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business statistics communicating
Business Statistics 10th Global Edition David Groebner, Patrick Shannon, Phillip Fry - Solutions
According to the most recent study conducted by the U.S. Bureau of Labor Statistics, 28.1% of female spouses outearn their male counterparts (source: “Highlights of women’s earnings in 2014,” BLS Reports, Report 1058,November 2015). The file titled Gendergap contains the incomes of 150
A large grocery store chain believes that 80% of its customers use the store’s “Savings Card” when they make purchases. The manager in charge of the “Savings Card” program has randomly sampled 20 customers and observed whether or not they used the card.a. Assuming that the 80% use rate is
Managers at an electronics retailer have tracked the frequency with which product rebates are redeemed and found that for their company, 40% of all rebates are actually redeemed. Further, they found the following redemption rates: 50% for a $30 rebate on a$100 product, 10% for a $10 rebate on a
Radio frequency identification (RFID) is an electronic scanning technology that can be used to identify items in a number of ways. One advantage of RFID is that it can eliminate the need to manually count inventory, which can help improve inventory management. The technology is not infallible,
The Employee Benefit Research Institute reports that 58% of workers say they are confident they have saved enough for retirement (source: “The 2015 Retirement Confidence Survey: Having a retirement savings plan a key factor in Americans’ retirement confidence, EBRI Issue Brief #413, April
A manufacturing firm produces a product that has a ceramic coating. The coating is baked on to the product, and the baking process is known to produce 15% defective items (for example, cracked or chipped finishes). Every hour, 20 products from the thousands that are baked hourly are sampled from
A small hotel in a popular resort area has 20 rooms.The hotel manager estimates that 15% of all confirmed reservations are “no-shows.” Consequently, the hotel accepts confirmed reservations for as many as 25 rooms. If more confirmed reservations arrive than there are rooms, the overbooked
Recent ratings for the popular NCIS television show indicate that 7.5% of all television households tune in to the show. The ratings also show that 9.7% of all television households tune in to The Big Bang Theory.a. Suppose a consultant submits a report saying that it found no one in a sample of 25
A national retailer has tracked customers who visit its website and determined that 37% will make a purchase from the website within six months of their first website visit. Eight people who visit the website are selected at random as a sample.a. Determine the expected number in the sample who will
Assume that for an ad campaign to be successful, at least 80% of those seeing a television commercial must be able to recall the name of the company featured in the commercial one hour after viewing the commercial.Before distributing an ad campaign nationally, an advertising company plans to show
Cancer is a global medical concern and around half of the patients diagnosed with cancer do succumb to it.There are many types of cancer treatments including chemotherapy, hormone therapies, biological therapies, and bisphosphonates. A cancer treatment center selected 20 patients to receive an
Hewlett-Packard receives large shipments of microprocessors from Intel Corp. It must try to ensure the proportion of microprocessors that are defective is small. Suppose HP decides to test five microprocessors out of a shipment of thousands of these microprocessors.Suppose that if at least one of
According to NBCNews.com, 38% of the voters in California voted for Mitt Romney, the Republican candidate for President in 2012 (source: “Presidential election results,” http://nbcnews.com, updated Feb. 9, 2016). A small startup company in San Jose, California, has ten employees.a. How many of
Magic Valley Memorial Hospital administrators have recently received an internal audit report that indicates that 15% of all patient bills contain an error of one form or another. After spending considerable effort to improve the hospital’s billing process, the administrators are convinced that
Given a binomial distribution with n = 8 and p = 0.40, obtain the following:a. the meanb. the standard deviationc. the probability that the number of successes is larger than the meand. the probability that the number of successes is within {2 standard deviations of the mean
Use the binomial distribution in which n = 6 and p = 0.3 to calculate the following probabilities:a. x is at most 1b. x is at least 2c. x is more than 5d. x is less than 6
Use the binomial distribution table to determine the following probabilities:a. n = 6, p = 0.08; find P1x = 22b. n = 9, p = 0.80; determine P1x 6 42c. n = 11, p = 0.65; calculate P12 6 x … 52d. n = 14, p = 0.95; find P1x Ú 132e. n = 20, p = 0.50; compute P1x 7 32
A random variable follows a binomial distribution with a probability of success equal to 0.45. For n = 11, finda. the probability of exactly 1 successb. the probability of 4 or fewer successesc. the probability of at least 8 successes
A random variable follows a binomial distribution with a probability of success equal to 0.65. For a sample size of n = 7, finda. the probability of exactly 3 successesb. the probability of 4 or more successesc. the probability of exactly 7 successesd. the expected value of the random variable
Assuming the binomial distribution applies with a sample size of n = 15, finda. the probability of 5 or more successes if the probability of a success is 0.30b. the probability of fewer than 4 successes if the probability of a success is 0.75c. the expected value of the random variable if the
Find the probability of exactly 5 successes in a sample of n = 10 when the probability of a success is 0.70.
