According to a recent Gallup poll, 62% of Americans took a vacation away from home in 2017. Suppose two Americans are randomly selected. a. What is the probability that both took a vacation away from home in 2017? b. What is the probability that neither took a vacation away from home in 2017? c. What is the probability that at least one of them took a vacation away from home in 2017?
> In 2015, the National Highway Traffic Safety Administration reported the number of pedestrian fatalities in San Francisco County was 24 and that the number in Los Angeles County was 209. Can we conclude that pedestrians are safer in San Francisco than in
> Two sections of statistics are offered, the first at 8 a.m. and the second at 10 a.m. The 8 a.m. section has 25 women, and the 10 a.m. section has 15 women. A student claims this is evidence that women prefer earlier statistics classes than men do. What
> The marriage and divorce rates are given per 1000 people in various years. Find the divorce rate as a percentage of the marriage rate and comment on the trend over time. (Source: https://www.cdc.gov/nchs)
> A recent study found that highly experienced teachers may be associated with higher student achievement. Suppose fourth-grade students at an elementary school are randomly assigned to one of eight teachers. Teachers Nagle, Crouse, Warren, Tejada, and Tra
> A medical practice group consists of seven doctors, four women and three men. The women are Drs. Town, Wu, Hein, and Lee. The men are Drs. Marland, Penner, and Holmes. Sup-pose new patients are randomly assigned to one of the doctors in the group. a. Lis
> A bag of candy contains 3 red candies and 7 brown candies. A friend says the probability of reaching the bag without looking and pulling out a red candy is 30% because 3 out of 10 candies are red. Is this an example of an empirical probability or a theor
> A student flips a coin 10 times and sees that it landed on tails 4 times. Based on this, the student says that the probability of getting a tail is 40%. Is the student referring to an empirical probability or a theoretical probability? Explain.
> The projected U.S. population is given for different decades. The projected number of people 65 years of age or older is also given. Find the percentage of people 65 or over and comment on the trend over time. Numbers are in millions of people (Source: 2
> A person was trying to figure out the probability of getting two heads when flipping two coins. He flipped two coins 10 times, and in 2 of these 10 times, both coins landed heads. On the basis of this outcome, he claims that the probability of two heads
> A Monopoly player claims that the probability of getting a 4 when rolling a six-sided die is 1/6 because the die is equally likely to land on any of the six sides. Is this an example of an empirical probability or a theoretical probability? Explain.
> Suppose you are carrying out a randomized experiment to test if there is a difference in the amount of information remembered between students who take notes using a computer versus those who take notes by hand using pen and paper. You have 20 college st
> If we flip a coin 10 times, what percentage of the time will the coin land on heads? A first step to answering this question is to simulate 10 flips. Use the random number table in Appendix A to simulate flipping a coin 10 times. Let the digits 0, 1,
> A 2018 Marist poll found that interest in baseball has been declining recently in the United States. A random sample of U.S. adults were asked how much baseball they intended to watch this season. The results are shown in the following table. a. What pe
> In 2016 the Pew Research Center asked a sample of American adults which of the following they had done in the previous 12 months: read a book in any format, read a print book, read an e-book, and listened to an audio book. The percent-ages of who had eng
> In 2017 the Pew Research Center asked young adults aged 18 to 29 about their media habits. When asked, “What is the primary way you watch television?” 61% said online streaming service, 31% said cable/satellite subscription, and 5% said digital antenna.
