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Business Statistics 10th Global Edition David Groebner, Patrick Shannon, Phillip Fry - Solutions
Recall the Empirical Rule from Chapter 3. It states that if the data distribution is bell-shaped, then the interval m { s contains approximately 68% of the values, m { 2s contains approximately 95%, and m { 3s contains virtually all of the data values. The bell-shaped distribution referenced is the
Discuss the difference between discrete and continuous probability distributions. Discuss two situations in which a variable of interest may be considered either continuous or discrete.
The San Luis Obispo, California, Transit Program provides daily fixed-route transit service to the general public within the city limits and to Cal Poly State University’s staff and students. The most heavily traveled route schedules a city bus to arrive at Cal Poly at 8:54 a.m. The file titled
An article titled “You’re paying record ATM fees” by Kathryn Vasel states that the average ATM fee banks charge nonbank customers is $4.52 per transaction(source: http://money.cnn.com, Oct. 5, 2015). The file titled ATM Fees contains the ATM fees paid by a sample of individuals.a. Calculate
The Schoonover Manufacturing Company monitors the downtimes on its key fabricating machines. Data for the downtimes on one particular machine are in the file called Schoonover. Assuming that the downtimes are exponentially distributed, use the data in the file to find the probability that a
Currently, a manufacturing company experiences an average of 0.75 equipment-related shutdowns per shift and the downtimes are exponentially distributed. In testing, a new maintenance program reduced the frequency of equipment-related shutdowns to an average of 0.20 per shift, exponentially
A customer spent half an hour to travel to an automotive service center. The duration of waiting in a particular automotive service center is uniformly distributed between 40 minutes and 3 hours.a. Determine the density function for the waiting time in the particular automotive service center.b.
A car is running on petrol. The time that particular car can go on before it is running out of petrol is exponentially distributed with the average of 50 minutes.a. The next petrol station is less than 40 minutes away from the car. What is the probability for the car to reach the petrol station?b.
A car salesperson states that on an average two customers will buy a car from her every month.Assume that the probability distribution of the number of months a customer will buy a car from her is exponentially distributed.a. Calculate the probability that a customer will buy a car from her in less
The average time taken by a phone operator to complete a call is 4 minutes. Assume that the time is exponentially distributed. Find the probability that a phone operator took:a. more than 6 minutes to complete a call.b. less than 3 minutes to complete a call.c. between 2 and 8 minutes to complete a
A delicatessen is open 24 hours a day every day of the week. If, on the average, 20 orders are received by fax every two hours throughout the day, find thea. probability that a faxed order will arrive within the next 9 minutesb. probability that the time between two faxed orders will be between 3
The time to failure for a power supply unit used in a particular brand of personal computer (PC) is thought to be exponentially distributed with a mean of 4,000 hours as per the contract between the vendor and the PC maker. The PC manufacturer has just had a warranty return from a customer who had
According to a kindergarten teacher, the number of story books a child may read in a month is uniformly distributed from 2 to 8 books. Assuming each story book covers an average of 10 pages of words with pictures.a. Find the mean and standard deviation for the distribution.b. Find the probability
Assume that the time it takes to build a laser printer is uniformly distributed between 8 and 15 hours.a. What are the chances that it will take more than 10 hours to build a printer?b. How likely is it that a printer will require less than 9 hours?c. Suppose a single customer orders two
Suppose buses stop in front of your hotel every 20 minutes throughout the day. If you show up at the bus stop at a random moment during the day, determine the probability thata. you will have to wait more than 10 minutesb. you will have to wait only 6 minutes or lessc. you will have to wait between
The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.5 minutes.a. What is the probability that the time between the next two calls will be 45 seconds or less?b. What is the probability that the time between the next two
The useful life of an electrical component is exponentially distributed with a mean of 2,500 hours.a. What is the probability the circuit will last more than 3,000 hours?b. What is the probability the circuit will last between 2,500 and 2,750 hours?c. What is the probability the circuit will fail
Let x be an exponential random variable with l = 0.5.Calculate the following probabilities:a. P1x 6 52b. P1x 7 62c. P15 … x … 62d. P1x Ú 22e. the probability that x is at most 6
Suppose a random variable, x, has a uniform distribution with a = 5 and b = 9.a. Calculate P15.5 … x … 82.b. Determine P1x 7 72.c. Compute the mean, m, and standard deviation, s, of this random variable.d. Determine the probability that x is in the interval 1m { 2s2.