Suppose that 40% of all home buyers will do some remodeling to their home within the first five years of home ownership. Assuming this is true, use the binomial distribution to determine the probability that in a random sample of 20 homeowners, 2 or fewer will remodel their homes. Use the binomial
If a binomial distribution applies with a sample size of n = 20, finda. the probability of 5 successes if the probability of a success is 0.40b. the probability of at least 7 successes if the probability of a success is 0.25c. the expected value, n = 20, p = 0.20d. the standard deviation, n = 20, p
Use the binomial formula to calculate the following probabilities for an experiment in which n = 5 and p = 0.4:a. the probability that x is at most 1b. the probability that x is at least 4c. the probability that x is less than 1
For a binomial distribution with a sample size equal to 10 and a probability of a success equal to 0.30, what is the probability that the sample will contain exactly three successes? Use the binomial formula to determine the probability.
Suppose that 20% of credit cards have an outstanding balance at the credit card limit. A bank manager randomly selects 15 customers and finds 4 that have balances at the limit. Assume that the properties of the binomial distribution apply.a. What is the probability of finding 4 customers in a
Fiber Fabrics, Inc., makes boat tops for a number of boat manufacturers. Its 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 still under warranty. Data
Pfizer Inc. is the manufacturer of Revolution(Selamectin), a topical parasiticide used for the treatment, control, and prevention of flea infestation, heartworm, and ear mites for dogs and cats. One of its selling points is that it provides protection for an entire month. The file titled Fleafree
A national retailer has entered into an agreement with a publisher to begin selling a food and beverage magazine on a trial basis. The retailer pays $1.95 and sells the magazine for $3.49. During the trial period, the retailer placed 10 copies of the magazine in each of 150 stores throughout the
A large corporation in search of a CEO and a CFO has narrowed the fields for each position to a short list. The CEO candidates graduated from Chicago (C) and three Ivy League universities: Harvard (H), Princeton (P), and Yale (Y). The four CFO candidates graduated from MIT (M), Northwestern (N),
Moira works as the loan officer at a bank. Every day he needs to manage numerous loan applications by verifying each document provided by the applicants, which correspond with the bank’s policy. At the same time, she essentially distributes the approved loans into three categories based on the
A consumer electronics store stocks four alarm clock radios. If it has fewer than four clock radios available at the end of a week, the store restocks the item to bring the in-stock level up to four. If weekly demand is greater than the four units in stock, the store loses sales. The radio sells
Rossmore Brothers, Inc., sells plumbing supplies for commercial and residential applications. The company currently has only one supplier for a particular type of faucet. Based on historical data, the company has assessed the following probability distribution for the proportion of defective
Steve owns a stall in a cafeteria. He is investigating the number of food items wasted per day due to inappropriate handling. Steve recorded the daily number of food items wasted with respective probabilities in the following table:Number of Wasted Food Items Probability 5 0.20 6 0.12 7 0.29 8 0.11
Before a book is sent for printing, Anna, a proofreader, needs to ensure that there are no grammatical or typographical errors in any page. Based on her past experiences, she found the probability for the number of errors per page in a book shown as follows:Number of Errors Probability 2 0.19 3
Using historical records, a manufacturing firm has developed the following probability distribution for the number of days required to get components from its suppliers. The distribution is shown here, where the random variable x is the number of days.x P(x)2 0.15 3 0.45 4 0.30 5 0.075 6 0.025a.