> In California, about 92% of teens who take the written driver’s exam fail the first time they take it (www.teendrivingcourse.com). Suppose that Sam and Maria are randomly selected teenagers taking the test for the first time. a. What is the probability t
> Suppose all the days of the week are equally likely as birthdays. Alicia and David are two randomly selected, unrelated people. a. What is the probability that they were both born on Monday? b. What is the probability that Alicia OR David was born on Mon
> A 2016 Pew Research poll reported that 80% of Americans shop online. Assume the percentage is accurate. a. If two Americans are randomly selected, what is the probability that both shop online? b. If the two Americans selected are a married couple, expla
> The accompanying table gives the number of cable television subscribers (in millions) and the number of households with televisions (in millions) in the United States. Find the percentage of TV owners with cable subscriptions for each year and comment on
> A 2016 Pew Research poll reported that 27% of young adults aged 18 to 24 had used an online dating site. Assume the percentage is accurate. a. If two young adults are randomly selected, what is the probability that both have used an online dating site? b
> A 2017 Pew Research poll asked people if they agreed with this statement: The United States hasn’t gone far enough when it comes to giving women equal rights with men. 42% of men agreed with the statement and 57% of women agreed with the statement. Suppo
> According to a Pew Research poll conducted in 2016, 55% of men and 43% of women support the death penalty in cases of murder. Suppose these are accurate percentages. Now suppose a random man and a random woman meet. a. What is the probability that both s
> Use your general knowledge to label the following pairs of variables as independent or associated. Explain. a. The outcome on flips of two separate, fair coins. b. Breed of dog and weight of dog for dogs at a dog show.
> Use your general knowledge to label the following pairs of variables as independent or associated. Explain. a. For a sample of adults, gender and shoe size b. For a sample of football teams, win/loss record for the coin toss at the beginning of the game
> According to a Gallup poll conducted in 2017, 723 out of 1018 Americans surveyed said they believed global warming is occurring. If an American is selected at random, what is the probability that the person believes that global warming is occurring?
> According to a Gallup poll conducted in 2016, 627 out of 1012 Americans surveyed said they were dissatisfied with the country’s current gun laws. If an American is selected at random, what is the probability that the person is dissatisfied with the curre
> a. Explain how you could use a random number table to simulate rolling a fair six-sided die 20 times. Assume you wish to find the probability of rolling a 1. Then report a line or two of the random number table (or numbers generated by a computer or calc
> a. Explain how you could use a random number table (or the random numbers generated by software or a calculator) to simulate rolling a fair four-sided die 20 times. Assume you are interested in the probability of rolling a 1. Then report a line or two of
> Some estimates say that 10% of the population is left-handed. We wish to design a simulation to find an empirical probability that if five babies are born on a single day, one or more will be left-handed. Suppose we decide that the even digits (0, 2, 4,
> The accompanying table gives the population (in hundred thousands) and number of people not covered by health insurance (in hundred thousands) for the United States. Find the percentage of people not covered by health insurance for each of the given year
> A jury is supposed to represent the population. We wish to perform a simulation to determine an empirical probability that a jury of 12 people has 5 or fewer women. Assume that about 50% of the population is female, so the probability that a person who i
> The graph shows the average when a six-sided die is rolled repeatedly. For example, if the first two rolls resulted in a 6 and a 2, the average would be 4. If the next trial resulted in a 1, the new average would be (6 + 2 + 1)/3 = 3. Explain how the gra
> If you flip a fair coin repeatedly and the first four results are tails, are you more likely to get heads on the next flip, more likely to get tails again, or equally likely to get heads or tails?
> Consider two pairs of grandparents. The first pair has 4 grandchildren, and the second pair has 32 grand-children. Which of the two pairs is more likely to have between 40% and 60% boys as grandchildren, assuming that boys and girls are equally likely as
> Betty and Jane are gambling. They are cutting cards (picking a random place in the deck to see a card). Whoever has the higher card wins the bet. If the cards have the same value (for example, they are both eights), they try again. Betty and Jane do this
> Refer to the following figure. a. After a large number of flips, the overall proportion of heads “settles down” to nearly what value? b. Approximately how many coin flips does it take before the proportion of heads set
> Imagine flipping a fair coin many times. Explain what should happen to the proportion of heads as the number of coin flips increases.
