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statistical techniques in business
Statistical Techniques in Business and Economics 17th edition Douglas A. Lind, William G Marchal - Solutions
Twenty-two percent of all light emitting diode (LED) displays are manufactured by Samsung. What is the probability that in a collection of three independent LED HDTV purchases, at least one is a Samsung?
The probability a D-Link network server is down is .05. If you have three independent servers, what is the probability that at least one of them is operational?
You take a trip by air that involves three independent flights. If there is an 80% chance each specific leg of the trip is on time, what is the probability all three flights arrive on time?
Two components, A and B, operate in series. Being in series means that for the system to operate, both components A and B must work. Assume the two components are independent. What is the probability the system works under these conditions? The probability A works is .90 and the probability B
A puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column. The puzzle asks the reader to match each president with his vice president. If you make the matches randomly,
A computer password consists of four characters. The characters can be one of the 26 letters of the alphabet. Each character may be used more than once. How many different passwords are possible?
The state of Maryland has license plates with three numbers followed by three letters. How many different license plates are possible?
Reynolds Construction Company has agreed not to erect all “look-alike” homes in a new subdivision. Five exterior designs are offered to potential home buyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways can the
A new chewing gum has been developed that is helpful to those who want to stop smoking. If 60% of those people chewing the gum are successful in stopping smoking, what is the probability that in a group of four smokers using the gum at least one quits smoking?
Recent surveys indicate 60% of tourists to China visited the Forbidden City, the Temple of Heaven, the Great Wall, and other historical sites in or near Beijing. Forty percent visited Xi’an with its magnificent terra-cotta soldiers, horses, and chariots, which lay buried for over 2,000 years.
Several years ago, Wendy’s Hamburgers advertised that there are 256 different ways to order your hamburger. You may choose to have, or omit, any combination of the following on your hamburger: mustard, ketchup, onion, pickle, tomato, relish, mayonnaise, and lettuce. Is the advertisement correct?
Two boxes of men’s Old Navy shirts were received from the factory. Box 1 contained 25 mesh polo shirts and 15 Super-T shirts. Box 2 contained 30 mesh polo shirts and 10 Super-T shirts. One of the boxes was selected at random, and a shirt was chosen at random from that box to be inspected. The
A company is creating three new divisions and seven managers are eligible to be appointed head of a division. How many different ways could the three new heads be appointed?
An overnight express company must include five cities on its route. How many different routes are possible, assuming that it does not matter in which order the cities are included in the routing?
A telephone number consists of seven digits, the first three representing the exchange. How many different telephone numbers are possible within the 537 exchange?
A survey of 34 students at the Wall College of Business showed the following majors:Accounting..................................... 10Finance............................................. 5Economics........................................ 3Management....................................
The events A and B are mutually exclusive. Suppose P(A) = .30 and P(B) = .20. What is the probability of either A or B occurring? What is the probability that neither A nor B will happen?
The events X and Y are mutually exclusive. Suppose P(X) = .05 and P(Y) = .02. What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen?
Suppose the probability you will get an A in this class is .25 and the probability you will get a B is .50. What is the probability your grade will be above a C?
The probabilities of the events A and B are .20 and .30, respectively. The probability that both A and B occur is .15. What is the probability of either A or B occurring?
Wendy€™s offers eight different condiments (mustard, catsup, onion, mayonnaise, pickle, lettuce, tomato, and relish) on hamburgers. A store manager collected the following information on the number of condiments ordered and the age group of the customer.What can you conclude
The manager of Information Services at Wilkin Investigations, a private investigation firm, is studying the relationship between the age (in months) of a combination printer, copier, and fax machine and its monthly maintenance cost. For a sample of 15 machines, the manager developed the following
Listed below is the number of car thefts in a large city over the last week. Calculate the coefficient of skewness using both methods. 13 7 8 3 8 3 12 3
Listed below is the amount of commissions earned last month for the eight members of the sales staff at Best Electronics. Calculate the coefficient of skewness using both methods. 1,718.4 1,721.2 980.9 1,036.5 1,409.0 1,456.4 1,099.5 1,153.9
Walter Gogel Company is an industrial supplier of fasteners, tools, and springs. The amounts of its invoices vary widely, from less than $20.00 to more than $400.00. During the month of January the company sent out 80 invoices. Here is a box plot of these invoices. Write a brief report summarizing
The following box plot shows the number of daily newspapers published in each state and the District of Columbia. Write a brief report summarizing the number published. Be sure to include information on the values of the first and third quartiles, the median, and whether there is any skewness. If
In a study of the gasoline mileage of model year 2016 automobiles, the mean miles per gallon was 27.5 and the median was 26.8. The smallest value in the study was 12.70 miles per gallon, and the largest was 50.20. The first and third quartiles were 17.95 and 35.45 miles per gallon, respectively.
