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What was the primary use of statistics in ancient times?

In what ways can business statistics be useful in today’s business environment?

In 2002, the Cinergy Corporation sold 35,615 million cubic feet of gas to residential customers, an increase of 1.1% over the previous year. Does this information represent descriptive statistics or inferential statistics? Why?

An article in Runner’s World magazine described a study that compared the cardiovascular responses of 20 adult subjects for exercises on a treadmill, on a mini trampoline, and jogging in place on a carpeted surface. Researchers found average heart rates were significantly less on the mini trampoline than for the treadmill and stationary jogging. Does this information represent descriptive statistics or inferential statistics? Why?

What is the difference between a qualitative variable and a quantitative variable? When would each be appropriate?

Restaurants sometimes provide “customer reaction” cards so that customers can evaluate their dining experience at the establishment. What kinds of decisions might be made on the basis of this information?

What kinds of statistical data might a burglar alarm company employ in trying to convince urban homeowners to purchase its product?

The headline of an article in your daily newspaper begins “Research Study Reveals. . . .” As a statistics student who wishes to avoid accepting biased results, what single question should be foremost in your mind as you begin reading the article?

A research firm observes that men are twice as likely as women to watch the Super Bowl on television. Does this information represent descriptive statistics or inferential statistics? Why?

For each of the following, indicate the scale of measurement that best describes the information. 

a. In January 2003, Dell Corporation had approximately 39,100 employees.

b. USA Today reports that the previous day’s highest temperature
in the United States was 115 degrees in Death Valley, California.
c. An individual respondent answers “yes” when asked if TV contributes to violence in the United States.
d. In a comparison test of family sedans, a magazine rates the Toyota Camry higher than the VW Passat.

Generally, how do we go about deciding how many classes to use in a frequency distribution?

The National Safety Council reports the following age breakdown for licensed drivers in the United States.

Age (Years)                            Licensed Drivers (Millions)
under.........................................................................20 9.50
20–under 25.................................................................16.50
25–under 35................................................................ 34.02
35–under 45................................................................ 40.88
45–under 55................................................................ 40.74
55–under 65................................................................ 26.17
65 or over..................................................................... 28.90

Identify the following for the 35–under 45 class:
(a) Frequency, 

(b) Upper and lower limits, 

(c) Width,

(d) Midpoint.

The National Center for Health Statistics reports the following age breakdown of deaths in the United States during 2002.

Age (Years)                             Number of Deaths (Thousands)
under 15.................................................................................. 40.01
15–under 25........................................................................... 33.08
25–under 35........................................................................... 41.38
35–under 45........................................................................... 91.01
45–under 55......................................................................... 172.21
55–under 65......................................................................... 253.73
65–under 75......................................................................... 424.11
75 or over........................................................................... 1391.99

Identify the following for the 45–under 55 class:

(a) frequency, 

(b) upper and lower limits, 

(c) width,

(d) midpoint.

What is meant by the statement that the set of classes in a frequency distribution must be mutually exclusive and exhaustive?

For commercial banks in each state, the U.S. Federal Deposit Insurance Corporation has listed their total deposits (billions of dollars) as follows.


Construct a frequency distribution and a histogram for these data.

One of the ways Keynote Systems, Inc., measures Internet shopping site performance is by visiting a site and measuring how long it takes to come up on the user’s PC. In one such study, they found the average time for an Internet shopping site to come up was 21.80 seconds. Assume that website administrators for sears.com try their own site on 80 random occasions and come up with the times (in seconds) contained in data file XR02018. Generate a frequency distribution and histogram describing this information. Comment on whether the site seemed to be especially fast or slow coming up on any of the visits.

Construct a stem-and-leaf display for the following data:

Construct a stem-and-leaf display for the following data:
The following U.S. market shares for automobile and light-truck sales for 2001 and 2002 have been reported.


a. Express the data for the 2001 model year in the formof a bar chart.

b. Express the data for the 2002 model year in the form  of a bar chart.

For McDonald’s Corporation, net income per share of common stock was as follows for the period 1995–2005.


Construct a line graph describing these data over time.

For the period 1995–2005, McDonald’s Corporation paid the following dividends (rounded to nearest penny) per share of common stock.


Using these data and the data in Exercise 2.32, draw a line graph that describes both net income and dividend per share of common stock over time. (Both lines will be plotted on the same graph.)