> The table shows the results of rolling a fair six-sided die. Using the table, find the empirical probability of rolling a 1 for 20, 100, and 1000 trials. Report the theoretical probability of rolling a 1 with a fair six-sided die. Compare the empirical
> Refer to Histograms A, B, and C, which show the relative frequencies from experiments in which a fair six-sided die was rolled. One histogram shows the results for 20 rolls, one the results for 100 rolls, and another the results for 10,000 rolls. Which h
> a. Explain how you could use digits from a random number table to simulate rolling a fair six-sided die. b. Carry out your simulation beginning with line 3 of the random number table in Appendix A. Repeat your simulation 5 times. c. Use your simulation t
> The accompanying table gives the 2018 population and area (in square kilometers) of five U.S. cities. See page 39 for guidance. (Source: www.citymayors.com). a. Determine and report the ranking of the population density (people per square kilometer) by
> a. Use the line of random numbers below to simulate flipping a coin 20 times. Use the digits 0, 1, 2, 3, 4 to represent heads and the digits 5, 6, 7, 8, 9 to represent tails. 11164 … 36318 … 75061 … 37674 b. Based on these 20 trials, what is the simulate
> A true/false test has 20 questions. Each question has two choices (true or false), and only one choice is correct. Which of the following methods is a valid simulation of a student who guesses randomly on each question. Explain. (Note: there might be mor
> A multiple-choice test has 30 questions. Each question has three choices, but only one choice is correct. Using a random number table, which of the following methods is a valid simulation of a student who circles his or her choices randomly? Explain. (No
> What’s the probability of rolling two numbers whose sum is 7 when you roll two dice? The table below shows the outcome of ten trials in which two dice were rolled. a. List the trials that had a sum of 7. b. Based on these data, what&aci
> What’s the probability of getting at least one six when you roll two dice? The table below shows the outcome of five trials in which two dice were rolled. a. List the trials that had at least one 6. b. Based on these data, whatâ&#
> About 8 women in 100,000 have cervical cancer (C), so P(C) = 0.00008 and P(no C) = 0.99992. The chance that a Pap smear will incorrectly indicate that a woman without cervical cancer has cervical cancer is 0.03. Therefore, P (test pos | no C) = 0.03 Wha
> According to a study published in Scientific American, about 8 women in 100,000 have cervical cancer (which we’ll call event C), so P(C) = 0.00008. Suppose the chance that a Pap smear will detect cervical cancer when it is present is 0.84. Therefore, P (
> According to the National Center for Health Statistics, 52% of U.S. households no longer have a landline and instead only have cell phone service. Suppose three U.S. households are selected at random. a. What is the probability that all three have only c
> Assume that babies born are equally likely to be boys (B) or girls (G). Assume a woman has six children, none of whom are twins. Which sequence is more likely? Explain. Sequence A: GGGGGG Sequence B: GGGBBB
> The table gives the prison population and total population for a sample of states in 2014–15. (Source: The 2017 World Almanac and Book of Facts) Find the number of people in prison per thousand residents in each state and rank each sta
> College students who were drivers were asked if they had ever driven a car 100 mph or more (yes or no). The results are shown in the table, along with gender. a. There are two variables in the table, state what they are and whether each is categorical or
> Roll a fair six-sided die five times, and record the number of spots on top. Which sequence is more likely? Explain. Sequence A: 66666 Sequence B: 16643
> Imagine rolling a fair six-sided die three times. a. What is the theoretical probability that all three rolls of the die show a 1 on top? b. What is the theoretical probability that the first roll of the die shows a 6 AND the next two rolls both show a 1
> Imagine flipping three fair coins. a. What is the theoretical probability that all three come up heads? b. What is the theoretical probability that the first toss is tails AND the next two are heads?
> Using the table in exercise 5.53, determine whether being female is independent of choice of local TV. Explain your answer in the context of this problem.
> A 2018 Pew Research Center report asked people who got their news from television which television sector they relied on primarily for their news: local TV, network TV, or cable TV. The results were used to generate the data in the table below. a. Inclu
> When two dice are rolled, is the event “the first die shows a 1 on top” independent of the event “the second die shows a 1 on top”?
