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Business Statistics 10th Global Edition David Groebner, Patrick Shannon, Phillip Fry - Solutions
Shell Global reported the amount of gasoline sold daily at their petrol stations is uniformly distributed with a minimum of 3,000 gallons and a maximum of 7,000 gallons. A survey was conducted on the amount of gasoline sold daily by a random sample of 50 petrol stations owned by Shell.a. Calculate
Suppose at your university, some administrators believe that the proportion of students preferring to take classes at night exceeds 0.30. The president is skeptical and so has an assistant take a simple random sample of 200 students.Of these, 66 indicate that they prefer night classes. What is the
A company in Hawaii manages properties for owners and arranges for the properties to be rented. A property owner who is considering using the company is told that 10% of the bookings result in a cancellation.a. Assuming that the company’s number is correct, what is the probability that a random
When its ovens are working properly, the time required to bake fruit pies at Ellardo Bakeries is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. Yesterday, a random sample of 16 pies had an average baking time of 50 minutes.a. If Ellardo’s ovens are working
The Baily Hill Bicycle Shop sells mountain bikes and offers a maintenance program to its customers. The manager has found the average repair bill during the maintenance program’s first year to be $15.30 with a standard deviation of $7.00.a. What is the probability a random sample of 40 customers
If a population is known to be normally distributed, what size sample is required to ensure that the sampling distribution of x is normally distributed?
Consider the standard error of a sample proportion obtained from a sample of size 100.a. Determine the standard error obtained from a population with p = 0.1.b. Repeat part a for a population proportion equal to(1) 0.5 and (2) 0.9.c. Which population proportion results in the largest standard
A researcher has collected all possible samples of size 150 from a population and listed the sample means for each of these samples.a. If the average of the sample means is 450.55, what would be the numerical value of the true population mean? Discuss.b. If the standard deviation of the sample
Discuss why the sampling distribution is less variable than the population distribution. Give a short example to illustrate your answer.
A sample of size 30 is obtained from a population that has a proportion of 0.34. Determine the range of sampling errors possible when the sample proportion is used to estimate the population proportion. (Hint:Review the Empirical Rule.)
A study conducted by Reuters revealed that 14% of Fortune 1000 companies either terminated or froze their defined-benefit pension plans (source: Mark Miller, “The vanishing defined-benefit pension and its discontents,” www.reuters.com, May 6, 2014). As part of a study to evaluate how well its
A popular magazine aimed at IT professionals states that 65% of its subscribers have an annual income greater than $100,000. The magazine’s staff uses this high proportion of subscribers earning more than$100,000 as a selling point when trying to get companies to place advertisements with the
In 2015, the average hourly compensation (salary plus benefits) for federal workers was $40.32 (source: Chris Edwards, “Reducing the costs of federal worker pay and benefits,” www.downsizinggovernment.org, Oct. 1, 2015). The file titled Paychecks contains a random sample of the hourly amounts
The Bureau of Transportation Statistics releases information concerning the monthly percentage of U.S.airline flights that land no later than 15 minutes after scheduled arrival. Suppose that last year, the proportion of flights that met this criterion was 0.785. Each year, these data become
Several years ago, Procter & Gamble (P&G) merged with Gillette. One of the concerns after the merger was the increasing burden of retirement expenditures. An effort was made to encourage employees to participate in 401(k) accounts. Nationwide, 66% of eligible workers participated in these accounts.
