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business
business statistics in practice
Business Statistics For Contemporary Decision Making 3rd Canadian Edition Ken Black, Ignacio Castillo - Solutions
The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for “slightly higher pay.” In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly
An increasing number of consumers believe they have to look out for themselves in the marketplace. According to a survey conducted by the Yankelovich Partners for USA WEEKEND magazine, 60% of all consumers have called an information line for a product. Suppose a random sample of 25 consumers is
According to the Financial Planners Standards Council, 22% of certified financial planners (CFPs) earn between $100,000 and $149,999 per year. Thirty-two percent earn $150,000 or more. Suppose a complete list of all CFPs is available and 18 are randomly selected from that list.a. What is the
Shown here are the 10 Canadian provinces ranked by operating revenue for the hotels, motor hotels, and motels industry as compiled by Statistics Canada for a recent year.Suppose four of these provinces are selected randomly.a. What is the probability that exactly two provinces are west of
A western city has 18 police officers eligible for promotion. Eleven of the 18 are men. Suppose only five of the police officers are chosen for promotion and that one is a man. If the officers chosen for promotion had been selected by chance alone, what is the probability that one or fewer of the
Find the following values by using the Poisson formula.a. P (x = 5 | λ = 2.3)b. P (x = 2 | λ = 3.9)c. P (x ≤ 3 | λ = 4.1)d. P (x = 0 | λ = 2.7)e. P (x = 1 | λ = 5.4)f. P (4 < x < 8 | λ = 4.4)
Following are the three-year annualized returns for 14 popular mutual funds in a recent year.a. Calculate the mean, median, and mode.b. Calculate the range, interquartile range, mean absolute deviation, sample variance, and sample standard deviation.c. Compute the Pearsonian coefficient of skewness
On Monday mornings, a CIBC branch has only one teller window open for deposits and withdrawals. Experience has shown that the average number of arriving customers in a 4-minute interval on Monday mornings is 2.8, and each teller can serve more than that number efficiently. The random arrivals at
We show the companies with the largest oil-refining capacity in the world according to Forbes. Use these population data and answer the questions.a. What are the values of the mean and the median? Compare the answers and state which you prefer as a measure of location for these data and why.b. What
Suppose a market research firm enlisted 800 families in one Canadian city to participate in a study of expenditures for the December holiday season. Each family kept a log of spending for this holiday season and submitted their log to the market research firm. The following Excel descriptive output
Determine the interquartile range for the following data. 44 46 23 82 71 18 59 19 14 25 39 37 90 38 39 40 15 58 27 84 59 73 35 24 70
Construct a box-and-whisker plot for the following data. Do the data contain any outliers? Is the distribution of data skewed? 540 690 379 601 $10 623 527 570 503 559 477 495 558 495 574 590 490 562 588 602 609 580 497 541
Environmentalists are concerned about emissions of sulphur dioxide into the air. The average number of days per year in which sulphur dioxide levels exceed 150 mg/m3 in Milan, Italy, is 29. emissions of sulphur dioxide? What percentage of the years would exceed 37 days? What percentage of the years
Shown here are revenues of the top 10 fastest-growing companies as reported by Fortune in a recent year. Use this population data to compute a mean and a standard deviation for these 10 companies. Company Health Insurance Innovations Stamps.com Supernus Pharmaceuticals Applied
Use a business analytics approach to analyze the following data using descriptive statistics. Write a half-page report of your findings that might aid business people making decisions based on information gleaned from these data. 52 45 33 53 47 34 55 78 60 44 54 64 63 64 54
The following are the per capita GDP figures (rounded to the nearest hundred) for eight European countries according to the World Bank. The monetary figures are in international dollars; for comparison, the per capita GDP for Canada is INT $46,378.a. Compute the mean and standard deviation for
The following list shows the most popular stocks with investment clubs. Compute the mean, median, P30, P60, P90, Q1, Q3, range, and interquartile range. Company PepsiCo Intel Motorola Yum! Brands Merck & Co. AFLAC Diebold Nixdorf McDonald's Coca-Cola Lucent Technologies Home Depot Clayton Homes RPM
The latest Canadian census asked every household to report information on each person living there. Suppose for a sample of 30 households selected, the number of people living in each was reported as follows:Compute the mean, median, mode, range, lower and upper quartiles, and interquartile range
The latest Canadian census asked every household for the age of each person living there. Suppose that a sample of 40 households taken from the census data showed the age of the first person recorded on the census form to be as follows.