It has been estimated that 95.5% of U.S. households own a telephone and that 68.5% have cable television.

a. Why can’t this information be summarized in one pie chart?

b. Construct two separate pie charts to summarize telephone ownership and cable television service.

Federal outlays for national defense totaled $348 billion in 2002 compared with just $134 billion in 1980.

a. Using appropriate symbols that would reflect favorably on such an increase, construct a pictogram to compare 2002 with 1980.
b. Using appropriate symbols that would reflect unfavorably on such an increase, construct a pictogram to compare 2002 with 1980.

Differentiate between a positive linear relationship and a negative linear relationship between variables.

When there is no relationship between two variables, what will tend to be the slope of the best-fit straight line through the scatter diagram?

PC World reports the following text and graphics speeds (pages per minute, or ppm) for its top-rated inkjet printers.


a. Draw a scatter diagram representing these data. 

b. Using the “eyeball” method, fit a straight line to the data.
c. Does there appear to be any relationship between the variables? If so, is the relationship direct or inverse?

The following data represent x = the total number of businesses and y = the number of business failures in mountain states over a 1-year period.


a. Draw a scatter diagram representing these data.
b. Using the “eyeball” method, fit a straight line to the data.
c. Does there appear to be any relationship between the variables? If so, is the relationship direct or inverse?

The breakdown of U.S. cities having a population of at least 10,000 persons has been reported as follows.


a. How many cities have a population of at least 25,000 but less than 500,000?
b. How many cities have a population less than 250,000?
c. How many cities have a population of at least 100,000 but less than 1,000,000? What percentage of cities are in this group?
d. What is the class mark for the 100,000–under 250,000 class?
e. Convert the table to a relative frequency distribution.

The average daily cost to community hospitals for patient stays during 1993 for each of the 50 U.S. states was as follows:


These data are also provided in the file XR02057. SOURCE: Health Insurance Association of America, Source Book of Health Insurance Data 1995, p. 103.
a. Construct a stem-and-leaf display for these data.
b. Construct a frequency distribution.
c. Determine the interval width and the class mark for each of the classes in your frequency distribution.
d. Based on the frequency distribution obtained in part (b), draw a histogram and a relative frequency polygon.

In 2004, unemployment rates in the 50 U.S. states were reported as follows. These data are also provided in the file XR02058.


a. Construct a stem-and-leaf display for these data.
b. Construct a frequency distribution for these data.
c. Determine the interval width and the class mark for each of the classes in your frequency distribution.
d. Based on the frequency distribution obtained in part (b), draw a histogram and a relative frequency polygon to describe the data.

During 2001, sales of new, privately owned homes in the total United States and in the western states were broken down into price categories as follows:


Convert these data to relative frequency distributions, one for the total United States, the other for the western states. Do the results appear to suggest any differences between total U.S. prices and those in the western states?

The following stem-and-leaf output has been generated by Minitab. The data consist of three-digit integers.


a. From this display, is it possible to determine the exact values in the original data? If so, list the data values. If not, provide a set of data that could have led to this display.

b. Interpret the numbers in the leftmost column of the output.

For the period 1990–1999, the Bristol-Myers Squibb Company, Inc. reported the following amounts (in billions of dollars) for 

(1) Net sales and 

(2) Advertising and product promotion. The data are also in the file XR02062.


For these data, construct a line graph that shows both net sales and expenditures for advertising/product promotion over time. Some would suggest that increases in advertising should be accompanied by increases in sales. Do your line graphs seem to support this?

social scientist would like to use a pictogram in comparing the number of violent crimes against persons in 2006 with the comparable figure for 1960. Considering that she can select from a wide variety of symbols to demonstrate these frequencies, suggest several possible symbols that would tend to underscore the violence and/or human tragedy of such crimes.

For 1979 through 1998, the net rate of investment income for U.S. life insurance companies was as follows. What was the mean net rate of investment income for this period? The median?

The following is a list of closing prices for 15 stocks widely held by Merrill Lynch account holders. What was the average closing price for this sample of stocks? The median closing price?


A student scored 90 on the midterm exam, 78 on the final exam, and 83 on the term project. If these three components are weighted at 35%, 45%, and 20%, respectively, what is the weighted mean for her course performance?

Provide a real or hypothetical example of a situation where the range could be misleading as a measure of dispersion.