Airgistics provides air consolidation and freightforwarding services for companies that ship their products internationally. Airgistics currently believes that it achieves a 96% on-time performance for its customers. A random sample of 200 customer shipments was selected for study, and 188 of them
The prospective customers for a beauty company in India constitute 58% women and 42% men. The company, Ayuur, launched an aggressive marketing campaign and, as reported in a survey of 50 customers, this increased the percentage of the female group to 60% and the male group to 48%. Select a random
Ten percent of engineers (electrical, mechanical, civil, and industrial) are women (source: Rebecca Adams,“40 Percent of female engineers are leaving the field.This might be why,” www.huffingtonpost.com, Aug. 12, 2014). Suppose a random sample of 50 engineers is selected.a. How likely is it
During the national sports day held at Kuala Lumpur, a number of athletes tested positive for the hidden presence of banned supplements and lost the opportunity to compete in the games. There was about 1% reported violations of anti-doping rules from the entire population of athletes. You have been
The National Service Training Program is Malaysia’s national service program, which began in December 2003, for 18-year-old youths at risk. During one year, around 85,000 youths participated in the program, of which 51,000 were satisfied with it. Recently a researcher would like to study the life
United Manufacturing and Supply makes sprinkler valves for use in residential sprinkler systems. United entered into a contract to supply 40,000 sprinkler valves. The contract called for at least 97% of the valves to be free of defects. Before shipping the valves, United managers tested 200
A survey is conducted from a population of people of whom 40% have a college degree. The following sample data were recorded for a question asked of each person sampled, “Do you have a college degree?”YES NO NO YES YES YES YES YES YES YES YES NO NO NO YES NO YES YES NO NO NO YES YES YES NO YES
Given a population in which the probability of a success is p = 0.40, if a sample of 1,000 is taken,a. Calculate the probability the proportion of successes in the sample will be less than 0.42.b. What is the probability the proportion of successes in the sample will be greater than 0.44?7-52. A
Given a population in which the proportion of items with a desired attribute is p = 0.50, if a sample of 200 is taken,a. Find the probability the proportion of successes in the sample will be between 0.47 and 0.51.b. Referring to parta, what would the probability be if the sample size were 100?
Given a population in which the proportion of items with a desired attribute is p = 0.25, if a sample of 400 is taken,a. What is the standard deviation of the sampling distribution of p?b. What is the probability the proportion of successes in the sample will be greater than 0.22?
The proportion of items in a population that possess a specific attribute is known to be 0.70.a. If a simple random sample of size n = 100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.65, what is the sampling error?b. Referring to parta, what is
If a random sample of 200 items is taken from a population in which the proportion of items having a desired attribute is p = 0.30, what is the probability that the proportion of successes in the sample will be less than or equal to 0.27?
A population has a proportion equal to 0.30. Calculate the following probabilities with n = 100:a. P1 p … 0.352b. P1 p 7 0.402c. P10.25 6 p … 0.402d. P1 p Ú 0.272.
The file Salaries contains the annual salary for all faculty at a small state college in the Midwest. Assume that these faculty salaries represent the population of interest.a. Compute the population mean and population standard deviation.b. Develop a frequency distribution of these data using 10
Referring to Exercise 7-42, the data file called CEO Compensation contains data for highly paid CEOs.Treat the values as the population. If a random sample of size 5 was selected from this population, what is the largest possible sampling error that could occur when estimating the population mean?
