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mathematics
introductory statistics exploring the world through data
Introductory Statistics Exploring The World Through Data 3rd Edition Robert Gould, Rebecca Wong, Colleen N. Ryan - Solutions
Whales have one of the longest gestation periods of any mammal. According to whalefacts.org, the mean gestation period for a whale is 14 months. Assume the distribution of gestation periods is Normal with a standard deviation of 1.2 months.a. Find the standard score associated with a gestational
According to dogtime.com, the mean weight of an adult St. Bernard dog is 150 pounds. Assume the distribution of weights is Normal with a standard deviation of 10 pounds.a. Find the standard score associated with a weight of 170 pounds.b. Using the Empirical Rule and your answer to part a, what is
Use technology or a Normal table to find each of the following. Include an appropriately labeled sketch of the Normal curve for each part with the appropriate area shaded.a. Find the probability that a z-score will be 2.12 or greater.b. Find the probability that a z-score will be less than -0.74.c.
Use technology or a Normal table to find each of the following. Include an appropriately labeled sketch of the Normal curve for each part with the appropriate area shaded.a. Find the probability that a z-score will be 2.03 or less.b. Find the probability that a z-score will be -1.75 or more.c. Find
Use the table or technology to find the answer to each question. Include an appropriately labeled sketch of the Normal curve for each part. Shade the appropriate region. A section of the Normal table is provided in the previous exercise.a. Find the area to the left of a z-score of 0.92.b. Find the
Use the table or technology to find the answer to each question. Include an appropriately labeled sketch of the Normal curve for each part. Shade the appropriate region. A section of the Normal table is provided.a. Find the area in a Standard Normal curve to the left of 1.13.b. Find the area in a
Quantitative SAT scores are approximately Normally distributed with a mean of 500 and a standard deviation of 100. Choose the correct StatCrunch output for finding the probability that a randomly selected person scores less than 450 on the quantitative SAT and report the probability as a percentage
Assume college women’s heights are approximately Normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. Choose the Stat- Crunch output for finding the percentage of college women who are taller than 67 inches and report the correct percentage. Round to one decimal
Assume that the lengths of pregnancy for humans is approximately Normally distributed, with a mean of 267 days and a standard deviation of 10 days. Use the Empirical Rule to answer the following questions. Do not use the technology or the Normal table. Begin by labeling the horizontal axis of the
a. Find the probability of having 0, 1, or 2 girls in a family of two children and display the probability distribution in a table.b. Make a graph of the probability distribution.
a. From your answers in Exercise 6.7, find the probability of getting 0 ups, 1 up, or 2 ups when flipping two thumbtacks, and report the distribution in a table.b. Make a probability distribution graph of this. 6.10 Two Children Using your list of outcomes.
Make a list of all possible outcomes for gender when a family has two children. Assume that the probability of having a boy is 0.50 and the probability of having a girl is also 0.50. Find the probability of each outcome in your list.
Determine whether each of the following variables would best be modeled as continuous or discrete.a. The weight of a car in poundsb. The weight of a car in kilograms
Determine whether each of the following variables would best be modeled as continuous or discrete.a. The height of a person in inchesb. The weight of a person in pounds
Determine whether each of the following variables would best be modeled as continuous or discrete.a. The number of cars passing through an intersection in one hourb. The weight of a person
Determine whether each of the following variables would best be modeled as continuous or discrete.a. The height of a high-rise apartment buildingb. The number of floors in a high-rise apartment building
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 cardb. A diamondc. A face card (jack, queen, or king)d. A ninee. A king or queenData From Exercise 5.11:There are
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, explain why they would not be considered independent
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. Suppose the Pew Research Center polled
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 percentages of who had engaged in each of these activities is shown in
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.Watch a great deal . . . . . . . . .
A 2016 Pew Research poll asked respondents about their reading habits during the past year. The results are shown in the table.Read no books . . . . . . . . . . . . . . . . 26%Read
A 2017 Pew Research poll found that 72% of Democrats and 36% of Republicans felt that colleges and universities have a positive effect on the way things are going in the United States. If 1500 Democrats and 1500 Republicans were surveyed, how many from each group felt that colleges and universities
A 2017 Pew Research poll found that 28% of cell phone users do not use a screen lock for security on their smartphones. If 500 smartphone users were surveyed, how many do not use a screen lock on their smartphones?