A Polk Company survey found that households with someone who frequently plays golf have a median income of $54,826, compared to a median of $37,354 for all households. Under the assumption that the golfing households surveyed by the company could have been represented by the 100 incomes in file XR03036: 

a. Construct and interpret the box-and-whisker plot for the data.
b. Standardize the data, then determine the mean and standard deviation of the standardized values.

What is the coefficient of determination and what does it tell us about the relationship between two variables?

For a set of data, r2 is 0.64 and the variables x and y are inversely related. What is the numerical value of r?

The American Association of Retired Persons (AARP) has compiled data on death rates (deaths per 1000 people) from heart disease and cancer for the 50 states. The states and their respective death rates from these two diseases are provided in data file XR03046. Generate a scatter diagram with axes of your choice, fit a linear equation to the data, then determine and interpret the coefficients of correlation and determination. For many of the Exercises 3.48–3.64, a computer and statistical software will be desirable and useful. However, any necessary calculations can also be done with the aid of a pocket calculator. For readers using statistical software, keep in mind the file naming key for example, the data for Exercise 3.57 will be in data file XR03057.

During fiscal year 1986, McDonnell Douglas Corporation was second only to Lockheed Missiles & Space Company in net value of U.S. Department of Defense prime contract awards over $25,000 for research, development, test, and evaluation. The work awarded to McDonnell Douglas was done in 20 locations, with a breakdown (millions of dollars) as follows:


a. Determine the mean, median, and mode for these data.

b. In this case, does the mode appear to be a good measure of the typical amount of work that was awarded to a McDonnell division during that year? Why or why not?

The frequency distribution for population density (persons per square mile) for the 50 U.S. states is as follows:

Population Density                   Number of States
0–under 100............................................................ 27
100–under 200........................................................ 11
200–under 300......................................................... 4
300–under 400.......................................................... 1
400–under 500.......................................................... 2
500–under 600.......................................................... 1
600–under 700.......................................................... 0
700–under 800.......................................................... 1
800–under 900.......................................................... 1
900–under 1000........................................................ 0
1000–under 1100...................................................... 1
1100–under 1200...................................................... 1

Does this distribution appear to be symmetrical? If not, is it skewed positively or negatively?

For a sample of 5 different years from the period 1960 through 1998, it is found that U.S. work stoppages involving at least 1000 workers occurred 268 times in one of these years, with 424, 235, 145, and 44 work stoppages in the other four.
a. Determine the mean, median, range, and midrange.
b. Calculate the mean absolute deviation.
c. Calculate the standard deviation and variance.

A law enforcement agency, administering breathalyzer tests to a sample of drivers stopped at a New Year’s Eve roadblock, measured the following blood alcohol levels for the 25 drivers who were stopped:

a. Calculate the mean and standard deviation for this sample.
b. Use Chebyshev’s theorem to determine the minimum percentage of observations that should fall within k 1.50 standard deviation units of the mean. Do the sample results support the theorem?
c. Calculate the coefficient of variation for these data.

According to the Energy Information Administration, the average U.S. household spends $1338 per year for utilities (including heat, electricity, cooling, and water). The averages by region were as follows: Northeast ($1644), Midwest ($1396), South ($1328), and West ($1014). Assume that the findings for the Northeast could have been based on the utility expenditures reported by 250 households, with the data in file XR03065. 

a. Confirm the mean and determine the median and the standard deviation of the utility expenditures.
b. Generate and interpret the box-and-whisker plot for the households from this region.
c. From the results in parts (a) and (b), do there appear to be any “outlier” households? If so, for what reason(s) might energy-conservation officials wish to examine the habits or characteristics of these households?

Bride’s magazine reports the cost of the average honeymoon as $3657. Assume that their findings could have been based on the honeymoon expenditures of a sample consisting of 300 couples whose costs are listed in data file XR03066.

a. Confirm the mean and determine the median and the standard deviation of the honeymoon expenditures for this sample.
b. Generate and interpret the box-and-whisker plot for the couples in the sample. 

c. From the results in parts (a) and (b), do there appear to be any “outlier” couples who have spent an unusually large amount of money on their honeymoon? If so, what kinds of companies or organizations might have an interest in finding out how to identify such couples before they’ve made their honeymoon plans?