Hispanic Business, Inc. compiled a list of the top advertisers cultivating the Hispanic market in the U.S. These data (US$ millions) were entered into a spreadsheet and analyzed. Study the output and describe the expenditures of these top Hispanic market advertisers. 1 2 Mean 3 Standard deviation 4
The sales volumes for the top real estate brokerage firms in Canada for a recent year were analyzed using descriptive statistics. The mean annual dollar volume for these firms was $551 million, the median was $319 million, and the standard deviation was $959 million. Compute the value of the
The top 20 Canadian ports in a recent year, ranked by total tonnage (in millions of tonnes), were as follows.a. Construct a box-and-whisker plot for these data.b. Discuss the shape of the distribution from the plot.c. Are there outliers?d. What are they and why do you think they are outliers?
The Globe and Mail compiled a list of the top 100 public companies in Canada according to profit. Leading the list is the Toronto- Dominion Bank, followed by the Bank of Nova Scotia. The following Excel descriptive statistics output describes the profits for these 100 companies. Study the output
Many large companies are located around the world. The number of employees for 46 of the largest employers with headquarters outside the United States were analyzed with Excel’s descriptive statistics feature. The data follow. Summarize what you have learned about the number of employees for
The Competitive Media Reporting and Publishers Information Bureau compiled a list of the top 25 advertisers in the U.S. for a recent year. The total advertising expenditures for each company (US$ thousands) were analyzed. Study this output and summarize the expenditures of the top 25 advertisers in
Use the values in the matrix to solve the equations given.a. P ( A ∪ D ) = ____b. P ( E ∪ B ) = ____c. P ( D ∪ E ) = ____d. P ( C ∪ F ) = ____ A B с D 5 10 00 8 E 8 6 2 F 12 4 5
According to a recent census, the average annual salary of a worker in Edmonton, Alberta, is $30,468. Suppose the median annual salary for a worker in this group is $26,721 and the mode is $25,000. Is the distribution of salaries for this group skewed? If so, how and why? Which of these measures of
A small company has 20 employees. Six of these employees will be selected randomly to be interviewed as part of an employee satisfaction program.a. How many different groups of six can be selected?b. In how many different sequences can the six employees be selected?
Use the values in the matrix to solve the equations given.a. P ( A ∪ F ) = ____b. P ( E ∪ B ) = ____c. P ( B ∪ C ) = ____d. P ( E ∪ F ) = ____ E A 0.10 B 0.04 C D 0.27 0.31 F 0.03 0.12 0.06 0.07
A company’s customer service toll-free telephone system is set up so that the caller has six options. Each of these six options leads to a menu with four options. For each of these four options, three more options are available. For each of these three options, another three options are
Given P (A) = 0.10, P (B) = 0.12, P (C) = 0.21, P (A ∩ C) = 0.05 , and P (B ∩ C) = 0.03, solve the following.a. P ( A ∪ C ) = ____b. P ( B ∪ C ) = ____c. If A and B are mutually exclusive, P ( A ∪ B ) = ____
According to a survey, 16% of the population is technology driven. However, these figures vary by region. For example, in British Columbia the figure is 20% and in Manitoba the figure is 17%. Sixteen percent of the Canadian population in general is in BC and 3.7% of the Canadian population is in
Suppose that 47% of all Canadians have flown in an airplane at least once and that 28% of all Canadians have ridden on a train at least once. What is the probability that a randomly selected Canadian has either ridden on a train or flown in an airplane? Can this problem be solved? Under what