The file CEO Compensation contains data on the top paid executives in 2014 (source: “Fortunate 50 data,”Pittsburgh Post-Gazette, www.post-gazette.com, June 14, 2015).a. Treating the data in the file as the population of interest, compute the population mean and standard deviation for CEO
Bruce Leichtman is president of Leichtman Research Group, Inc. (LRG), which specializes in research and consulting on broadband, media, and entertainment industries. In a recent survey, the company determined the cost of HDMI Digital Antenna systems ranged from about $25 to $200 (source:
Acee Bottling and Distributing bottles and markets Pepsi products in southwestern Vermont. The average fill volume for Pepsi cans is supposed to be 12 ounces.The filling machine has a known standard deviation of 0.05 ounce. Each week, the company selects a simple random sample of 60 cans and
One of the top-selling video games is Call of Duty:Black Ops. While prices vary widely depending on store or website, the suggested retail price for this video game is $59.95. The file titled Black Ops contains a random sample of the retail prices paid for Call of Duty: Black Ops.a. Calculate the
Newspaper advertisements can increase the reach of any type of business. Alice is going to advertise a health product she has developed in a local newspaper.She is trying to find a newspaper that will meet her needs and budget. Her first consideration is the daily sales made by the newspapers. One
Following a university’s entry requirements, students are required to sit for an English test on the day of enrollment. The average score of students taking the entire test is 78 and it has a standard deviation of 13. An English lecturer wonders whether her students have improved their English
Mileage ratings for cars and trucks generally come with a qualifier stating actual mileage will depend on driving conditions and habits. Ford states the Ecoboost F-150 3.5-L V6 will average 20 miles per gallon with combined town and country driving (source: www.ford.com/trucks). Assume the mean
A fast food restaurant manager claims that they have an average time of 4.2 minutes with a standard deviation of 1.3 minutes as the duration between a customer entering the restaurant and the food being served to them. Brandon visited the restaurant every day and disagrees with the information
Sands, Inc., makes particleboard for the building industry. Particleboard is built by mixing wood chips and resins together and pressing the sheets under extreme heat and pressure to form a 4-feet * 8-feet sheet that is used as a substitute for plywood. The strength of the particleboard is tied to
Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours.a. What is the probability that a single battery randomly selected from the population will have a life between 70 and 80 hours?b. What is
SeaFair Fashions relies on its sales force of 220 to do an initial screening of all new fashions. The company is bringing out a new line of swimwear and has invited 40 salespeople to its Orlando home office. An issue of constant concern to the SeaFair sales office is the volume of orders generated
In a certain region of country A, the average duration of first-time marriages that end in divorce is 7.8 years with a standard deviation of 2.2 years. To investigate this further, a random sample of 30 first-time marriages are selected and the durations (in years) of each, ending in divorce, are
Scott Barker, a local vegetable hawker, claims that the pumpkins sold at his store have an average weight of 14 pounds with a standard deviation of 2.15 pounds.You bought six pumpkins from his store and found an average weight of 12.5 pounds.a. Find the probability that the average weight of
Consider a normal distribution with mean = 12 and standard deviation = 90. Calculate P1x 7 362 for each of the following sample sizes:a. n = 1b. n = 9c. n = 16d. n = 25
Given a distribution that has a mean of 40 and a standard deviation of 13, calculate the probability that a sample of 49 has a sample mean that isa. greater than 37b. at most 43c. between 37 and 43d. between 43 and 45e. no more than 35
A random sample of 100 items is selected from a population of size 350. What is the probability that the sample mean will exceed 200 if the population mean is 195 and the population standard deviation equals 20?(Hint: Use the finite population correction factor since the sample size is more than 5%
Suppose nine items are randomly sampled from a normally distributed population with a mean of 100 and a standard deviation of 20. The nine randomly sampled values are 125 95 66 116 99 91 102 51 110 Calculate the probability of getting a sample mean that is smaller than the sample mean for these
If a population is known to be normally distributed with m = 250 and s = 40, what will be the characteristics of the sampling distribution for x based on a random sample of size 25 selected from the population?
A normally distributed population has a mean of 500 and a standard deviation of 60.a. Determine the probability that a random sample of size 16 selected from this population will have a sample mean less than 475.b. Determine the probability that a random sample of size 25 selected from the
Suppose that a population is known to be normally distributed with m = 2,000 and s = 230. If a random sample of size n = 8 is selected, calculate the probability that the sample mean will exceed 2,100.
A population with a mean of 1,250 and a standard deviation of 400 is known to be highly skewed to the right. If a random sample of 64 items is selected from the population, what is the probability that the sample mean will be less than 1,325?