During 1999, 1,220,130 college-bound high school seniors took the Scholastic Aptitude Test (SAT). The average score on the mathematics component was 511, with a standard deviation of 114.We are assuming that the SATmath scores in data file XR03067 could have been the math scores for a sample of 400 college-bound seniors who took the SAT that year. (An important note: The mean and the standard deviation for our sample are close, but not exactly the same as the mean and standard deviation of the population from which the sample was obtained this is a key concept that is central to Chapter 8, Sampling Distributions.) Based on the assumed sample data in file XR03067, 

a. Determine the mean, the median, and the standard deviation of the math scores in the sample.
b. Generate and interpret the box-and-whisker plot for the math scores in the sample.

c. What math score would a test-taker have to achieve to be higher than 75% of the sample members? To be higher than 25% of the sample members?

Generate appropriate descriptive statistics of the screening test scores for those who did not default on their computer loan. Be sure to include the mean and the third quartile. Do the same for those who did default, then compare the results. Is the mean score on the screening test higher for those who did not default?

In the descriptive statistics of the screening test scores for the students who did not default, identify the value of the third quartile and interpret its meaning. If this numerical value had been established as a cutoff for receiving a computer loan, what percentage of those who repaid would have been denied a loan in the first place? Comment on the advisability of setting a cutoff score that is this high.

Construct adjacent dotplots (use box plots if the dotplot feature is not available on your computer statistical package) and visually compare the screening test scores of students who did not default on their computer loan to the scores of those who defaulted. Does the distribution of screening test scores for those who did not default appear to be shifted to the right of the distribution of scores for those who did default?

Based on your results and responses to the previous questions, does the screening test appear to be potentially useful as one of the factors in helping Baldwin predict whether a given applicant will end up defaulting on his or her computer loan?

A published article reports that 60% of U.S. households have cable television. The president of an electronics firm clips the item from the paper and files it under “Cable TV data.” Would this material be considered primary data or secondary data?

What are the major approaches to carrying out survey research?

Comment on the appropriateness of the question, “Have you ever broken the law and endangered the lives of others by running a red light?”

A research firm finds that only 33% of those who reported buying Kellogg’s Frosted Flakes had actually purchased the product during the period monitored. What type of survey research error does this represent?

A company has constructed two prototypes of a new personal digital assistant (PDA) and would like to find out which one of the two looks easier to use. Of the three types of surveys discussed in this section, which one would the company not wish to employ?

In studying the effectiveness of monetary rewards on seat belt usage, a firm has been giving out lottery tickets to employees wearing their belts when entering the company parking area. At the end of each week, the holder of the winning ticket gets a free dinner at a local restaurant. Before the experiment, only 36% of employees wore seat belts. After 1 month of the lottery, the usage rate is up to 57%. 

a. Identify the dependent and independent variables in this experiment.
b. Is a control group involved in this experiment? If so, who?

A direct-mail firm tries two different versions of a mailing, one of which includes a 50-cent monetary incentive for the respondent. Responses to the mailing with the incentive were 15% higher than for a similar mailing without it. 

a. Identify the dependent and independent variables in this experiment.
b. Is a control group involved in this experiment? If so, who?

In a health study, the dietary habits of 420,000 men were examined over a 3-year period. For those who ate  no fried foods, the death rate was 1208 per 100,000 man-years. For men who consumed fried foods more than 15 times a week, the corresponding rate was only 702. Considering that the relative ages of members of these two groups were not mentioned, critique the internal validity of the experiment.

When traveling, some motorists assume that a restaurant has good food and reasonable prices if there are a lot of trucks parked outside. What other observed characteristics of a restaurant might a traveler use in deciding whether to stop and eat?

Besides accounting and financial information, what are some of the other sources of internal secondary data?

Using your browser’s “people finder” capability, find out how many telephone listings are in your state for people with the same last name as yours. How many listings are there in your state for people named Smith?

Using one or more search engines and key words of your choice, find 

(a) A website that reports the average life span of Saint Bernard dogs and 

(b) A website that advises business professionals on strategies for writing an effective memo.

What is the difference between a sample and a census? Why can it be advantageous to select a sample instead of carrying out a census?

Provide a real or hypothetical example of a situation in which the sampling process is destructive.

Differentiate between the terms parameter and statistic. Which one will be the result of taking a sample?

To impress the interviewer, many respondents in a survey of 400 persons exaggerated their annual incomes by anywhere from 2% to 50%. Does such exaggeration represent sampling error or nonsampling error? Explain.

In survey research, what are some of the methods by which we can reduce nonsampling error?