A bag contains a number of colored cubes: 10 red, 5 white, 20 blue, and 15 black. One cube is chosen at random. What is the probability that the cube is the following:a. Blackb. Red or whitec. Not blued. Neither red nor whitee. Are the events described in parts (b) and (d) complements? Why or why
A Gallup poll conducted in 2017 asked people, “Do you think marijuana use should be legal?”In response, 75% of Democrats, 51% of Republicans, and 67% of Independents said Yes. Assume that anyone who did not answer Yes answered No. Suppose the number of Democrats polled was 400, the number of
The Pew Research Center asked a sample of Americans, “Do you know someone who has entered a long-term relationship via online dating?” The table gives the total number of people by level of educational attainment (rounded) and the percentage who said Yes.a. Make a two-way table of counts (not
In order to practice law, lawyers must pass the bar exam. In California, the passing rate for first-time bar exam test takers who attended an accredited California law school was 70%. Suppose two test-takers from this group are selected at random.a. What is the probability that they both pass the
In addition to behind-the-wheel tests, states require written tests before issuing drivers licenses. The failure rate for the written driving test in Florida is about 60%. Suppose three drivers’ license test-takers in Florida are randomly selected. Find the probability of the following:a. All
Construct a two-way table with 80 men and 100 women in which both groups show an equal percentage of right-handedness.
Construct a two-way table with 80 men and 100 women in which these is a higher percentage of left-handed is higher for women than for men.
In 2016 a Pew Research poll asked a sample of Americans if they agreed with this statement: The Earth is warming mostly due to human activity. Responses and the political affiliation of respondents were recorded and are shown in the following table.a. Fill in the row and column totals for the
Refer to the table in exercise 5.109.a. If one person is chosen randomly from the group, what is the probability that the person is a Republican (conservative or moderate/ liberal)?b. If one person is chosen randomly from the group, what is the probability that the person disagrees with the
Refer to the table in exercise 5.109. Suppose one person is selected at random from this group. Find the probability the person is a Conservative Republican and agrees with the statement.Data From Exercise 5.109: Conser- Moderatel Moderate/ vative Liberal Conservative Liberal Republican Republican
Refer to the table in exercise 5.109. Suppose one person is selected at random from this group. Find the probability the person agrees with the statement and is a liberal Democrat.Data From Exercise 5.109: Conser- Moderatel Moderate/ vative Liberal Conservative Liberal Republican Republican
Refer to the table in exercise 5.109. Suppose one person is selected at random from this group. What is the probability the person is a liberal or moderate/conservative Democrat. Are these events mutually exclusive? Why or why not?Data From Exercise 5.109: Conser- Moderatel Moderate/ vative Liberal
Refer to the table in exercise 5.109. Suppose one person is selected at random from this group. What is the probability the person is a conservative or a moderate/ liberal Republican? Are these events mutually exclusive? Why or why not?Data From Exercise 5.109: Conser- Moderatel Moderate/ vative
Refer to the table in exercise 5.109. Suppose one person is selected at random from this group. Find the probability the person is a Liberal Democrat or said No. Are these events mutually exclusive? Why or why not?Data From Exercise 5.109: Conser- Moderatel Moderate/ vative Liberal Conservative
Refer to the table in exercise 5.109. Suppose one person is selected at random from this group. Find the probability the person said yes or is a moderate/conservative Democrat. Are these events mutually exclusive? Why or why not?Data From Exercise 5.109: Conser- Moderatel Moderate/ vative Liberal
Refer to the table in exercise 5.109. Suppose one person is selected at random from this group.a. Find the probability that the person agreed with the statement, given that the person is a liberal Democrat.b. Find the probability that the person agreed with the statement, given that the person is a
Refer to the table in exercise 5.109. Suppose one person is selected at random from this group.a. Find P(no| conservative Republican)b. Find P(no| Republican)c. Find P(liberal Democrat | yes)Data From Exercise 5.109: Conser- Moderatel Moderate/ vative Liberal Conservative Liberal Republican
Suppose a person is randomly selected. Label each pair of events as mutually exclusive or not mutually exclusive.a. The person is taller than 70 inches; the person is maleb. The person does not own a pet; the person owns a guinea pig
Suppose a person is randomly selected. Label each pair of events as mutually exclusive or not mutually exclusive.a. The person is 40 years old; the person is not old enough to drink alcohol legallyb. The person plays tennis; the person plays the cello.
In the game Yahtzee, five dice are rolled at the same time. Bonus points are awarded if at least three of the dice land on the same number. The table below shows the outcomes for five trials.a. List the outcomes that had at least three of the dice land on the same number.b. Based on these data,
A multiple-choice test has 10 questions. Each question has four choices, but 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 more than one valid method.)a. Ten digits are selected
A busy street has three traffic lights in a row. These lights are not synchronized, so they run independently of each other. At any given moment, the probability that a light is green is 60%. Assuming that there is no traffic, follow the steps below to design a simulation to estimate the
A soda-bottling plant has a flaw in that 20% of the bottles it fills do not have enough soda in them. The sodas are sold in six-packs. Follow these steps to carry out a simulation to find the probability that three or more bottles in a six-pack will not have enough soda.a. Identify the action with
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. If the two young adults chosen were Facebook
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. Suppose these are accurate percentages. Now
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 support the death penalty?b. What is the
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 current gun laws?