> When people fold their hands together with interlocking fingers, most people are more comfortable with one of two ways. In one way, the right thumb ends up on top, and in the other way, the left thumb is on top. The table shows the data from one group of
> Assume a person is selected randomly from the group of people represented in the table in exercise 5.41. The probability the person says “Hasn’t Gone Far Enough” given that the person is a woman is 57/100 or 57%. The probability that person is a woman gi
> Refer to the table in Exercise 5.41. Suppose a person is randomly selected from this group. Is being female independent of answering “Hasn’t Gone Far Enough”?
> Ring sizes typically range from about 3 to about 14. Based on what you know about gender differences, if we randomly select a person, are the event that the ring size is smaller than 5 and the event that the person is a male independent or associated? Ex
> The 2017 World Almanac and Book of Facts reported that in 2016, M&Ms had sales of approximately $3.48 million and that this accounted for 12.95% of the total chocolate candy sales. What was the total amount of chocolate candy sales?
> Suppose a person is chosen at random. Use your knowledge about the world to decide whether the event that the person has brown eyes and the event that the person is female are independent or associated. Explain.
> About 12% of men and 10% of women are left-handed. If we select a person at random, are the event that the person is male and the event that the person is left-handed independent or associated?
> Suppose a person is chosen at random. Use your understanding about the world of basketball to decide whether the event that the person is taller than 6 feet and the event that the person plays professional basketball are independent or associated. Explai
> Use the data in exercise 5.43 for this problem. Note: Your answers to each of these three questions should not be the same. a. Find the probability that a randomly selected person did not have a child under 18 years old, given that they said No. b. Find
> A Gallup poll asked people with and without children under 18 years old if they frequently experienced stress. The results are shown in the table below. (Source: Gallup.com) a. Find the probability that a randomly chosen person from this group said &aci
> A driving exam consists of 30 multiple-choice questions. Each of the answers is either right or wrong. Suppose that the probability of making fewer than 7 mistakes is 0.23 and the probability of making from 7 to 15 mistakes is 0.41. Find the probability
> An exam consists of 12 multiple-choice questions. Each of the 12 answers is either right or wrong. Suppose the probability a student makes fewer than 3 mistakes on the exam is 0.48 and the probability that a student makes from 3 to 8 (inclusive) mistakes
> When a certain type of thumbtack is tossed, the probability that it lands tip up is 60%, and the probability that it lands tip down is 40%. All possible outcomes when two thumbtacks are tossed are listed. U means the tip is Up, and D means the tip is Dow
> When a certain type of thumbtack is tossed, the probability that it lands tip up is 60%. All possible outcomes when two thumbtacks are tossed are listed. U means the tip is up, and D means the tip is down. UU … UD … DU … DD a. What is the probability of
> A 2018 Pew poll asked U.S. adults how often they go online. The responses are shown in the table. a. What percentage of respondents go online less than once a day? b. In a group of 500 U.S. adults, how many would you expect go online almost constantly o
> The 2017 World Almanac and Book of Facts reported that the U.S. occupation projected to grow the most is personal care aide. By 2024 there will be a need for 160,328 personal care aides, a growth of about 26% over 2014 levels. How many personal care aide
> A 2018 Marist poll asked respondents what superpower they most desired. The distribution of responses are shown in the table. a. What percentage of those surveyed wanted to be able to fly or teleport? b. If there were 1200 people surveyed, h
> Political science researchers often classify voters according to their political party preference, using four categories: Democrat, Republican, Other political parties (including Libertarians and Independents, for example), and Decline to State/No Party
> A college conducted a student survey to learn about commute patterns. Students were given a choice of three options: car, bus, or other. When looking at the survey results, 42% of students responded “car,” and 23% responded “bus.” Assuming all students a
> One of the authors did a survey to determine the effect of students changing answers while taking a multiple-choice test on which there is only one correct answer for each question. Some students erase their initial choice and replace it with another. It
> Assume that the only grades possible in a history course are A, B, C, and lower than C. The probability that a randomly selected student will get an A in a certain history course is 0.18, the probability that a student will get a B in the course is 0.25,
> Roll a fair six-sided die. a. What is the probability that the die shows an even number or a number less than 4 on top? b. What is the probability the die shows an odd number or a number greater than 4 on top?