Attendees at an industrial trade show are given the opportunity to fill out a card that entitles them to receive a free software package from the sponsoring firm. The cards are placed in a bin, and 30 winners will be drawn. Considering the 30 winners as a sample from all of the persons filling out such cards, is this a probability sample or a nonprobability sample? What specific type of probability or nonprobability sample does this procedure represent?

To obtain a sample of the invoices over the past year, a clerk uses the computer to select all invoice numbers that are a multiple of 13. If the invoice numbers are sequential, beginning with 1, what type of sample does this represent?

A study found that the average American buys 4.6 movie tickets per year, compared to just 1.9 for the average Spaniard. Assuming that the data values in file XR04049 represent the number of movie ticket purchases reported by 100 American respondents,
a. Select a simple random sample of 20 data values. Compute the sample mean. 

b. Select another simple random sample of 20 data values, and compute the mean.
c. To two decimal places, compare the mean of the sample in part (a) with the mean of the sample in part (b). Are the values identical? Would you expect them to be? How do they compare to the mean of the 100 data values from which the samples were drawn? (We will learn more about this topic in Chapter 8, Sampling Distributions.)

One of the capabilities on the Internet is called “reverse lookup.” Enter the residential telephone number for someone you know. Evaluate the accuracy of the name and address provided, along with the validity of the map that can be generated as additional information. Was the reverse lookup successful in identifying the person’s e-mail address as well?

A researcher wants to find out to what extent local residents participate in the recreation and entertainment activities available in their community. She selects a simple random sample of numbers from the telephone directory and proceeds to call these numbers between 6 P.M. and 9 P.M. If the line is busy or if there is no answer, she uses the next number on her list as a replacement. Comment on both the randomness and the representatives of the sample of persons who end up being interviewed.

To test the effectiveness of a new type of plastic handcuffs, a law enforcement agency puts the cuffs on a sample of 30 persons who belong to the local weightlifting club. None is able to break free from the cuffs. What type of sampling technique does this represent? Explain
your reasoning.

Of a company’s 1000 employees, 200 are managers, 700 are factory employees, and 100 are clerical. In selecting a sample of 100 employees, a researcher starts at the beginning of the alphabet and continues until she has collected the names of 20 managers, 70 factory employees, and 10 clerical workers. What type of sampling technique does this represent? Explain your reasoning.

college of business has 20 faculty members in Accounting, 30 in Marketing, 20 in Management, 15 in Finance, and 15 in Information Systems. The dean of the college asks her secretary to arbitrarily select 4, 6, 4, 3, and 3 persons from the respective departments to serve on a faculty committee. Is this a probability sample or a nonprobability sample? What specific type of probability or nonprobability sample does this procedure represent?

In 2001, the average U.S. production employee worked 34.2 hours per week. An assistant in the human resources department of Acme Eyebolts, Inc., is curious as to how the workers in her company compared to this figure during the first week of this month. The assistant will be reaching her conclusions based on a simple random sample of 30 data values out of the 300 Acme workers’ weekly hours listed in file XR04073. Help the assistant by generating the simple random sample and computing its mean. Based on the sample, compare the Acme workweek with that of production workers nationally.

Data from the Federal Bureau of Investigation show that 1 of every 189 motor vehicles was stolen during 2000. Applying this statistic to 5 motor vehicles randomly selected from the nation’s vehicle population:
a. What is the probability that none of the 5 motor vehicles will be stolen?
b. What is the probability that all 5 motor vehicles will be stolen?
c. How many possibilities exist in which 2 of the 5 motor vehicles are stolen?

Collecting data on traffic accident fatalities, the National Highway Traffic Safety Administration has found that 47.1% of the victims have 0.0% blood alcohol content (BAC), 7.0% of the victims have from 0.01 to 0.07% BAC, and 45.9% of the victims have at least 0.08% BAC. For a randomly selected victim:
a. What is the probability that the victim’s BAC was at least 0.01%?
b. Given that the victim had been drinking prior to the accident, what is the probability that this victim’s BAC was at least 0.08%?

When we are considering n objects taken r at a time, with r > 1, why will the number of combinations be less than the number of permutations?

When we are considering n objects taken r at a time, with r > 1, why will the number of combinations be less than the number of permutations?

A state’s license plate has 6 positions, each of which has 37 possibilities (letter, integer, or blank). If the purchaser of a vanity plate wants his first three positions to be ROY, in how many ways can his request be satisfied?