Shown here are 19 oil-refining companies. Some of the companies are privately owned and others are state owned. Suppose six companies are randomly selected.a. What is the probability that exactly one company is privately owned?b. What is the probability that exactly four companies are privately
Determine the mean, the variance, and the standard deviation of the following discrete distribution. x 1 2 3 4 5 P(x) 0.238 0.290 0.177 0.158 0.137
Suppose 20% of the people in a city prefer Pepsi-Cola as their soft drink of choice. If a random sample of six people is chosen, the number of Pepsi drinkers can range from zero to six. Shown here are the possible numbers of Pepsi drinkers in a sample of six people and the probability of that
Determine the mean, the variance, and the standard deviation of the following discrete distribution. X 0 1 123 2 4 567 5 6 P(x) 0.103 0.118 0.246 0.229 0.138 0.094 0.071 0.001
Eighty-three percent of the Canadian population now live in urban areas.2 Assume that about 15% of all Canadian adults care for ill relatives and that 11% of adults living in urban areas care for ill relatives.a. Use the general law of multiplication to determine the probability of randomly
A survey estimated that 67% of all households with television subscribe to a digital streaming service. Seventy-four percent of all households with television have two or more TV sets. Suppose 55% of all households with television subscribe to a digital streaming service and have two or more TV
In a recent consumer payment study, respondents were asked which payment type feels safest for online purchases. Credit card was selected as safest by 42% of the respondents. None of the respondents selected both credit card and debit card. Forty-seven percent selected neither credit card nor debit
According to Statistics Canada figures, 28.3% of all Canadians are in the 0–24 age bracket, 13.8% are in the 25–34 age bracket, 13.2% are in the 35–44 age bracket, and 44.6% are in the 45 and older age bracket. Suppose a market research study shows that Canadians use their leisure time in
The Report on Business Top 1,000 ranks 1,000 Canadian companies using various criteria. Of the top 20 companies by number of employees, 4 are banks. Suppose four companies are randomly selected.a. What is the probability that none of the companies are banks?b. What is the probability that all four
Over three decades ago, four businesspeople who had experience in retailing natural foods through food stores believed that there was a demand for a supermarket for natural foods. As a result, in 1980 in Austin, Texas, they founded the first Whole Foods Market store in a building that had around
In a recent survey, buyers were asked a series of questions with regard to Internet usage. One question asked was how they would use the Internet if security and other issues could be resolved. Suppose that 78% said they would use it for pricing information, 75% said they would use it to send
Assume that a study has shown that about half of all Canadian workers who change jobs cash out their pension plans rather than leaving the money in the account to grow. The percentage is much higher for workers with small pension plan balances. In fact, 87% of workers with pension plan accounts
Suppose the average number of annual trips per family to amusement parks in Canada is Poisson distributed, with a mean of 0.6 trips per year. What is the probability of randomly selecting a Canadian family and finding the following?a. The family did not make a trip to an amusement park last year.b.