Determine the median and the first and third quartiles in the following data. 6.02 7.30 11.86 7.99 12.71 5.24 6.67 10.39 7.59 12.22 8.03 13.07 8.35 13.59 8.81 13.89 9.45 15.42 10.37 9.61
Determine the median and the first and third quartiles in the following data. 47 49 49 53 54 55 55 59 46 51 54
Describe the differences between a histogram and a stem-and-leaf display.
Bidwell Electronics Inc. recently surveyed a sample of employees to determine how far they lived from corporate headquarters. The results are shown below. Compute the mean and the standard deviation. Distance (mlles) Frequency O up to 5 4 2.5 5 up to 10 15 7.5 10 up to 15 27 12.5 15 up to 20 20 up
The Kentucky Derby is held the first Saturday in May at Churchill Downs in Louisville, Kentucky. The race track is one and one-quarter miles. The following table shows the winners since 1990, their margin of victory, the winning time, and the payoff on a $2 bet.a. Determine the mean and median for
The enrollments of the 13 public universities in the state of Ohio are listed below.University of Akron.......................................................................... 26,106Bowling Green State University..................................................... 18,864Central State
The first Super Bowl was played in 1967. The cost for a 30-second commercial was $42,000. The cost of a 30-second commercial for Super Bowl 50 was $4.6 million. What was the geometric mean rate of increase for the 50 year period?
The American Diabetes Association recommends a blood glucose reading of less than 130 for those with Type 2 diabetes. Blood glucose measures the amount of sugar in the blood. Below are the readings for February for a person recently diagnosed with Type 2 diabetes.a. What is the arithmetic mean
Rolland Poust is a sophomore in the College of Business at Scandia Tech. Last semester he took courses in statistics and accounting, 3 hours each, and earned an A in both. He earned a B in a 5-hour history course and a B in a 2-hour history of jazz course. In addition, he took a 1 hour course
The Split-A-Rail Fence Company sells three types of fence to homeowners in suburban Seattle, Washington. Grade A costs $5.00 per running foot to install, Grade B costs $6.50 per running foot, and Grade C, the premium quality, costs $8.00 per running foot. Yesterday, Split-A-Rail installed 270 feet
A recent study of the laundry habits of Americans included the time in minutes of the wash cycle. A sample of 40 observations follows. Determine the mean and the median of a typical wash cycle. 35 39 40 37 33 33 37 37 37 36 39 37 33 38 35 28 32 46 39 37 37 39 38 38 32 44 39 31 28 36 31 31 29 34 35
The Citizens Banking Company is studying the number of times the ATM located in a Loblaws Supermarket at the foot of Market Street is used per day. Following are the number of times the machine was used daily over each of the last 30 days. Determine the mean number of times the machine was used per
A sample of households that subscribe to United Bell Phone Company for landline phone service revealed the following number of calls received per household last week. Determine the mean and the median number of calls received. 52 43 42 41 46 39 30 32 38 18 12 37 46 34
Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22.a. Compute the mean and median number of apples in a bag.b. Verify that Σ(x − x̅) = 0.
When we compute the mean of a frequency distribution, why do we refer to this as an estimated mean?
The following graph portrays the distribution of the number of spicy chicken sandwiches sold at a nearby Wendy€™s for the last 141 days. The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67.If we use the Empirical Rule, sales will be between what two
According to Chebyshev’s theorem, at least what percent of any set of observations will be within 1.8 standard deviations of the mean?
The mean income of a group of sample observations is $500; the standard deviation is $40. According to Chebyshev’s theorem, at least what percent of the incomes will lie between $400 and $600?
The personnel files of all eight employees at the Pawnee location of Acme Carpet Cleaners Inc. revealed that during the last 6-month period they lost the following number of days due to illness:All eight employees during the same period at the Chickpee location of Acme Carpets revealed they lost
It is estimated that 60% of U.S. households subscribe to cable TV. You would like to verify this statement for your class in mass communications. If you want your estimate to be within 5 percentage points, with a 95% level of confidence, how many households should you sample?
You need to estimate the mean number of travel days per year for salespeople. The mean of a small pilot study was 150 days, with a standard deviation of 14 days. If you must estimate the population mean within 2 days, how many salespeople should you sample? Use the 90% confidence level.