After conducting a five-day travel fair at the Mid-valley Exhibition Hall, Harmony Tour and Travel is reviewing the number of complaints received per day. Following are the number of complaints with their respective probabilities received by the company in a day:Number of Complaints Probability 1
Examine the following probability distribution:x 5 10 15 20 25 30 35 40 45 50 P(x) 0.01 0.05 0.14 0.20 0.30 0.15 0.05 0.04 0.01 0.05a. Calculate the expected value and standard deviation for this random variable.b. Denote the expected value as m. Calculate m - s and m + s.c. Determine the
Consider the following discrete probability distribution:x P(x)5 0.10 10 0.15 15 0.25 20 0.50a. Calculate the expected value of the random variable.b. Let y = x + 5. Calculate the expected value of the new random variable y.c. Let z = 5x. Calculate the expected value of the new random variable z.d.
Two six-sided dice are rolled and the random variable x is the sum of the values produced by each die.a. List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x.b. Calculate the variance of x.c. Calculate the standard
Given the following discrete probability distribution:x P(x)100 0.25 125 0.30 150 0.45a. Calculate the expected value of x.b. Calculate the variance of x.c. Calculate the standard deviation of x.
Consider the following discrete probability distribution:x P(x)3 0.13 6 0.12 9 0.15 12 0.60a. Calculate the variance and standard deviation of the random variable.b. Let y = x + 7. Calculate the variance and standard deviation of the random variable y.c. Let z = 7x. Calculate the variance and
Because of weather issues, the number of days next week that the captain of a charter fishing boat can leave port is uncertain. Let x = number of days the boat is able to leave port per week. The following probability distribution for the variable, x, was determined based on historical data when
Given the following discrete probability distribution:x P(x)50 0.375 65 0.15 70 0.225 75 0.05 90 0.20a. Calculate the expected value of x.b. Calculate the variance of x.c. Calculate the standard deviation of x.
If the Prudential Insurance Company surveys its customers to determine the number of children under age 22 living in each household,a. What is the random variable for this survey?b. Is the random variable discrete or continuous?
Two numbers are randomly drawn without replacement from a list of five. If the five numbers are 2, 2, 4, 6, 8, what is the probability distribution of the sum of the two numbers selected? Show the probability distribution graphically.
An economics quiz contains six multiple-choice questions. Let x represent the number of questions a student answers correctly.a. Is x a continuous or discrete random variable?b. What are the possible values of x?