Ship collisions in the Vancouver harbour are rare. Suppose the number of collisions is Poisson distributed, with a mean of 1.2 collisions every four months.a. What is the probability of having no collisions occur over a four-month period?b. What is the probability of having exactly two collisions
In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was determined that 20% of all stock investors are retired people. In addition, 40% of all adults invest in mutual funds. Suppose a random sample of 25 stock investors is taken. What is the probability that exactly
According to the Heart and Stroke Foundation of Canada, in a recent year 17.6% of Canadians between the ages of 65 and 79 report having heart disease or stroke. Suppose you live in a province where the environment is conducive to good health and low stress and you believe these conditions promote
Suppose a survey reveals that 69% of Canadian workers say job stress causes frequent health problems. One in four said they expected to burn out on the job in the near future. Thirty-two percent said they thought seriously about quitting their job last year because of workplace stress. Forty-nine
Suppose that the probability that a passenger files a complaint with the Canadian Transportation Agency about a particular airline is 0.000014. Suppose 100,000 passengers who flew with this particular airline are randomly contacted.a. What is the probability that exactly five passengers filed
According to a recent census, about 63% of Manitoba residents live in cities with a population of 10,000 or more people. A catalogue sales company in Ontario just purchased a list of Manitoba consumers. Its market analyst randomly selects 25 people from this list.a. What is the probability that
Determine the probabilities for the following normal distribution problems.a. μ = 604 , σ = 56.8 , x ≤ 635b. μ = 48 , σ = 12 , x < 20c. μ = 111 , σ = 33.8 , 100 ≤ x < 150d. μ = 264 , σ = 10.9 , 250 < x < 255e. μ = 37 , σ = 4.35 , x > 35f. μ = 156 , σ = 11.4 , x ≥ 170
Recent market research reported that HP controlled 23% of the PC market in Canada. Suppose a business analyst randomly selects 130 recent purchasers of PCs in Canada.a. What is the probability that more than 35 PC purchasers bought an HP computer?b. What is the probability that between 24 and 34 PC
During the summer at a small private airport in western British Columbia, the unscheduled arrival of airplanes is Poisson distributed with an average arrival rate of 1.12 planes per hour.a. What is the average interarrival time between planes?b. What is the probability that at least 2 hours will
Tool workers are subject to work-related injuries. One disorder, caused by strains to the hands and wrists, is called carpal tunnel syndrome. It strikes as many as 23,000 workers per year. It is estimated that the average cost of this disorder to employers and insurers is approximately $30,000 per
During the dry month of August, one Canadian city has measurable rain on average only 2 days per month. If the arrival of rainy days is Poisson distributed in this city during the month of August, what is the average number of days that will pass between measurable rain? What is the standard
The exponential distribution can be used to solve Poisson-type problems in which the intervals are not time. According to SITA, the Geneva-based organization that provides World Tracer and other logistical technology to the air transport industry, 26.04-million checked bags were damaged, delayed,
Income tax returns one year averaged $1,332 in refunds for taxpayers. One explanation of this figure is that taxpayers would ratherhave the government keep back too much money during the year than owe it money at the end of the year. Suppose the average amount of tax at the end of a year is a
Tompkins International reports that the mean clear height for a Class A warehouse in the U.S. is about 6.7 m. Suppose clear heights are normally distributed and that the standard deviation is 1.2 m. A Class A warehouse in the U.S. is randomly selected.a. What is the probability that the clear
Suppose that the annual employer participation in the Canada/ Quebec Pension Plan (CPP/QPP) per employee is normally distributed with a standard deviation of $625, but the mean is unknown. If 73.89% of such employer contributions are greater than $1,700, what is the mean annual employer
One study on managers’ satisfaction with management tools reveals that 59% of all managers use self-directed work teams as a management tool. Suppose 70 managers selected randomly in Canada are interviewed. What is the probability that fewer than 35 use self-directed work teams as a management
Marriott of business travellers who take trips of five nights or more. According to this study, 37% of these travellers enjoy sightseeing more than any other activity that they do not get to do as much at home. Suppose 120 randomly selected business travellers who take trips of five nights or more
Data accumulated by Environment Canada show that the average wind speed in kilometres per hour for Victoria International Airport, located on the Saanich Peninsula in British Columbia, is 9.3. Suppose wind speed measurements are normally distributed for a given geographic location. If 22.45% of the