You want to estimate the mean family income in a rural area of central Indiana. The question is, how many families should be sampled? In a pilot sample of 10 families, the standard deviation of the sample was $500. The sponsor of the survey wants you to use the 95% confidence level. The estimate is
A survey of 25 randomly sampled judges employed by the state of Florida found that they earned an average wage (including benefits) of $65.00 per hour. The sample standard deviation was $6.25 per hour.a. What is the population mean? What is the best estimate of the population mean?b. Develop a 99%
A survey of 36 randomly selected iPhone owners showed that the purchase price has a mean of $650 with a sample standard deviation of $24.a. Compute the standard error of the sample mean.b. Compute the 95% confidence interval for the mean.c. How large a sample is needed to estimate the population
You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95% confidence level and a margin of error of 2%. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your
Police Chief Edward Wilkin of River City reports 500 traffic citations were issued last month. A sample of 35 of these citations showed the mean amount of the fine was $54, with a standard deviation of $4.50. Construct a 95% confidence interval for the mean amount of a citation in River City.
A random sample of 85 group leaders, supervisors, and similar personnel at General Motors revealed that, on average, they spent 6.5 years in a particular job before being promoted. The standard deviation of the sample was 1.7 years. Construct a 95% confidence interval.
There are 300 welders employed at Maine Shipyards Corporation. A sample of 30 welders revealed that 18 graduated from a registered welding course. Construct the 95% confidence interval for the proportion of all welders who graduated from a registered welding course.
The attendance at the Savannah Colts minor league baseball game last night was 400. A random sample of 50 of those in attendance revealed that the mean number of soft drinks consumed per person was 1.86, with a standard deviation of 0.50. Develop a 99% confidence interval for the mean number of
A large on-demand, video streaming company is designing a large-scale survey to determine the mean amount of time corporate executives watch on-demand television. A small pilot survey of 10 executives indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. The
A population’s standard deviation is 10. We want to estimate the population mean within 2, with a 95% level of confidence. How large a sample is required?
The Columbus, Ohio Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes spent traveling.
Merrill Lynch Securities and Health Care Retirement Inc. are two large employers in downtown Toledo, Ohio. They are considering jointly offering child care for their employees. As a part of the feasibility study, they wish to estimate the mean weekly child-care cost of their employees. A sample of
Dr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a population standard deviation of 2.44 words per essay. For her 10 a.m. section of
Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 2.30 gallons. From his records, he selects a random sample
Refer to the previous exercise. Instead of 49, suppose that 64 Americans were surveyed about their weekly expenditures on coffee. Assume the sample mean remained the same.a. What is the 95% confidence interval estimate of μ?b. Explain why this confidence interval is narrower than the one
A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean.
A sample of 49 observations is taken from a normal population with a standard deviation of 10. The sample mean is 55. Determine the 99% confidence interval for the population mean.
Refer to the Lincolnville School District bus data. Information provided by manufacturers of school buses suggests the mean maintenance cost per year is $4,400 per bus with a standard deviation of $1,000. Compute the mean maintenance cost for the Lincolnville buses. Does the Lincolnville data seem
Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,000 pounds and the standard deviation is 150 pounds. Assume that the opulation follows the normal distribution. Forty trucks are randomly selected and weighed. Within what limits will
In the United States, the mean age of men when they marry for the first time follows the normal distribution with a mean of 29 years. The standard deviation of the distribution is 2.5 years. For a random sample of 60 men, what is the likelihood that the age when they were first married is less than
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $165,000. This distribution follows the normal distribution with a standard deviation of $40,000.a. If we select a random sample of 50 households, what is the
Majesty Video Production Inc. wants the mean length of its advertisements to be 30 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 16 ads produced by Majesty.a. What can we say about the
In establishing warranties on HDTVs, the manufacturer wants to set the limits so that few will need repair at the manufacturer’s expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV, the mean number of months until
Refer to the Lincolnville School District bus data.a. Refer to the maintenance cost variable. The mean maintenance cost for last year is $4,552 with a standard deviation of $2332. Estimate the number of buses with a maintenance cost of more than $6,000. Compare that with the actual number. Create a
Management at Gordon Electronics is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5% of production based on past experience. Past records indicate weekly production follows the normal distribution. The mean of this distribution is 4,000
The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,200. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 820 pages. The manufacturer wants to
In economic theory, a “hurdle rate” is the minimum return that a person requires before he or she will make an investment. A research report says that annual returns from a specific class of common equities are distributed according to a normal distribution with a mean of 12% and
The SAT Reasoning Test is perhaps the most widely used standardized test for college admissions in the United States. Scores are based on a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the
Given the following hypotheses:H0: μ = 400H1: μ ≠ 400A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:a. State the decision rule.b. Compute the value of the test statistic.c.
