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mathematics
statistics
Elementary Statistics 3rd Canadian Edition Mario F. Triola - Solutions
Refer to Data Set 1 in Appendix B. Use box plots to compare the weights of discarded paper to the weights of discarded plastic.
Compare the two box plots from Exercises 1 and 2. How would you describe the shape of the distribution in the two sets of data? Are they uniform, skewed, or bell-shaped?
The box plots discussed in this section are often called skeletal (or regular) box plots. Modified box plots are constructed as follows:a. Calculate the difference between the quartiles Q3 and Q, and denote it as IQR (interquartile range), so that IQR = Q3 - Q,.b. Draw the box with the median and
Refer to Data Set 4 in Appendix B and construct a box plot for the annual precipitation of the cities listed.
In "Ages of Oscar-Winning Best Actors and Actresses" by Richard Brown and Gretchen Davis (Mathematics Teacher magazine), box plots are used to compare the ages of actors and actresses at the time they won Oscars. The results for 34 recent winners from each category are listed below. Use box-plots
Refer to Data Set 9 in Appendix B for these two data sets: pulse rates of those who smoke and pulse rates of those who don't smoke. Construct a box plot for each data set. Based on the results, do pulse rates of the two groups appear to be different? If so, how? Is this the result you would expect?
Refer to Data Set 9 in Appendix B for these two data sets: pulse rates of males and pulse rates of females. Construct a box plot for each data set. Based on the results, do pulse rates of the two groups appear to be different? If so, how? (Exclude the 8 and 15, which must be errors.)
Refer to Data Set 10 in Appendix B. Use box plots to compare the one-year return of U.S. equity funds to that of the funds other than U.S. equity.
Refer to Data Set 11 in Appendix B. Use box plots to compare the weights of red M&M candies to the weights of yellow M&M candies.
Refer to Data Set 13 in Appendix B. Construct a box plot for the weights of quarters. Compare the shape of the resulting box plot to the generic shapes. Based on the box plot, what do you conclude about the nature of the distribution?
Refer to Data Set 12 in Appendix B. Construct a box plot for the 50 digits from the Lotto 6/49 bonus draw. Compare the shape of the resulting box plot to the generic shapes. Based on the box plot, do the Lotto 6/49 results appear to be occurring as expected?
A family living in Ontario collected the data from their natural gas bills to monitor their consumption of gas and to try to save money. The following values are the cubic feet of gas used each month for five years. Using the lowest volume as the lower limit of the first class, construct a
Given below are numbers taken from the hydro bills of the family mentioned in Exercise 1. The numbers represent the usage of hydro (in kilowatt-hours) every two months for six years.Find the (a) Mean, (b) Median, (c) Mode, (d) Midrange, (e) Range, (f) Standard deviation, (g) Variance, (h) Qv (i)
Scores on a test of depth perception have a mean of 200 and a standard deviation of 40. a. Is a score of 260 unusually high? Explain. b. What is the z score corresponding to 185? c. Assuming that the scores have a bell-shaped distribution, what does the empirical rule say about the percentage of
The accompanying table lists times (in years) required to earn an honors bachelor's degree for a sample of undergraduate students. Use the table to find the mean and standard deviation. Based on the results, is it unusual for an undergraduate to require eight years to earn a bachelor's degree?
Using the frequency table given in Exercise 12, construct the corresponding relative frequency histogram.
An industrial psychologist gave a subject two different tests designed to measure employee satisfaction. Which score is better: a score of 57 on the first test, which has a mean of 72 and a standard deviation of 20, or a score of 450 on the second test, which has a mean of 500 and a standard
Refer to the two box plots below. The first box plot represents a sample of skulls of male Egyptians from about 4000 BCE, whereas the second box plot represents a sample of male Egyptian skulls from about 150 CE (in mm, based on data from Ancient Races of the Thebaid by Thomson and
Statistics Canada did a study of environmental impacts on health in five provinces. Listed below are five age-standardized mortality rates selected by cause (per 100,000 population). Construct a Pareto chart summarizing the given data. Lung cancer: 296 Heart disease: 959 Respiratory disease: 297
Construct a relative frequency table (with 10 classes) for the data in Exercise 1.
Construct a histogram that corresponds to the frequency table from Exercise 1.
For the data in Exercise 1, find(a) Qv(b) P45, and(c) The percentile corresponding to the volume of 125 cu. ft.
Use the frequency table from Exercise 1 to find the mean and standard deviation for the volumes.
Use the data from Exercise 1 for the first two years to construct a stem-and-leaf plot with 7 rows.
Use the data from Exercise 1 to construct a box plot.