Suppose that the Canadian national average wait time for patients to see a doctor in a walk-in clinic is 21.3 minutes. Suppose such wait times are normally distributed with a standard deviation of 6.7 minutes. Some patients will have to wait much longer than the mean to see the doctor. In fact,
Suppose the average Canadian household spends $2,100 a year on all types of insurance. Suppose the figures are uniformly distributed between the values of $400 and $3,800. What are the standard deviation and the height of this distribution? What proportion of households spends more than $3,000 a
Determine the probability or area for the portions of the z distribution described.a. z ≥ 1.96b. z < 0.73c. − 1.46 < z ≤ 2.84d. − 2.67 ≤ z ≤ 1.08e. − 2.05 < z ≤ − 0.87
The average fill volume of a regular can of soft drink is 355.0 mL. Suppose the fill volume of these cans ranges from 354.0 mL to 355.8 mL and is uniformly distributed. What is the height of this distribution? What is the probability that a randomly selected can contains more than 355.2 mL of
The Canadian Newspaper Association releases figures on the top newspapers in Canada. Shown here are the top 20 daily newspapers in Canada ranked according to circulation.Suppose a business analyst wants to sample a portion of these newspapers and compare the sizes of the business sections of the
An office in Calgary, Alberta, has 24 workers including management. Eight of the workers commute to work from Airdrie. Suppose six of the office workers are randomly selected.a. What is the probability that all six workers commute from Airdrie?b. What is the probability that none of the workers
According to Statistics Canada, 16% of the workers in Calgary use public transportation. If 25 Calgary workers are randomly selected, what is the expected number to use public transportation? Graph the binomial distribution for this sample. What are the mean and the standard deviation for this
According to a study, the proportion of Canadian households relying solely on a cellphone for telephone service is about 13%. A marketing analyst randomly selects 50 Canadian households.a. How many households would the analyst expect to rely solely on a cellphone?b. What is the probability that
The following table lists the 28 largest Canadian universities according to full-time undergraduate enrolment figures. The province of location is given in parentheses.a. If five different universities are selected randomly from the list, what is the probability that three of them have enrolments
According to the Canadian Medical Association, about 55% of all Canadian physicians under the age of 35 are women. Your company has just hired eight physicians under the age of 35 and only two are women. If a group of women physicians under the age of 35 want to sue your company for discriminatory
In one western city, the government has 14 repossessed houses, which are evaluated to be worth about the same. Ten of the houses are on the north side of town and the rest are on the west side. A local contractor submitted a bid to purchase four of the houses. Which houses the contractor will get
Study the following output. Discuss the type of distribution, the mean, the standard deviation, and why the probabilities fall as they do. Probability Density Function Binomial with n = 15 and p = 0.36 x
Study the following output. Explain the distribution in terms of shape and mean. Are these probabilities what you would expect? Why or why not? A B 1 x Values Poisson Probabilities: λ = 2.78 234567 0 1 2 3 4 5 8 6 9 7 10 8 11 9 12
Mercedes and BMW have been competing head-to-head for market share in the luxury-car market for more than three decades. Back in 1959, BMW (Bayerische Motoren Werke) almost went bankrupt and nearly sold out to Daimler-Benz, the maker of Mercedes-Benz cars. BMW was able to recover to the point that
Public Citizen’s Health Research Group studied the serious disciplinary actions that were taken during a recent year against nonfederal medical doctors in the U.S. The American average was 3.05 serious actions per 1,000 doctors. Assume that the Canadian average is the same; moreover, assume that
1. List four important properties of the normal distribution.2. Why are z values important when dealing with a normal distribution?3. How does the variable x relate to the mean μ of a normal distribution given information about the z value? Match the information in column 1 with the corresponding
Find the probabilities for the following exponential distribution problems.a. P(x ≥ 3 | λ = 1.3)b. P(x < 2 | λ = 2.0)c. P(1 ≤ x ≤ 3 | λ = 1.65)d. P(x > 2 | λ = 0.405)
Statistics Canada reports that one in four people 15 years of age or older volunteers some of his or her time. If this figure holds for the entire population and if a random sample of 150 people 15 years of age or older is taken, what is the probability that more than 50 of those sampled do