The mean income per person in the United States is $50,000, and the distribution of incomes follows a normal distribution. A random sample of 10 residents of Wilmington, Delaware, had a mean of $60,000 with a standard deviation of $10,000. At the .05 level of significance, is that enough evidence
Refer to the following table and the example just completed. With n = 100, σ = 400, xÌ…c= 9,922 and μ1= 9,880, verify that the probability of a Type II error is .1469. Probablity of Type ll Εποr () Selected Power of a Mean (H,) Test (1 – B) 9,820 .0054
Refer to the following table and the example just completed. With n = 100, σ = 400, xÌ…c= 10,078, and μ1 = 10,100, verify that the probability of a Type II error is .2912. Probablity of Type ll Εποr () Selected Power of a Mean (H,) Test (1 – B) 9,820
The management of KSmall Industries is considering a new method of assembling a computer. The current assembling method requires a mean time of 60 minutes with a standard deviation of 2.7 minutes. Using the new method, the mean assembly time for a random sample of 24 computers was 58 minutes. Using
A recent national survey found that parents read an average (mean) of 10 books per month to their children under five years old. The population standard deviation is 5. The distribution of books read per month follows the normal distribution. A random sample of 25 households revealed that the mean
A recent survey by nerdwallet.com indicated Americans paid a mean of $6,658 interest on credit card debt in 2017. A sample of 12 households with children revealed the follow mounts. At the .05 significance level is it reasonable to conclude that these households paid more interest? 7077 7381
A recent article in The Wall Street Journal reported that the home equity loan rate is now less than 4%. A sample of eight small banks in the Midwest revealed the following home equity loan rates (in percent):At the .01 significance level, can we conclude that the home equity loan rate for small
The number of €œdestination weddings€ has skyrocketed in recent years. For example, many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than $30,000.
The North Valley Real Estate data reports information on the homes sold last year.Adam Marty recently joined North Valley Real Estate and was assigned twenty homes to market and show. When he was hired, North Valley assured him that the twenty homes would be fairly assigned to him. When he reviewed
Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season.a. Conduct a test of hypothesis to determine whether the mean salary of the teams was different from $100.0 million. Use the .05 significance level.b. Using a 5% significance level,
Do married and unmarried women spend the same amount of time per week using Facebook? A random sample of 45 married women who use Facebook spent an average of 3.0 hours per week on this social media website. A random sample of 39 unmarried women who regularly use Facebook spent an average of 3.4
Mary Jo Fitzpatrick is the vice president for Nursing Services at St. Luke€™s Memorial Hospital. Recently she noticed in the job postings for nurses that those that are unionized seem to offer higher wages. She decided to investigate and gathered the following information.Would it be
Listed below are the 25 players on the opening-day roster of the 2016 New York Yankees Major League Baseball team, their salaries, and fielding positions.Sort the players into two groups, all pitchers (relief and starting) and position players (all others). Assume equal population standard
The Tampa Bay (Florida) Area Chamber of Commerce wanted to know whether the mean weekly salary of nurses was larger than that of school teachers. To investigate, they collected the following information on the amounts earned last week by a sample of school teachers and a sample of nurses.Is it
The probability that the cause and the cure for all cancers will be discovered before the year 2020 is .20. What viewpoint of probability does this statement illustrate?
The number of times a particular event occurred in the past is divided by the number of occurrences. What is this approach to probability called?
The marketing research department at Pepsico plans to survey teenagers about a newly developed soft drink. Each will be asked to compare it with his or her favorite soft drink.a. What is the experiment?b. What is one possible event?
Sam Snead’s restaurant in Conway, South Carolina, offers an early bird special from 4–6 pm each week day evening. If each patron selects a Starter Selection (4 options), an Entrée (8 options), and a Dessert (3 options), how many different meals are possible?
A representative of the Environmental Protection Agency (EPA) wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples are possible?
A pollster randomly selected 4 of 10 available people. How many different groups of 4 are possible?
Refer to the following table.a. Determine P(A1).b. Determine P(B1 | A2).c. Determine P(B2 and A3). Flrst Event Second Event A, A, 3 Total A, B, 2 B2 Total 3 4 10 3
All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .75, the probability the second truck is available is .50, and the probability that both trucks are available is .30, what is the probability neither truck is available?
Suppose P(X1) = .75 and P(Y2 | X1) = .40. What is the joint probability of X1 and Y2?
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