Determine the following:a. the probability that a uniform random variable whose range is between 10 and 30 assumes a value in the interval (10 to 20) or (15 to 25)b. the quartiles for a uniform random variable whose range is from 4 to 20c. the mean time between events for an exponential random
A continuous random variable is uniformly distributed between 100 and 150.a. What is the probability a randomly selected value will be greater than 135?b. What is the probability a randomly selected value will be less than 115?c. What is the probability a randomly selected value will be between 115
A file titled Tuition contains the percent change in in-state tuition for 50 universities (source: The College Board, “Annual survey of colleges,” October 2015).a. Produce a relative frequency histogram for these data. Does it seem plausible that the data are from a population that has a normal
The file titled Drug$ contains daily cost data for a drug used to treat lung disease.a. Produce a relative frequency histogram for these data. Does it seem plausible the data were sampled from a population that was normally distributed?b. Compute the mean and standard deviation for the sample data
A November 13, 2015, report titled “The cost of hiring a new employee” by Annie Mueller (www.investopedia.com) indicated that the average cost for an American company to fill a job vacancy was $3,500. Sample data showing costs to hire employees are in a file titled Hired.a. Produce a relative
A senior loan officer for Whitney National Bank has recently studied the bank’s real estate loan portfolio and found that the loan balances are approximately normally distributed with a mean of $155,600 and a standard deviation equal to $33,050. As part of an internal audit, bank auditors
Jeff is a server developer in designing databases and is responsible for ensuring the server’s stability, reliability, and performance. Several complaints have been received from the customer services department on the instability of the server. To address the complaints and provide a solution,
MP-3 players are wonderful devices for people who want to have access to their favorite music and videos in a portable format. They can store massive numbers of songs and videos. Although owners have the potential to store lots of data, suppose the actual disk storage being used is normally
A Coca-Cola bottling plant’s product line includes 12-ounce cans of Coke products. The cans are filled by an automated filling process that can be adjusted to any mean fill volume and that will fill cans according to a normal distribution. However, not all cans will contain the same volume due to
A maternity wear designer sells dresses and pants priced around $150 each for an average total sale of$1,200. The total sale has a normal distribution with a standard deviation of $350.a. Calculate the probability that a randomly selected customer will have a total sale of more than $1,500.b.
The HR manager of a factory is reviewing the pay for part-time workers to determine a new policy for them.By referring to other factories’ pay scales, two types of payment system seem to be popular. The first type shows that the part-time workers are being paid $200 for the first hour and $50 for
Students in a classroom claim that they don’t have enough time to study due to too much homework being assigned to them. A teacher is interested to determine the time his students spend in completing homework assignments per day. He found that the time his students spent on homework assignments
A private equity firm is evaluating two alternative investments. Although the returns are random, each investment’s return can be described using a normal distribution. The first investment has a mean return of$2,000,000 with a standard deviation of $125,000. The second investment has a mean
Philips is a leading health technology company in improving consumers’ health and home care. One of its most popular products is LED lights, designed to provide a safer light source. A hardware store sells the lights on an average of 35 units per day with the standard deviation of 2.1 units.
An Internet retailer stocks a popular electronic toy at a central warehouse that supplies the eastern United States. Every week, the retailer makes a decision about how many units of the toy to stock. Suppose that weekly demand for the toy is approximately normally distributed with a mean of 2,500
The average number of acres burned by forest and range fires in a large county in the West is 5,300 acres per year, with a standard deviation of 750 acres. The distribution of the number of acres burned is normal.a. Compute the probability that more than 6,000 acres will be burned in any year.b.
An expensive watch is powered by a 3-volt lithium battery expected to last three years. Suppose the life of the battery has a standard deviation of 0.3 year and is normally distributed.a. Determine the probability that the watch’s battery will last longer than 3.5 years.b. Calculate the
Doggie Nuggets Inc. (DNI) sells large bags of dog food to warehouse clubs. DNI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms.a. What is the probability that
A global financial institution transfers a large data file every evening from offices around the world to its London headquarters. Once the file is received, it must be cleaned and partitioned before being stored in the company’s data warehouse. Each file is the same size and the times required
A random variable is normally distributed with a mean of 60 and a standard deviation of 9.a. What is the probability that a randomly selected value from the distribution will be less than 46.5?b. What is the probability that a randomly selected value from the distribution will be greater than 78?c.
