certain items. Past experience suggests that the probability of a maximum claim is .01. What premium should be charged if the company wants to make a pro t of
A medical laboratory receives 40 blood specimens to check for HIV. Eight actually contain HIV. A worker is accidentally exposed to five specimens.(a) Use Excel to calculate the entire hypergeometric probability distribution.(b) What is the probability that none contained HIV?(c) Fewer than
(a) Check whether the binomial approximation is acceptable in each of the following hypergeometric situations. (b) Find the binomial approximation (using Appendix A) for each probability requested. (c) Check the accuracy of your approximation by using Excel to find the actual hypergeometric
Two hundred employee travel expense reimbursement vouchers were led last year in the - finance department at Ramjac Corporation. Of these, 20 contained errors. A corporate auditor audits a sample of five vouchers. Let X be the number of incorrect vouchers in the sample.(a) Justify the use of the
A law enforcement agency processes 500 background checks for rearms purchasers. Fifty applicants are convicted felons. Through a clerk's error, 10 applicants are approved without checking for felony convictions.(a) Justify the use of the binomial approximation.(b) What is the probability that none
Four hundred automobiles are to be inspected for California emissions compliance. Of these, 320 actually are compliant but 80 are not. A random sample of 6 cars is chosen.(a) Justify the use of the binomial approximation.(b) What is the probability that all are compliant?(c) At least 4?
Find each geometric probability. a. P(X = 5) when π = .50 b. P(X = 3) when π = .25 c. P (X = 4) when π = .60
In the Ardmore Hotel, 20 percent of the guests (the historical percentage) pay by American Express credit card. (a) What is the expected number of guests until the next one pays by American Express credit card? (b) What is the probability that the first guest to use an American Express is within
In a certain Kentucky Fried Chicken franchise, half of the customers request "crispy" instead of "original," on average.(a) What is the expected number of customers before the next customer requests "crispy"?(b) What is the probability of serving more than 10 customers before the first request for
The height of a Los Angeles Lakers basketball player averages 6 feet 7.6 inches (i.e., 79.6 inches) with a standard deviation of 3.24 inches. To convert from inches to centimeters, we multiply by 2.54.(a) In centimeters, what is the mean?(b) In centimeters, what is the standard deviation?(c) Which
July sales for Melodic Kortholt, Ltd., average μ1 = $9,500 with σ12 5 $1,250. August sales average μ2 = $7,400 with σ22 = $1,425. September sales average μ3 $8,600 with σ32 = $1,610. (a) Find the mean and standard deviation of total sales for the third quarter. (b) What assumptions are you
A lottery ticket has a grand prize of $28 million. The probability of winning the grand prize is .000000023. Based on the expected value of the lottery ticket, would you pay $1 for a ticket? Show your calculations and reasoning clearly.
The mean January temperature in Fort Collins, CO, is 37.1o F with a standard deviation of 10.3o F. Express these Fahrenheit parameters in degrees Celsius using the transformation C = 5/9F – 17.78.
There are five accounting exams. Bob's typical score on each exam is a random variable with a mean of 80 and a standard deviation of 5. His final grade is based on the sum of his exam scores. (a) Find the mean and standard deviation of Bob's point total assuming his performances on exams are
The probability that a 30-year-old white male will live another year is .99863. What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy? (Data are from National Center for Health Statistics, National Vital Statistics Reports 59, no. 4 [March

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