Given below are times (in seconds) between an order being placed and the food being received at a McDonald's drive-through window. Find the (a) Mean, (b) Median, (c) Mode, (d) Midrange, (e) Range, (f) Standard deviation, and (g) Variance.135 90 85 121 83 69 87 159 177 135 227
The amounts of time (in hours) spent on paperwork in one day were obtained from a sample of office managers with the results given below: 3.7 2.9 3.4 0.0 1.5 1.8 2.3 2.4 1.0 2.0 4.4 2.0 4.5 0.0 1.7 4.4 3.3 2.4 2.1 2.1 a. Find the mean, median, mode, and midrange. b.
a. A set of data is at the nominal level of measurement and you want to obtain a representative data value. Which of the following is most appropriate: mean, median, mode, or midrange? Why? b. A sample is obtained by telephoning the first 250 people listed in the local telephone directory. What
Which of the following values cannot be probabilities? 0, 0.0001, -0.2, 3/2, 2/3, √2
A survey was done across five provinces to determine the mortality rate of lung cancer among male patients. Of 1000 patients who were tracked during this survey, 295 eventually succumbed to the disease (based on data from Statistics Canada). If a male lung cancer patient is selected at random, what
In a study of blood donors, 225 were classified as group O and 275 had a classification other than group O. What is the approximate probability that a person will have group O blood?
A recent census by Statistics Canada showed there are 54,946 police officers in Canada. Of this number, 188 serve in Prince Edward Island. If a police officer is randomly selected from across Canada, what is the probability that she or he is serving in Prince Edward Island?
a. If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in Japan. Ignore leap years, b. If a person is randomly selected, find the probability that his or her birthday is in November. Ignore leap years.
In a study of brand recognition, 831 consumers knew of Campbell's Soup, and 18 did not (based on data from Total Research Corporation). Use these results to estimate the probability that a randomly selected consumer will recognize Campbell's Soup. How do you think this probability value compares to
In a Bruskin/Goldring Research poll, respondents were asked how a fruitcake should be used. One hundred thirty-two respondents indicated that it should be used for a doorstop, and 880 other respondents cited other uses, including birdfeed, landfill, and a gift. If one of these respondents is
In a survey of Canadian workers who worked more than 50 hours per week, it was found that 334 workers surveyed were under 35 years of age and 401 workers were 35 to 55 years old. If one worker from this survey is selected at random, what is the probability that she or he is 35 years or older? Based
Among 400 randomly selected drivers in the 20-24 age bracket, 136 were in a car accident during the last year (based on data from the National Safety Council). If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will be in a car accident during
In a survey of Canadians who had just purchased new vehicles, 1521 bought pick-up trucks, 1849 bought sport utility vehicles (SUVs), and 1671 bought passenger vehicles. Use these results to estimate the probability that a new vehicle purchaser will buy an SUV. What would this result indicate to
When the allergy drug Seldane was clinically tested, 70 people experienced drowsiness and 711 did not (based on data from Merrell Dow Pharmaceuticals, Inc.). Use this sample to estimate the probability of a Seldane user becoming drowsy. Based on the result, is drowsiness a factor that should be
a. What is P(A) if event A is that February has 30 days this year? b. What is P(A) if event A is that November has 30 days this year? c. A sample space consists of 500 separate events that are equally likely. What is the probability of each? d. On a mid-term exam, each question has 5 possible
A Statistics Canada study of deaths by cancer by age group showed 579 deaths in the 0-29 age group, 10,456 deaths in the 30-59 age group, and 42,928 deaths in the 60-and-over age group. Find the probability that randomly selected cancer mortality will be a person in the first age group.
A study of credit-card fraud was conducted by MasterCard International, and the accompanying table is based on the results. If one case of credit-card fraud is randomly selected from the cases summarized in the table, find the probability that the fraud resulted from a counterfeit card.
A Gallup survey about tooth brushing resulted in the sample data in the given table. If one of the respondents is randomly selected, find the probability of getting someone who brushes three times per day, as dentists recommend.
A couple plans to have 2 children. a. List the different outcomes according to the gender of each child. Assume that these outcomes are equally likely. b. Find the probability of getting 2 girls. c. Find the probability of getting exactly 1 child of each gender.
A couple plans to have 4 children. a. List the 16 different possible outcomes according to the gender of each child. Assume that these outcomes are equally likely. b. Find the probability of getting all girls. c. Find the probability of getting at least 1 child of each gender. d. Find the
On a quiz consisting of 3 true/false questions, an unprepared student must guess at each one. The guesses will be random.