A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the distribution,a. What value will be exceeded 10% of the time?b. What value will be exceeded 85% of the time?c. Determine two values of which the smaller has
Assume that a random variable is normally distributed with a mean of 1,500 and a variance of 324.a. What is the probability that a randomly selected value will be greater than 1,550?b. What is the probability that a randomly selected value will be less than 1,485?c. What is the probability that a
A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean.a. What is the probability that a randomly selected value from the distribution will be greater than 2.1 standard deviations above the mean?b. What is the probability that a randomly selected
A random variable is known to be normally distributed with the following parameters:m = 5.5 and s = 0.50a. Determine the value of x such that the probability of a value from this distribution exceeding x is at most 0.10.b. Referring to your answer in parta, what must the population mean be changed
A population is normally distributed with m = 100 and s = 20.a. Find the probability that a value randomly selected from this population will be greater than 130.b. Find the probability that a value randomly selected from this population will be less than 90.c. Find the probability that a value
For the following normal distributions with parameters as specified, calculate the required probabilities:a. m = 5, s = 2; calculate P10 6 x 6 82.b. m = 5, s = 4; calculate P10 6 x 6 82.c. m = 3, s = 2; calculate P10 6 x 6 82.d. m = 4, s = 3; calculate P1x 7 12.e. m = 0, s = 3; calculate P1x 7 12.
A random variable, x, has a normal distribution with m = 13.6 and s = 2.90. Determine a value, x0, so thata. P1x 7 x02 = 0.05.b. P1x … x02 = 0.975.c. P1m - x0 … x … m + x02 = 0.95.
Consider a random variable, z, that has a standardized normal distribution. Determine the following probabilities:a. P10 6 z 6 1.962b. P1z 7 1.6452c. P11.28 6 z … 2.332d. P1-2 … z … 32e. P1z 7 -12
For a standardized normal distribution, determine a value, say z0, so thata. P10 6 z 6 z02 = 0.4772b. P1-z0 … z 6 02 = 0.45c. P1-z0 … z … z02 = 0.95d. P1z 7 z02 = 0.025e. P1z … z02 = 0.01
For a standardized normal distribution, calculate the following probabilities:a. P10.00 6 z … 2.332b. P1-1.00 6 z … 1.002c. P11.78 6 z 6 2.342
For a standardized normal distribution, calculate the following probabilities:a. P1z 6 1.52b. P1z Ú 0.852c. P1-1.28 6 z 6 1.752
For a normally distributed population with m = 200 and s = 20, determine the standardized z-value for each of the following:a. x = 225b. x = 190c. x = 240
Covercraft manufactures covers to protect automobile and boat interiors and finishes. Its Block-It 200 Series fabric has a limited two-year warranty. Periodic testing is done to determine if the warranty policy should be changed. One such study examined those covers that became unserviceable while
Darlington Industries produces a wide array of home safety and security products, including smoke alarms.As part of its quality-control program, it constantly tests to assure that the alarms work. A change in the manufacturing process requires the company to determine the proportion of alarms that
A 23-mile stretch of a two-lane highway east of Paso Robles, California, was once considered a “death trap”by residents of San Luis Obispo County. Formerly known as “Blood Alley,” Highway 46 gained notoriety for the number of fatalities (29) and crashes over a 240-week period. More than
The manager of an online shopping website has determined that an average of 11 customers per minute make a purchase on Saturdays. The manager believes that each customer’s purchase is independent and has decided to model the number of purchases per minute using a Poisson probability
A large mail sorting center finds that, on average, 0.5% of all letters have an incorrect address.a. What is the probability that in a random sample of 500 letters at the center exactly 5 letters have an incorrect address?b. What is the probability that the random variable x, where x = Number of
A machine produces parts continuously throughout the day with an overall defect rate of 0.80%. Periodically a random sample of 50 parts is sampled, and if 3 or more are found to be defective the machine is stopped and adjusted.a. What is the probability that in the next sample of 50 parts the
If 80% of all college students in the United States text during classes, calculate the probabilities of the following events from a random sample of 15 college students:a. exactly 9 text during classb. more than 6 text during classc. between 3 and 12 text during class
If 80% of all business airline travelers prefer to carry on baggage rather than check it, calculate the probabilities of the following events from a random sample of 25 business travelers:a. exactly 15 prefer to carry on baggageb. fewer than 5 prefer to check baggagec. more than 10 prefer to carry
If 70% of all Millennials are currently saving for retirement, calculate the probabilities of the following events from a random sample of 15 Millennials:a. exactly 5 are saving for retirementb. more than 7 are saving for retirementc. between 3 and 8 are saving for retirementd. fewer than 6 are
On a busy weekend, a hotel has 20 rooms that are not occupied. Suppose that smoking is allowed in 8 of the rooms. A small tour group arrives that has four smokers and six nonsmokers. The desk clerk randomly selects 10 rooms and gives the keys to the tour guide to distribute to the travelers.a.