In advertising her oceanfront cottage for summer rental, a property owner can specify 

(1) Whether or not pets are permitted, 

(2) Whether the rent will be $700, $900, or $1200 per week, 

(3) Whether or not children under 10 are allowed, and 

(4) Whether the maximum stay is 1, 2, or 3 weeks. How many different versions of the ad can be generated?

Ten prominent citizens have been nominated for a community’s “Citizen of the Year” award. First- and second-place trophies are awarded to the two persons receiving the highest and second-highest number of votes. In how many different ways can the trophies be awarded?

A committee consists of eight members, each of whom may or may not show up for the next meeting. Assuming that the members will be making independent decisions on whether or not to attend, how many different possibilities exist for the composition of the meeting?

A tax accountant has three choices for the method of treating one of a client’s deductions. After this choice has been made, there are only two choices for how a second deduction can be treated. What is the total number of possibilities for the treatment of the two deductions?

A magician has two coins: one is unbalanced and lands heads 60% of the time; the other is fair and lands heads 50% of the time. A member of the audience randomly selects one of the coins and flips it. The result is heads.

a. What is the prior probability that the fair coin was selected?
b. Given additional information in the form of the single flip that came up heads, what is the revised probability that the coin is the fair one?

Of employed U.S. adults age 25 or older, 90.3% have completed high school, while 30.8% have completed college. For H  completed high school, C  completed college, and assuming that one must complete high school before completing college, construct a tree diagram to assist your calculation of the following probabilities for an employed U.S. adult:

a. P(H)
b. P(C|H)
c. P(H and C)
d. P(H and C’)

Through April 30 of the 1999 filing season, 13.7% of all individual U.S. tax returns were prepared by H&R Block.

a. If two individuals are randomly selected from those filing tax returns during this period, what is the probability that both of their tax returns were prepared by H&R Block?
b. In part (a), what is the probability that neither return was prepared by H&R Block? 

c. In part (a), what is the probability that exactly one of the two returns was prepared by H&R Block?

A study by the U.S. Energy Information Administration found that 84.3% of U.S. households with incomes under $10,000 did not own a dishwasher while only 21.8% of those in the over-$50,000 income range did not own a P(AB)  dishwasher. If one household is randomly selected from each income group, determine the probability that
a. neither household will own a dishwasher.
b. both households will own a dishwasher.
c. the lower-income household will own a dishwasher, but the higher-income household will not.
d. the higher-income household will own a dishwasher, but the lower-income household will not.

What is the difference between a marginal probability and a joint probability?

Using the information presented in the table in Exercise 5.15, calculate the following probabilities:

a. P(D or N) 

b. P(D′ or N′)
c. P(D or N′) 

d. P(D′ or N)

In 2003, Entergy Corporation had 2,631,752 electricity customers. Of these, 86.0% were in the residential category (R); 11.8% were commercial (C); 1.6% were industrial (I); and 0.6% were government and municipal (G).
a. Draw a Venn diagram representing events R, C, I, and G.
b. What is the value of P(R)?
c. What is the value of P(C or G)?
d. What is the value of P(R or C′)?

It has been reported that the 44,300 employees of Northwest Airlines are distributed among the following corporate functions:


For the sample space consisting of Northwest employees:
a. Draw a Venn diagram representing events A, B, C, D, and E.
b. What is the value of P(A)?
c. What is the value of P(A or B)?
d. What is the value of P(A or D′)?

In 2005, McDonald’s had 31,886 restaurants systemwide. Of these, 18,334 were operated by franchisees, 9283 by the company, and 4269 by affiliates. What is the probability that a randomly selected McDonald’s restaurant is operated by either a franchisee or an affiliate?

A survey of employees at a large company found the following relative frequencies for the one-way distances they had to travel to arrive at work:


a. What is the probability that a randomly selected individual will have to travel 11 or more miles to work?
b. What is the probability that a randomly selected individual will have to travel between 6 and 15 miles to work?
c. Draw a Venn diagram that includes the relative frequency probabilities in the table. 

d. Using the letter identifications provided, calculate the following probabilities: P(A or B or E); P(A or F); P(A or B); P(A or B or C).

Using the table in Exercise 5.12, what is the probability that a randomly selected victim would have been at least 60 years old and have had a blood alcohol level of at least 0.10%?

The following contingency table of frequencies is based on a 5-year study of fire fatalities in Maryland. For purposes of clarity, columns and rows are identified by the letters A–C and D–G, respectively.


a. For this table, identify any two events that are mutually exclusive.

b. For this table, identify any two events that intersect.

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