The Center for Generational Kinetics had categorized the American workforce as follows: (1) Traditionalists (born before 1945); (2) Baby Boomers (born 1945 to 1964);(3) Generation X (born 1965 to 1976); (4) Millennials–Generation Y (born 1977 to 1995); (5) Generation Z(born 1996 or after)
The Employee Benefit Research Institute (EBRI) issued a report in 2015 that stated 55% of workers are confident they have enough money for a comfortable retirement.(Source: R. Helman, C. Copeland, and J. VanDerhei,“The 2015 Retirement Confidence Survey: Having a retirement savings plan a key
Continuing with the ECCO company from Exercise 4-83, when a customer returns one of the alarms under warranty, the quality manager logs data on the product. From the data available in the Ecco file, use relative frequency to answer these questions.a. If a part was made in the Salt Lake City plant,
The ECCO company makes backup alarms for machinery like forklifts and commercial trucks. When a customer returns one of the alarms under warranty, the quality manager logs data on the product. From the data available in the file named Ecco, use relative frequency to answer the following
A survey of 300 CEOs was conducted in which the CEOs were to list their corporation’s geographical location: Northeast (NE), Southeast (SE), Midwest(MW), Southwest (SW), and West (W). They were also requested to indicate their company’s industrial type:Communications (C), Electronics (E),
In a large metropolitan area, 65% of commuters ride the train only, 18% ride the bus only, and 6% ride both the train and the bus to get to the central business district.a. What is the probability that a randomly selected commuter does not ride the train to the central business district?b. What is
In a large shipment of electronic parts, 0.015 are bad.The parts are tested using a machine that correctly identifies bad parts as defective with a probability of 0.98, and correctly identifies good parts as nondefective with a probability of 0.95.a. If a part is randomly sampled from the shipment
A large coffeehouse has found that 50% of all customers order food, 80% order coffee, and 40% order both. What is the probability that a customer at the coffeehousea. Orders food but no coffee?b. Orders coffee but no food?c. Orders neither coffee nor food?
After spending some time studying company e-mail accounts, the manager of computer security for a large insurance company has determined that 25% of all e-mail messages sent to employee computers are spam.If 80% of all spam e-mails sent to personal accounts contain the word guarantee in the Subject
Based on a survey conducted by students in the Recreational Management degree program, 65% of students at the university own a mountain bike, 25%own a road bike, and 6% own both a mountain bike and a road bike.a. What is the probability that a randomly selected student at this university has a
Thirty-five percent of all customers of a large, national financial institution manage their accounts online.What is the probability that in a random sample of three customers from the financial institution’s database,a. All three manage their accounts online?b. Exactly two manage their accounts
Five hundred smartphone owners were asked if they use their phones to download sports scores. The responses are summarized in the following table:Yes No Total Male 195 105 300 Female 70 130 200 Total 265 235 500a. What is the probability that a randomly sampled respondent from this group has used
A manufacturing firm has two suppliers for an electrical component used in its process: one in Mexico and one in China. The supplier in Mexico ships 82% of all the electrical components used by the firm and has a defect rate of 4%. The Chinese supplier ships 18% of the electrical components used by
Fifty chief executive officers of small to medium-sized companies were classified according to their gender and functional background as shown in the table below:Functional Background Male Female Total Marketing 4 10 14 Finance 11 5 16 Operations 17 3 20 Total 32 18 50a. If a chief executive is
An investment firm is thinking of opening a skiing facility in Colorado. It is trying to decide whether to open an area catering to family skiers or to some other group. To help make its decision, it gathers the following information. Let A1 = Family will ski A2 = Family will not ski B1 = Family
Recently, several long-time customers at the Sweet Haven Chocolate Company have complained about the quality of the chocolates. It seems there are several partially covered chocolates being found in boxes. The defective chocolates should have been caught when the boxes were packed. The manager is
Ponderosa Paint and Glass makes paint at three plants. It then ships the unmarked paint cans to a central warehouse. Plant A supplies 50% of the paint, and past records indicate that the paint is incorrectly mixed 10%of the time. Plant B contributes 30%, with paint mixed incorrectly 5% of the time.