The process used to make poker chips varies slightly between manufacturers. ChipLab supplies casino chips for most of the casino in the United States with a daily production of 10,000 chips. Recently the company found that a batch of 30 chips manufactured by them contained 5 chips that do not
Yann Tiersen, a French musician and composer, is best known for his crisp piano ballads and accordion waltzes. He is going to have a classical concert in a grand opera house. His concert is selling two types of tickets—the Gold Reserved seats that sell for $240 per ticket and the Platinum
A Malaysian Volkswagen dealer has total cash rebates of up to RM150,000 per day for the new Volkswagen Passat. The manager of the dealership summarized the number of cars sold per day with their respective probabilities as shown in the following table:Daily Number of Cars Sold Probability 0 0.12 1
Stafford Production, Inc., is concerned with the quality of the parts it purchases that will be used in the end items it assembles. Part number 34-78D is used in the company’s new laser printer. The parts are sensitive to dust and can easily be damaged in shipment even if they are acceptable when
Jamba Juice is a leading manufacturer and exporter of the best fruit juices across markets. They sell fresh juice in glass bottles. An earlier report shows that the bottles used by them indicate 1% having one or more faults.The company uses a sample of 20 bottles from their production line for
OZ Plumbing & Heating is the main piping contractor for a developer. In a recent development project, 15 out of 50 home owners complained that their pipes leaked.To verify this, the developer randomly selected 10 homes and run a defect check. The developer decided to change their piping contractor
Your company president has told you that the company experiences product returns at the rate of two per month with the number of product returns distributed as a Poisson random variable. Determine the probability that next month there will bea. no returnsb. one returnc. two returnsd. more than two
The University of Michigan’s Population Studies Center provides teaching, learning, training, and conducting research in the area of population studies.One of their records had a list of women who gave birth to at least 25 children before the 19th century.Recently one of its research students was
Keith is an athletic trainer at Delia University and he is invited to send his athletes to attend a nationwide competition. He needs to make decisions based on the chances of winning the competition, previous records showing they have an 80% chance of winning. He selected 10 of his best athletes to
The McMillan Newspaper Company sometimes makes printing errors in its advertising and is forced to provide corrected advertising in the next issue of the paper. The managing editor has done a study of this problem and found the following data:No. of Errors x Relative Frequency 0 0.56 1 0.21 2 0.13
Consider an experiment in which a sample of size n = 5 is taken from a binomial distribution.a. Calculate the probability of each value of the random variable for the probability of a success equal to(1) 0.1, (2) 0.25, (3) 0.50, (4) 0.75, and (5) 0.9.b. Which probabilities produced a right-skewed
Beginning statistics students are often puzzled by two characteristics of distributions in this chapter: (1) the trials are independent, and (2) the probability of a success remains constant from trial to trial. Students often think these two characteristics are the same. The questions in this
Discuss the basic differences and similarities between the binomial distribution and the Poisson distribution.
How is the shape of the binomial distribution changed for a given value of p as the sample size is increased?Discuss.
Three discrete distributions were discussed in this chapter. Each was defined by a random variable that measured the number of successes. To apply these distributions, you must know which one to use. Describe the distinguishing characteristics for each distribution.