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 is chosen for the jury is a woman is 50%.
Imagine flipping a fair coin many times. Explain what should happen to the proportion of heads as the number of coin flips increases.
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 to find the empirical probability of rolling a
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 37674b. Based on these 20 trials, what is the simulated
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.a. Twenty digits are selected using a row from a random number table.
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.a. The digits 1, 2, and 3 represent the
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’s the empirical probability of rolling two numbers whose sum is
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, what’s the empirical probability of rolling at least one 6 with two
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 cell phone service?b. What is the probability
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
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.Data From Exercise 5.53: Local TV Network TV Cable TV Total Men 66 48 58 Women 82 54 56 Total
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. Include the row totals, column totals, and the grand
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 given that the person says “Hasn’t
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”?Data From Exercise 5.41: Hasn't Gone Far Has Been Has Gone Enough about Right Too Far Total Men 42 44 14 100 Women 57 34 6. 100 Total
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?
Use the data in exercise 5.43 for this problem.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 the probability that a randomly selected person said No, given that the person did not have a child under 18 years old.c.
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.a. Find the probability that a randomly chosen person from this group said “Yes,” given that the person has a child under 18 years old.b. Find
A person is selected randomly from the entire group whose responses are summarized in the table for exercise 5.41. We want to find the probability that the person selected is a male who said “hasn’t gone far enough.”a. Which of the following statements best described the question?i.
A recent Pew Research poll asked respondents to fill in the blank to this question:“The country ____ when it comes to giving equal rights to women” with one of three choices. The results are shown in the following table using a sample size of 100 men and 100 women.a. A person is selected
A 2018 Pew poll asked U.S. adults how often they go online. The responses are shown in the table.Almost constantly . . . . . . . . . . . . . . . 26%Several times a day . . . . . . . . . . . . . . . 43%About once a day . . . . . . . . . . . . . . .
A 2018 Marist poll asked respondents what superpower they most desired. The distribution of responses are shown in the table.Superpower PercentageTravel in time . . . . . . . . . 29%Read minds . . . . . . . . . 20%Ability to fly .
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 Preference. The political party breakdown in
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 answered this survey questions, what
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.Data From Exercise 5.19: Took a Vacation Yes No Total College Graduate 200 50 250 Not a College Graduate 135 115 250 Total 335 165 500
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.Data From Exercise 5.19: Took a Vacation Yes No Total College Graduate 200 50 250 Not a College Graduate 135 115 250 Total 335 165 500
Suppose a student is selected at random from a large college population.a. Label each pair of events as mutually exclusive or not mutually exclusive.i. The students is a Chemistry major; the student works on campus.ii. The student is a full-time student; the student is only taking one 3-unit
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 married.b. Give an example of two events that
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)?Data From Exercise 5.23:A Pew Research poll asked
A Pew Research poll asked respondents to fill in the blank to this question: Compared to other industries there is _____ discrimination against women in the tech industry. Responses separated by gender are shown in the following table. The results are shown using a sample size of 280 men and 150
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 that the person a Republican who said
A Gallup poll asked a sample of voters if marijuana should be legalized. Voters’ responses and political party affiliation are in the table.a. If a person is randomly selected from this group, find the probability that the person is a Republican.b. If a person is randomly selected from this
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.a. If a person is randomly selected from this group, find the probability of the following:i. The person is maleii. The person has read a book in the
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 group.a. If a person is randomly selected from
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.)Data From Exercise 5.11:There are four suits:
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 equally likely, find the probability of having
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 sample space are equally likely, find each of the
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 that a guess on one question will be incorrect?
There are four suits: clubs (♣), diamonds (♦), hearts (❤), and spades (♠), and the following cards appear in each suit: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king. The jack, queen, and king are called face cards because they have a drawing of a face on them. Diamonds and hearts are
For each of the values, state whether the number could be the probability of an event. Give a reason for your answers.a. 99%b. 0.9c. 9.9d. 0.0099e. -0.90
For each of the values, state whether the number could be the probability of an event. Give a reason for your answers.a. 0.26b. -0.26c. 2.6d. 2.6%e. 26
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 Tran are considered highly experienced. Teachers
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. Suppose new patients are randomly assigned to one of the doctors in the group.a. List the equally likely outcomes that could occur
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 theoretical probability?
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.
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, 2, 3, 4 represent heads and the digits 5, 6, 7,
The figure shows a scatterplot of the wages and educational level of some people. Describe what you see. Explain the trend and mention any unusual points. 70 60 50 40 30 20 10 8 10 12 14 16 18 20 Years of Education Wages (dollars per hour) ..
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