The Badke Foundation was set up by the Fred Badke family following his death in 2001. To help in the solicitation of contributions, the foundation was considering the idea of hiring a consulting company that specialized in this activity. Leaders of the consulting company maintained in their
Maher, Barney, and White LLC is a legal firm with 40 employees. All of the firm’s employees are eligible to participate in the company’s 401(k) plan, and the firm is proud of its 100% participation rate.The file MBW 401 contains last year’s year-end 401(k) account balance for each of the
Wilson Lumber Company is a privately held company that makes cedar siding, cedar lumber, and cedar fencing products. The major cost of production is the cedar logs that are the raw material necessary to make the finished cedar products. The dollar value to be achieved from a log depends initially
The file Dow Jones contains date, open, high, low, close, and volume for the Dow Jones Industrial Average (DJIA) for almost eight years of trading days.a. Assuming that the data in the file constitute the population of interest, what is the population mean closing value for the DJIA?b. Using Excel,
The file titled Clothing contains the monthly retail sales ($millions) of U.S. women’s clothing stores for 70 months. A sample taken from this population to estimate the average sales in this time period follows:2,942 2,574 2,760 2,939 2,642 2,905 2,568 2,677 2,572 3,119 2,697 2,884 2,632 2,742
The file 2015 Cardinals shows the player positions and annual salaries for the Arizona Cardinals NFL players (source: www.spotrac.com/nfl).a. Calculate the average total salary for the Arizona Cardinals.b. Calculate the smallest sample mean for total salary and the largest sample mean for total
A computer lab at a small college has 25 computers. Twice during the day, a full scan for viruses is performed on each computer. Because of differences in the configuration of the computers, the times required to complete the scan are different for each machine. Records for the scans are kept and
An investment advisor has worked with 24 clients for the past five years. Following are the percentage rates of average five-year returns that these 24 clients experienced over this time on their investments:11.2 11.2 15.9 2.7 4.6 7.6 15.6 1.3 3.3 4.8 12.8 14.9 10.1 10.9 4.9 -2.1 12.5 3.7 7.6 4.9
Princess Cruises offered a 9-day voyage from Beijing to Bangkok during the time period from May to August. The announced price, excluding airfare, for a room with an ocean view or a balcony was listed as$3,475. Cruise fares usually are quite variable due to discounting by the cruise line and travel
The administrator at Saint Frances Hospital is concerned about the amount of overtime the nursing staff is incurring and wonders whether so much overtime is really necessary. The hospital employs 60 nurses. Following is the number of hours of overtime reported by each nurse last week. These data
The Anasazi Real Estate Company has 20 listings for homes in Santa Fe, New Mexico. The number of days each house has been on the market without selling is as follows:26 45 16 77 33 50 19 23 55 107 88 15 7 19 30 60 80 66 31 17a. If we consider these 20 values to be the population of interest, what
An Internet service provider states that the average number of hours its customers are online each day is 3.75. Suppose a random sample of 14 of the company’s customers is selected and the average number of hours that they are online each day is measured. The sample results are 3.11 1.97 3.52
The department manager of a local retail outlet found that after restructuring the sales department, by reducing the sales force costs, the costs had fallen.Despite this the frontline sales representatives began to undertake support tasks like creating reports, tracking orders, and developing sales
Eric is an administrator at a local sales department. His manager assigned him to create a report on the number of stages in changing from Unqualified to Qualified for all 25 sales representatives in the team. The number of stage changes mentioned in his report is as follows:13 5 12 7 6 5 6 14 9 2
Consider the following population:3 6 9a. Calculate the population mean.b. Select, with replacement, and list each possible sample of size 2. Also, calculate the sample mean for each sample.c. Calculate the sampling error associated with each sample mean.d. Assuming that each sample is equally
Assume that the following represent a population of N = 16 values:25 12 21 13 19 17 15 18 23 16 18 15 22 14 23 17a. Compute the population mean.b. If a random sample of n = 9 includes the following values:12 18 13 17 23 14 16 25 15 compute the sample mean and calculate the sampling error for this
Assume that the following represent a population of N = 24 values:10 14 32 9 34 19 31 24 33 11 14 30 6 27 33 32 28 30 10 31 19 13 6 35a. If a random sample of n = 10 items includes the following values, compute the sampling error for the sample mean:32 19 6 11 10 19 28 9 13 33b. For a sample of
Consider the following population:18 26 32 17 34 17 17 22 29 24 24 35 13 29 38 The following sample was drawn from this population:35 18 24 17 24 32 17 29a. Determine the sampling error for the sample mean.b. Determine the largest possible sampling error for this sample of n = 8.