A national convenience store chain determines that 70%of gas purchases are made with a credit or debit card.a. Indicate the type of probability assessment method that the gas station manager would use to assess this probability.b. In one local store, 10 randomly chosen customers were observed. All
FM Auto Workshop is conducting a study for its two branches (FM1 and FM2) on oil changes and tire rotations. Two hundred customers were involved in the study. Thirty-six out of 119 oil change customers visited FM2. Thirty-five customers went to FM1 for their tire rotations.a. Find the probability
An April 14, 2015, article by Kara Brandeisky on Money magazine’s website states that overall the chance of being audited by the IRS in 2014 was 0.86%. If a person’s adjusted gross income was between $50,000 and $74,999, the chance of being audited drops to 0.53%, and for those with incomes
When customers call into a bank’s customer service phone line, they are asked to complete a survey on service quality at the end of the call. Six out of ten customers agree to do the survey. Of those who agree, 58% actually respond to all the questions.a. Calculate the probability that a randomly
An accounting professor at a state university in Vermont recently gave a three-question multiple-choice quiz.Each question had four optional answers.a. What is the probability of getting a perfect score if you were forced to guess at each question?b. Suppose it takes at least two correct answers
Examine the following table:A A Totals B 200 800 1,000 B 300 700 1,000 Totals 500 1,500 2,000a. Calculate the following probabilities:P1A2, P1A2, P1A B2, P1A B2, P1A B2, and P1A B2.b. Show that (1) A and B, (2) A and B (3) A and B, and (4) A and B are dependent events.
Consider the following table:A A Totals B 800 200 1,000 B 600 400 1,000 Totals 1,400 600 2,000 Explore the complements of conditional events:a. Calculate the following probabilities:P1A B2, P1A B2, P1A B2, P1A B2.b. Now determine which pair of events are complements of each other. (Hint: Use the
Examine the relationship between independent, dependent, and mutually exclusive events. Consider two events A and B that are mutually exclusive such that P1A2 0.a. Calculate P1A B2.b. What does your answer to part a say about whether two mutually exclusive events are dependent or independent?c.
Discuss what is meant by subjective probability. Provide a business-related example in which subjective probability assessment would likely be used. Also, provide an example of when you have personally used subjective probability assessment.
Discuss what is meant by the relative frequency assessment approach to probability assessment. Provide a business-related example, other than the one given in the text, in which this method of probability assessment might be used.
Discuss what is meant by classical probability assessment and indicate why classical assessment is not often used in business applications.
A scooter manufacturing company is notified whenever a scooter breaks down, and the problem is classified as being either mechanical or electrical. The company then matches the scooter to the plant where it was assembled. The file Scooters contains a random sample of 200 breakdowns. Use the data in
A report indicated the average number of days it takes for an American company to fill a job vacancy is 48 days. Sample data similar to those used in the study are in a file titled Hired. Categories for the days and hire cost are provided under the headings “Time” and“Cost,” respectively.a.
The loan manager for High Desert Bank selected a sample of the loans her bank has made in the past year.The file High Desert Banking contains information on the loan amount, the type of loan, and the region of the state where the loan was made.a. What is the probability of randomly selecting a loan
A survey asked what the most important reason was that people give for not using a wireless phone exclusively. The responses were: (1) Like the safety of traditional phone, (2) Like having a land line for a backup phone, (3) Pricing not attractive enough,(4) Weak or unreliable cell signal at home,
Continuing with the survey done by the managers of the hotel chain, based on the data from the survey, found in the file HotelSurvey, determine the following probabilities using the relative frequency assessment method.a. Of two customers selected, what is the probability that neither will be on a
A hotel chain conducted a survey of its guests. Sixtytwo surveys were completed. Based on the data from the survey, found in the file HotelSurvey, answer the following questions using the relative frequency assessment method.a. Of two customers selected, what is the probability that both will be on
ECCO is a company that makes backup alarms for commercial vehicles and heavy-duty equipment like forklifts. The data file ECCO contains warranty claim data as well as the associated manufacturing plant, complaint code, and shift for each alarm that is manufactured.a. Based on the data provided,
A box of 50 remote control devices contains three that have a defective power button. If devices are randomly sampled from the box and inspected one at a time, determinea. The probability that the first control device is defective.b. The probability that the first control device is good and the
Suppose an auditor has 18 tax returns, 12 of which are for physicians. If three of the 18 tax returns are randomly selected, then what is the probability that at least one of the three selected will be a physician’s tax return?