> Roll a fair six-sided die. a. What is the probability that the die shows an even number or a number greater than 4 on top? b. What is the probability the die shows an odd number or a number less than 3 on top?
> Refer to the table in exercise 5.19. Suppose we select one person at random from this group. Name a pair of events that are not mutually exclusive.
> Referring to the table given in exercise 5.19, name a pair of mutually exclusive events that could result when one person is selected at random from the entire group.
> Suppose a person is selected at random from a large population. a. Label each pair of events as mutually exclusive or not mutually exclusive. i. The person has traveled to Mexico; the person has traveled to Canada. ii. The person is single; the person is
> Make a two-way table from Table 1 for gender and hair color. Put the labels Male and Female across the top and Brown, Black, Blonde, and Red and then tally the data. a. Report how many are in each cell. b. Find the sums of each row and column and the gr
> Suppose a person is selected at random from a large population. a. Label each pair of events as mutually exclusive or not mutually exclusive. i. The person has traveled to Mexico; the person has traveled to Canada. ii. The person is single; the person is
> Use the data in exercise 5.23 to answer the following: a. What is the probability that a randomly selected person is a woman and said “more.” b. What is the probability that a randomly selected person is a woman or said “more” (or both)?
> A Pew Research poll asked respondents to fill in the blank to this question:Â Compared to other industries there is _____ discrimination against women in the tech industry. Responses separated by gender are shown in the following table. The re
> Use the data in exercise 5.21 to answer the following: a. If a person is chosen randomly from this group, what is the probability that the person is an Independent and said “Yes”? b. If a person is chosen randomly from this group, what is the probability
> A Gallup poll asked a sample of voters if marijuana should be legalized. Voters’ responses and political party affiliation are in the table. (Source: Gallup.com) a. If a person is randomly selected from this group, find the probability
> The Pew Research Center asked a sample of adults if they had read a book in any format in the previous 12 months. The results are shown in the table. (Source: Pewinternet.org) a. If a person is randomly selected from this group, find the probability of
> The Gallup poll asked respondents if they had taken a vacation in the last year. The respondents were separated into two groups: those who had graduated from college and those who had not. Numbers in the table are based on sample sizes of 250 in each gro
> If one card is selected from a well-shuffled deck of 52 cards, what is the probability that the card will be a club OR a diamond OR a heart? What is the probability of the complement of this event? (Refer to exercise 5.11 for information about cards.)
> What is the probability that a baby will be born on a Friday OR a Saturday OR a Sunday if all the days of the week are equally likely as birthdays?
> The sample space shows all possible sequences of child gender for a family with 3 children. The table is organized by the number of girls in the family a. How many outcomes are in the sample space? b. If we assume all outcomes in the sample space are eq
> Make a two-way table from Table 1A for gender and living situation. Put the labels Male and Female across the top and Dorm and Commuter on the side and then tally the data. See page 38 for guidance. a. Report how many are in each cell. b. Find the sums
> The sample space given here shows all possible sequences for tossing a fair coin 4 times. The sequences have been organized by the number of tails in the sequence. a. How many outcomes are in the sample space? b. Assuming all of the outcomes in the samp
> Consider a multiple-choice test with a total of four possible options for each question. a. What is the probability of guessing correctly on one question? (Assume that there are three incorrect options and one correct option.) b. What is the probability
> a. On a true/false quiz in which you are guessing, what is the probability of guessing correctly on one question? b. What is the probability that a guess on one true/false question will be incorrect?
> Refer to exercise 5.11 for information about cards. If you draw one card randomly from a standard 52-card playing deck, what is the probability that it will be the following: a. A black card b. A diamond c. A face card (jack, queen, or king) d. A nine e.