The following population is provided:17 15 8 12 9 7 9 11 12 14 16 9 5 10 14 13 12 12 11 9 14 8 14 12 Further, a simple random sample from this population gives the following values:12 9 5 10 14 11 Compute the sampling error for the sample mean in this situation.
The following data are the 16 values in a population:10 5 19 20 10 8 10 2 14 18 7 8 14 2 3 10a. Compute the population mean.b. Suppose a simple random sample of 5 values from the population is selected with the following results:5 10 20 2 3 Compute the mean of this sample.c. Based on the results
A population has a mean of 125. If a random sample of 8 items from the population results in the following sampled values, what is the sampling error for the sample?103 123 99 107 121 100 100 99
Championship Billiards, owned by D & R Industries, in Lincolnwood, Illinois, provides some of the finest billiard fabrics, cushion rubber, and component parts in the industry. It sells billiard cloth in bolts and half-bolts.A half-bolt of billiard cloth has an average length of 35 yards with widths
The Future-Vision Digital and Satellite TV Company recently surveyed its customers. A total of 548 responses were received. Among other things, the respondents were asked to indicate their household income. The data from the survey are found in a file named Future-Vision.a. Develop a frequency
Team Marketing Report (TMR) produces the Fan Cost Index™ (FCI) survey, which tracks the cost of attendance for a family of four at National Football League (NFL)games. The FCI includes four average-price tickets, four small soft drinks, two small beers, four hot dogs, two game programs, parking,
Midwest Fan Manufacturing Inc. is a distributor of quality ventilation equipment. Midwest Fan’s products include the AXC range hood exhaust fans. The file titled Fan Life contains the length of life of 125 randomly chosen AXC fans that were used in an accelerated lifetesting experiment.a. Produce
The Hydronics Company’s research and development department came up with two weight-loss products. To determine whether these products are effective, the company has conducted a test. A total of 300 people who were 30 pounds or more overweight were recruited to participate in the study. Of these,
The Cozine Corporation runs the landfill operation outside Little Rock, Arkansas. Each day, each of the company’s trucks makes several trips from the city to the landfill. On each entry, the truck is weighed. The data file Cozine contains a sample of 200 truck weights. Determine the mean and
A manufacturing process applies a coating to a product in order to protect it from scratches. If the thickness of the coating follows a uniform distribution between 15 and 25 microns, determinea. the mean thickness of the protective coatingb. the standard deviation of the thickness of the
If the average amount of time customers spent online at an Internet retailer’s site is assumed to be normally distributed with mean of 36 minutes and a standard deviation of 6 minutes, determinea. the probability a customer spends less than 30 minutes on the siteb. the probability a customer
If the time required to assemble a product is normally distributed with a mean of 180 minutes and a standard deviation of 15 minutes, finda. the probability that the product’s assembly time would be less than 168 minutesb. the probability that the product’s assembly time would be greater than
Assume that the amount of time eighth-graders take to complete an assessment examination is 78 minutes with a standard deviation of 12 minutes.a. What proportion of eighth-graders complete the assessment examination in 72 minutes or less?b. What proportion of eighth-graders complete the assessment
If the number of hours between servicing required for a particular snowmobile engine is exponentially distributed with an average of 118 hours, determine the probability that a randomly selected enginea. will run at least 145 hours before servicing is neededb. will run at most 161 hours before
The personnel manager for a large company is interested in the distribution of sick-leave hours for employees of her company. A recent study revealed the distribution to be approximately normal, with a mean of 58 hours per year and a standard deviation of 14 hours.An office manager in one division
A manager of a plywood plant organized a study of the diameters of trees that are shipped to the mill. After collecting a large amount of data on diameters, he concluded that the diameter is approximately normally distributed with a mean of 14.25 inches and a standard deviation of 2.92 inches.