Both parents have the brown/blue pair of eye-colour genes, and each parent contributes one gene (for one of those colours) to a child. Assume that if the child has at least one brown gene, that colour will dominate and the eyes will be brown. (Actually, the determination of eye colour is somewhat
Find the actual odds against correctly guessing the answer to a multiple-choice question with 5 possible answers.
Find the actual odds against randomly selecting someone who is left-handed, given that 10% of us are left-handed.
a. The probability of a 7 in roulette is 1/38. Find the actual odds against 7. b. If you bet $2 on the number 7 in roulette and you win, the casino gives you $72, which includes the $2 bet. First identify the net profit, then find the payoff odds. c. How do you explain the discrepancy between the
a. In the casino game craps, you can bet that the next roll of the two dice will result in a total of 2. The probability of rolling 2 is 1/36. Find the odds against rolling 2. b. If you bet $5 that the next roll of the dice will be 2, you will collect $155 (including your $5 bet) if you win. First
If the actual odds against event A are a:b, then P(A) = b/(a + b). Find the probability of Horse Cents winning his next race, given that the actual odds against his winning are 10:3.
The stem-and-leaf plot summarizes the time (in hours) that managers spend on paperwork in one day (based on data from Adia Personnel Services). Use this sample to estimate the probability that a randomly selected manager spends more than 2.0 hours per day on paperwork.
After collecting IQ scores from hundreds of subjects, a box plot is constructed with this five-number summary: 82, 91, 100, 109, 118. If one of the subjects is randomly selected, find the probability that his or her IQ score is greater than 109.
In part (a) of Exercise 13, leap years were ignored in finding the probability that a randomly selected person will have a birthday on October 18. a. Recalculate this probability, assuming that a leap year occurs every 4 years. (Express your answer as an exact fraction.) b. Leap years occur in
a. If two flies land on an orange, find the probability that they are on points that are within the same hemisphere, b. Two points along a straight stick are randomly selected. The stick is then broken at those two points. Find the probability that the three resulting pieces can be arranged to form
We noted in this section that for the experiment of rolling a pair of dice, there are 36 simple events that form the sample space: 1-1, 1-2, . . . , 6-6. Find the probability of rolling a pair of dice and getting a total of 4.
Refer to Data Set 11 in Appendix B. Based on those sample results, estimate the probability that when a plain M&M candy is randomly selected, it will be red.
Refer to Data Set 8 in Appendix B. Based on those sample results, estimate the probability that a randomly selected statistics student has at least one credit card.
According to a survey sent out by Deloitte Touche Tohamatsu to British Columbia's top CEOs, 20 out of the 80 respondents possess an MBA. What is the estimated probability of a British Columbian top CEO having an MBA? Does it appear that an MBA is a requirement for the position?
The Kelly-Lynne Advertising Company is considering a computer campaign that targets teenagers. In a survey of 1066 teens, 181 had a computer on-line service in their household. If a teen is randomly selected, estimate the probability that he or she will have access to an on-line service in his or
In a survey of college students, 1162 stated that they cheated on an exam and 2468 stated that they did not (based on data from the Josephson Institute of Ethics). If one of these college students is randomly selected, find the probability that he or she cheated on an exam.
Are the two events mutually exclusive (that is, not overlapping) for a single procedure? a. Selecting a geometric shape Selecting an octahedron b. Selecting a survey subject who is a member of the Liberal party Selecting a survey subject opposed to all welfare plans c. Spinning a roulette wheel and
Refer to the data set in Exercise 9, and find the probability of getting someone who is in the 18-21 age bracket or someone who responded. Exercise 9. Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 84 people in the 18-21 age
Problems of sexual harassment have received much attention in recent years. In one survey, 420 workers (240 of whom are men) considered a friendly pat on the shoulder to be a form of harassment, whereas 580 workers (380 of whom are men) did not consider that to be a form of harassment (based on
Refer to the data set in Exercise 11, and find the probability of randomly selecting a man or someone who does not consider a pat on the shoulder to be a form of harassment.
A survey of 100 businesspeople showed that 25 owned copiers, 50 owned printers, and 13 owned both types of equipment. If a businessperson is selected at random from this sample, find the probability of getting someone who owns a copier or a printer.
Refer to the data set in Exercise 13, and find the probability of getting a businessperson who does not own a copier or a printer.