Statistics Canada reports that of people who usually work fulltime, the average number of hours worked per week is 42.2. Assume that the number of hours worked per week for those who usually work full-time is normally distributed. Suppose 12% of these workers work more than 48 hours. Based on this
According to Alberta Egg Producers, Alberta egg farmers produce millions of eggs every year. Suppose egg production per year in Alberta is normally distributed, with a standard deviation of 83-million eggs. If during only 3% of the years Alberta egg farmers produce more than 2,655-million eggs,
The Canada Mortgage and Housing Corporation lists average monthly apartment rents for many cities in Canada. According to its report, the average cost of renting a two-bedroom apartment in Halifax is $833. Suppose that the standard deviation of the cost of renting a two-bedroom apartment in Halifax
Statistics Canada reports that the average annual family income in Regina is $81,832. Suppose annual family income in Regina is normally distributed, with a standard deviation of $7,712. A Regina family is randomly selected.a. What is the probability that the family’s income is more than
Suppose the average speeds of passenger trains travelling from Winnipeg to Churchill in Manitoba are normally distributed, with a mean average speed of 142 km/h and a standard deviation of 10.3 km/h.a. What is the probability that a train will average less than 110 km/h?b. What is the probability
According to Statistics Canada, about 71% of commuters in Canada drive to work. Suppose 150 Canadian commuters are randomly sampled.a. What is the probability that fewer than 105 commuters drive to work?b. What is the probability that between 110 and 120 (inclusive) commuters drive to work?c. What
It has been reported that the mean western Canadian production of wheat and durum over a 10-year period was 22.45-million tonnes. Assume that the Canadian production of wheat over this period has been approximately uniformly distributed. If the height of this distribution is 8.94-million tonnes,
According to The Polk Company, a survey of households using the Internet to buy or lease cars reported that 81% were seeking information about prices. In addition, 44% were seeking information about products offered. Suppose 75 randomly selected households that are using the Internet to buy or
Coastal businesses in the Atlantic provinces worry about the threat of hurricanes during the season from June through October. Suppose the arrival of hurricanes during this season is Poisson distributed, with an average of three hurricanes threatening Atlantic Canada during the 5 month season. If a
The U.S. Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a university degree, the mean pre-tax family income is US $85,200. Suppose that 60% of the pre-tax family incomes when the head of the household has a
It has been reported that the average operating cost of an MD-80 jet airliner is $2,087 per hour. Suppose the operating costs of an MD-80 jet airliner are normally distributed with a standard deviation of $175 per hour. What cost would 20% of the operating costs be less than? What cost would 65% of
According to the Canadian Newspaper Association, the average daily circulation of The Globe and Mail based on recent figures is 302,190. Suppose the standard deviation is 7,308. Assume the paper’s daily circulation is normally distributed. On what percentage of days would it surpass a circulation
Supermarkets usually become busy at about 5 p.m. on weekdays, because many workers stop by on the way home to shop. Suppose at that time arrivals at a supermarket’s express checkout station are Poisson distributed, with an average of 0.8 people/minute. If the clerk has just checked out the last
According to Canadian Radio-television and Telecommunications Commission, the average number of hours of TV viewing among adults is 27 hours per week.4 Suppose the standard deviation is 6.7 hours and a random sample of 42 Canadian households is taken.a. What is the probability that the sample
The same study mentioned above found that 36% of Canadians rely on pharmacists for drug information. Suppose 200 Canadians are randomly surveyed.a. What is the probability that fewer than 90 of the Canadians rely on pharmacists for drug information?b. What is the probability that more than 100 of
Let’s assume that the average annual consumption of fresh fruit per person in a recent year is 77.8 kg. Suppose the standard deviation of fresh fruit consumption is about 20 kg. Suppose an analyst took a random sample of 38 people and had them keep a record of the fresh fruit they ate for one
Suppose a small town in British Columbia contains 1,500 houses. A sample of 100 houses is selected randomly and evaluated by an appraiser.If the mean appraised value of a house in this town for all houses is $277,000, with a standard deviation of $10,500, what is the probability that the sample
Give an example of how convenience sampling could be used in a study of Report on Business Magazine’s Top 1,000 executives to measure corporate attitude toward paternity leave for employees.
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