A traffic control camera at a busy intersection records, on average, 5 traffic violations per hour. Assume that the random variable number of recorded traffic violations follows a Poisson distribution.a. What is the probability that the next recorded violation will occur within 5 minutes?b. How
A product made by a window manufacturer is constructed of two pieces of glass 0.125 inch thick, with a thin layer of vinyl sandwiched between them. The average thickness of the laminated safety glass is 0.25 inch. The thickness of the glass does not vary from the mean by more than 0.10 inch. Assume
The Shadow Mountain Golf Course is preparing for a major LPGA golf tournament. Since parking near the course is extremely limited (room for only 500 cars), the course officials have contracted with the local community to provide parking and a bus shuttle service. Sunday, the final day of the
Suppose eye shadow and eyeliner have a shelf life of up to three years, and the shelf lives of these two products are exponentially distributed with an average of one year.a. Calculate the probability that the shelf life of eye shadow will be longer than three years.b. Determine the probability
Assume that after the first 12 hours, the average remaining useful life of a particular battery (before recharging is required) is 9 hours and that the remaining time is exponentially distributed. What is the probability that a randomly sampled battery of this type will last between 15 and 17 hours?
Domino’s Pizza receives majority of its orders by telephone. The call center supervisor conducted a study on the duration an order had been taken. He found that the amount of time a customer was waiting to place an order was about 10 minutes. Assume that the distribution of time spent in taking
Two automatic dispensing machines are being considered for use in a fast-food chain. The first dispenses an amount of liquid that has a normal distribution with a mean of 11.9 ounces and a standard deviation of 0.07 ounce. The second dispenses an amount of liquid that has a normal distribution with
The Four Brothers Lumber Company is considering buying a machine that planes lumber to the correct thickness. The machine is advertised to produce “6-inch lumber” having a thickness that is normally distributed, with a mean of 6 inches and a standard deviation of 0.1 inch.a. If building
Drive-through services are very popular and convenient to consumers today. It provides a business that allows customers to purchase products without leaving their cars. McDonald’s has customers arriving at the drivethrough window at an average rate of three customers per minute and that their
Assume that the time required to receive a confirmation that an electronic transfer has occurred is uniformly distributed between 30 and 90 seconds.a. What is the probability that a randomly selected transfer will take between 30 and 45 seconds?b. What is the probability that a randomly selected
Suppose that, on average, 20 customers arrive every hour at a twenty-four-hour coffee shop. Assume that the time between customer arrivals is exponentially distributed. Determinea. the probability that a customer arrives within the next 2 minutesb. the probability that the time between two arriving
Revisit Exercise 6-55, but examine whether it would matter when you started monitoring the 911 calls if the time between occurrences had a uniform distribution with a mean of 2 and a range of 4.a. Calculate the probability that no call comes in during the first hour.b. Now suppose that you are
The exponential distribution has a characteristic that is called the “memoryless” property. This means P1X 7 x2 = P1X 7 x + x0 X 7 x02. To illustrate this, consider the calls coming into 911. Suppose that the distribution of the time between occurrences has an exponential distribution with a
Suppose you tell one of your fellow students that when working with a continuous distribution, it does not make sense to try to compute the probability of any specific value, since it will be zero. She says that when the experiment is performed, some value must occur; the probability can’t be
The probability that a value from a normally distributed random variable will exceed the mean is 0.50. The same is true for the uniform distribution. Why is this not necessarily true for the exponential distribution? Discuss and show examples to illustrate your point.
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