Cliff Summey is the quality-assurance engineer for Sticks and Stones Billiard Supply, a manufacturer of billiard supplies. One of the items that Sticks and Stones produces is sets of pocket billiard balls. Cliff has been monitoring the finish of the pocket billiard balls. He is concerned that sets
An employment agency survey contacted 130 small firms. One of the many inquiries was to determine the number of employees the firms had. The file titled Employees contains the responses by the firms. The number of employees was grouped into the following categories: (1) fewer than 20; (2) 20–99;
The 2014 State of Women-Owned Businesses report commissioned by American Express indicated 31% of private firms had female owners, 53% had male owners, and 16% had male and female co-owners (source:www.womenable.com). In one community, there are 100 privately owned firms. Ten privately owned firms
The owner of a local electronic store is checking the quality of toasters sold at his shop. He knows that out of 20, three toasters might have faulty timer knobs, which may fall off. He randomly selects five toasters for testing. Compute the probability fora. all the toasters’ timer knobs falling
The owner of Lucky Dogs sells spicy hot dogs from a pushcart. Lucky Dogs is open every day between 11:00 a.m. and 1:00 p.m. Assume the demand for spicy hot dogs follows a Poisson distribution with a mean of 50 per hour.a. What is the probability the owner will run out of spicy hot dogs over the
Fasteners used in a manufacturing process are shipped by the supplier to the manufacturer in boxes that contain 20 fasteners. Because the fasteners are critical to the production process, their failure will cause the product to fail. The manufacturing firm and the supplier have agreed that a random
Beacon Hill Trees & Shrubs currently has an inventory of 10 fruit trees, 8 pine trees, and 14 maple trees. It plans to give 4 trees away at next Saturday’s lawn and garden show in the city park. The 4 winners can select which type of tree they want. Assume they select randomly.a. What is the
John Thurgood founded a company that translates Chinese books into English. His company is currently testing a computer-based translation service. Since Chinese symbols are difficult to translate, John assumes the computer program will make some errors, but then so do human translators. The
A shipment of 20 hard drives was shipped to The Tech-Crew computer repair company. Four of them were defective. One of the technicians selected 5 of the hard drives to put in his parts inventory and then went on three service calls.a. Determine the probability that only 1 of the 5 hard drives is
Africa’s Safari Park is the best place to spot lions. You can see them regularly during the morning or afternoon drives. Assume that the number of lions that can be seen on a day trip in Safari Park is Poisson distributed with an average of 12 lions.a. Compute the probability of spotting more
A stock portfolio contains 20 stocks. Of these stocks, 10 are considered “large-cap” stocks, 5 are “mid cap,”and 5 are “small cap.” The portfolio manager has been asked by his client to develop a report that highlights 7 randomly selected stocks. When she presents her report to the
When things are operating properly, E-Bank United, an Internet bank, can process a maximum of 25 electronic transfers every minute during the busiest periods of the day. If it receives more transfer requests than this, then the bank’s computer system will become so overburdened that it will slow
Plywood contains minor imperfections that can be repaired with small “plugs.” One customer will accept plywood with a maximum of 3.5 plugs per sheet on average. Suppose a shipment was sent to this customer, and when the customer inspected two sheets at random, 10 plugged defects were counted.
Pacific Realty is helping a developer to sell their latest real-estate properties. To achieve maximum sales, Pacific Reality trains agents to sell the product to more than four houses per month. One of the agents established that the number of houses sold in a month is Poisson distributed with an
A random variable, x, has a hypergeometric distribution with N = 10, X = 7, and n = 4.Calculate the following quantities:a. P1x = 32b. P1x = 52c. P1x Ú 42d. Find the largest x so that P1x 7 x 2 7 0.25.
Determine the following values associated with a Poisson distribution with lt equal to 3:a. P1x … 32b. P1x 7 32c. P12 6 x … 52d. Find the smallest x so that P1x … x 2 7 0.50.
A corporation has 11 manufacturing plants. Of these, seven are domestic and four are located outside the United States. Each year, a performance evaluation is conducted for 4 randomly selected plants.a. What is the probability that a performance evaluation will include exactly 1 plant outside the
If a random variable follows a Poisson distribution with l = 20 and t = 12, find thea. expected value, variance, and standard deviation of this Poisson distributionb. probability of exactly 8 successes
A population of 10 items contains 3 that are red and 7 that are green. What is the probability that in a random sample of 3 items selected without replacement, 2 red and 1 green items are selected?
Consider a situation in which a used-car lot contains five Fords, four General Motors (GM) cars, and five Toyotas. If five cars are selected at random to be placed on a special sale, what is the probability that three are Fords and two are GMs?
Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to three per 15 minutes.a. Determine the probability that in a given 15-minute segment, no customers will arrive at the ATM.b. What is the probability that fewer than four
The mean number of errors per page missed by a proofreader at a major publishing company is thought to be 1.5, with the number of errors distributed according to a Poisson distribution. If three pages are examined, what is the probability that more than three errors will be observed?
International Data Corp. (IDC) has shown that the average return on business analytics projects was almost four-and-a-half times the initial investment(source: “IDC study finds analytics projects yield 431% average ROI,” www.idg.com/, October 2002).Analytics consists of tools and applications
An online shoe retailer has the goal of keeping the percent of returns due to incorrect size to no more than 5%. The file titled Shoesize contains a sample of 125 shoe sizes that were sent to customers and the sizes that were actually ordered.a. Determine the number of pairs of wrong-size shoes
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