Your company assigned two accident insurance plans(Plan 1 and Plan 2) among the full-time and part-time staffs. There are 70% of full-time staffs in the company and 60% of staffs had been assigned in Plan 2. Given Plan 1, the probability for full-time staff is 0.75 and the probability for part-time
A distributor of outdoor yard lights has four suppliers.This past season, she purchased 40% of the lights from Franklin Lighting, 30% from Wilson & Sons, 20%from Evergreen Supply, and the rest from A. L. Scott.In prior years, 3% of Franklin’s lights were defective, 6% of the Wilson lights were
Uncle John owns a roadside magazine stall. This morning it starts to rain. Given a rainy morning, the chance uncle John sold all his newspapers is 25%.When it is not a rainy morning, uncle John would have sold 85% of all his newspapers. The probability of a rainy morning is 0.125.a. What is the
A major electronics manufacturer has determined that when one of its televisions is sold, there is 0.08 chance that it will need service before the warranty period expires. It has also assessed a 0.05 chance that a digital video recorder (DVR) will need service prior to the expiration of the
Nikon is launching their new wireless transmitter, which implemented better send and receive technology.The signal is transmitted using the new model with probability 0.76 and using the old model with probability 0.34. The chance of receiving a signal given using the new model transmitter is 80%;
A corporation has 11 manufacturing plants. Of these, seven are domestic and four are outside the United States. Each year a performance evaluation is conducted for four randomly selected plants. What is the probability that a performance evaluation will include at least one plant outside the United
Vegetables from the summer harvest are processed at a food-processing plant. The manager has found a case of cans that have not been properly sealed. There are three lines that processed cans of this type, and the manager wants to know which line is most likely to be responsible for this mistake.
Online marketplaces such as Craigslist have become a popular way for individuals to buy and sell miscellaneous items. The table below shows the numbers of days products stayed active (not sold) on one of these sites and also the price range of the items.Days on the Website Price Range 1- 7 8 - 30
Dreamland has its own factory in manufacturing pillows. It manufactures two types of pillows—polyester pillows and memory foam pillows.Dreamland distributes its pillows to hospitals, hotels, and department stores. The following are the number of distributions made in a day:Pillow Type Hospitals
A government-sponsored subsidized housing construction contract is to be awarded on the basis of a blind drawing from those who have bid. In addition to the Hubble Company, five other companies have submitted bids.a. What is the probability of the Hubble Construction Company winning the bid?b.
RAC is an automotive dealer selling imported new cars, and a number of them are Japanese cars. The manager of RAC found that 60% of the customers visited them but didn’t purchase anything. About 25%bought an imported new car and 45% bought a Japanese car. What is the probability a customer
Cindy is planning for a day trip and is deciding whether to wear closed-toed shoes or sandals during her trip. She is also checking the weather reports. If the report indicates it will rain then she will wear closedtoed shoes; otherwise, she will wear a pair of sandals.The weather conditions state
Suppose the managers at FedEx Office wish to meet the increasing demand for color photocopies and to have more reliable service. (Refer to Exercise 4-36.) As a goal, they would like to have at least a 99.9% chance of being able to furnish a black-and-white copy or a color copy on demand. They also
A local FedEx Office has three black-and-white copy machines and two color copiers. Based on historical data, the chance that each black-and-white copier will be down for repairs is 0.10. The color copiers are more of a problem and are down 20% of the time each.a. Based on this information, what is
A hair salon caters to both men and women. In addition to hairstyles, the salon provides back and shoulder massages. In the past, 42% of men have requested a massage and 61% of women have requested a massage. The salon’s customers are 48.2%men and 51.8% women.a. If a customer arrives for a hair
Three events occur with probabilities P1E12 = 0.35, P1E22 = 0.25, P1E32 = 0.40. Other probabilities are P1B E12 = 0.25, P1B E22 = 0.15, P1B E32 = 0.60.a. Compute P1E1 B2.b. Compute P1E2 B2.c. Compute P1E3 B2.
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