Visitors to Yellowstone naturally want to see Old Faithful erupt, so the interval between eruptions becomes a concern for those with time constraints. If we randomly select one of the times represented in the table, what is the probability that it is at least one hour?Use the data in the
If we randomly select one of the times represented in the table, what is the probability that it is at least 70 min or between 60 and 79 min?Use the data in the accompanying table, which summarizes a sample of 200 times (in minutes) between eruptions of the Old Faithful Geyser in Yellowstone
P(not group O)
P(not type Rh+)
P(group B or type Rh")
Are the two events mutually exclusive (that is, not overlapping) for a single procedure? a. Buying a new Corvette that is free of defects Buying a car with inoperative headlights b. Selecting a math course Selecting a course that is interesting c. Selecting a person with blond hair (natural or
P(group O or group A)
P(group A or type Rh+)
P(group AB or type Rh")
P(group A or B or type Rh+)
a. If P(A or B) = 1/3, P(B) = 1/4, and P(A and B) = 1/5, find P(A). b. If P{A) = 0.4 and P(B) = 0.5, what is known about P(A or B) if A and B are mutually exclusive events? c. If P(A) = 0.4 and P(B) = 0.5, what is known about P(A or B) if A and B are not mutually exclusive events?
If events A and B are mutually exclusive and events B and C are mutually exclusive, must events A and C be mutually exclusive? Give an example supporting your answer.
How is the addition rule changed if the exclusive or is used instead of the inclusive or} Recall that the exclusive or means either one or the other, but not both.
Given that P(A or B) = P(A) + P(B) - P{A and B), develop a formal rule for P(A or B or C).
One version of DeMorgan's Law states: /'(neither A nor B) = P (A and B) = 1 - P(A or B) A survey was conducted to gauge support for a dedicated road tax. The respondents for a particular city were divided into those who live in the inner city and those who live in the suburbs. A third category was
a. If P(A) = 2/5, find P{A). b. According to a recent Interac survey, 28% of consumers use their debit cards in supermarkets. Find the probability that they use debit cards only in other stores or not at all.
a. Find P(A), given that P(A) = 0.228. b. Statistics Canada reports that 30% of Canadians own stocks. If you randomly select someone from Canada, what is the probability that he or she does not own stocks?
When playing blackjack with a single deck of cards at Casino Regina, you are dealt the first card from the top of a shuffled deck. What is the probability that you get (a) A club or an ace? (b) An ace or a 2?
If someone is randomly selected, find the probability that his or her birthday is not October 18, which is National Statistics Day in Japan. Ignore leap years.
Refer to Table 3-1 in this section. If one of the 2072 subjects is randomly selected, find the probability of getting someone who used Seldane or a placebo.
Refer to Table 3-1 in this section. If one of the 2072 subjects is randomly selected, find the probability of getting someone who used a placebo or experienced a headache.
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 84 people in the 18-21 age bracket and finds that 73 of them respond and 11 refuse to respond. When 275 people in the 22-29 age bracket are contacted, 255 respond and 20 refuse to
a. Attending classes in a statistics coursePassing a statistics courseb. Getting a flat tire on the way to class Sleeping too late for classc. Events A and B, where P(A) = 0.40, P(B) = 0.60, and P(A and B) = 0.20Given pair of events, classify the two events as independent or dependent. Some of the
The probability that a household has an annual income of $75,000 or more is 0.362. The probability that a household recycles regularly is 0.627. The probability that a household has an annual income under $75,000 and does not recycle regularly is 0.289.a. Create a contingency table based on these
A survey of 1000 people was conducted. The following facts were ascertained: • 40% of the respondents are male • 21% have an annual income under $25,000 • 57.2% have an annual income of at least $25,000 but less than $50,000 • 6% are males with an annual income under $25,000 • 6.3% are
a. Find the probability that when 1 of the 2000 subjects is randomly selected, the person chosen was victimized by an acquaintance or relative, given that he or she was robbed. b. Find the probability that when 1 of the 2000 subjects is randomly selected, the person chosen was robbed by an
Table is randomly selected, find the probability of getting someone who was victimized by a stranger or who was a homicide victim. b. If one of the crime victims represented in the table is randomly selected, find the probability of getting someone who was a homicide victim, given that the criminal
Based on the study results, what is the probability that if a disease-free person is randomly selected, they will test positive?
If a test subject is selected at random, what is the probability that he or she tests negative or is a subject known to be disease-free?
If a test subject is selected at random, what is the probability that he or she tests positive or is a subject known to be disease-free?
a. Finding your microwave oven inoperableFinding your battery-operated smoke detector inoperableb. Finding your kitchen light inoperable Finding your refrigerator inoperablec. Events A and B, where P{A) = 0.90, P(B) = 0.80, and P(A and B) = 0.72Given pair of events, classify the two events as
The probability that a realtor has less than 10 years of service is 0.875. The probability that a realtor has at least 10 but less than 20 years of service is 0.104. The probability that a realtor earns less than $100,000 annually given less than 10 years of service is 0.984. The probability that a
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