Question: If a person rolls a six-sided

> In a September 19, 2010, article in Parade Magazine written to Ask Marilyn, Marilyn vos Savant was asked the following: Four identical sealed envelopes are on a table, one of which contains $100. You are to select one of the envelopes. Then the game host

> Describe the difference between classical and empirical probability.

> You are planning a trip to a water park tomorrow and the weather forecaster says there is a 70% chance of rain. Explain what this result means.

> Describe what an unusual event is. Should the same cutoff always be used to identify unusual events? Why or why not?

> In computing classical probabilities, all outcomes must be equally likely. Explain what this means.

> Explain the Law of Large Numbers. How does this law apply to gambling casinos?

> A friend of yours regularly plays the lottery but has never won. She says that she feels really good about this weekend’s drawing because she is due for a winning ticket. Explain the flaw in your friend’s reasoning.

> The following is a quote by Pierre-Simon Laplace: “To discover the best treatment to use in curing a disease, it is sufficient to test each treatment on the same number of patients, while keeping all circumstances perfectly similar. The superiority of th

> In placebo- controlled clinical trials for the drug Viagra, 734 subjects received Viagra and 725 subjects received a placebo (subjects did not know which treatment they received). The table below summarizes reports of various side effects that were repor

> Let’s say a player typically gets a hit in 3 out of every 10 at-bats (for a 0.300 batting average). Suppose the player has not had a hit in his previous four at-bats. In baseball, you will often hear an announcer say, “This player is due for a hit.” What

> Two hundred people are asked to perform a taste test in which they drink from two randomly placed, unmarked cups and are asked which drink they prefer.

> Each year the National Football League (NFL) runs a combine in which players who wish to be considered for the NFL draft must participate in a variety of activities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 5_1_50 using the fil

> The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Construct a probability model for month in which the tornado occurred. (

> (a) In 2017, the median income of families in the United States was $60,336. What is the probability that a randomly selected family has an income greater than $60,336? (b) The middle 50% of enrolled freshmen at Washington University in St. Louis had SAT

> Conduct a survey in your school by randomly asking 50 students whether they drive to school. Based on the results of the survey, approximate the probability that a randomly selected student drives to school.

> You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the table below. Do you think the die is loaded? Why?

> Determine whether the probabilities below are computed using classical methods, empirical methods, or subjective methods. (a) The probability of having eight girls in an eight-child family is 0.00390625. (b) On the basis of a survey of 1000 families with

> In 2011, Six Flags St. Louis had 10 roller coasters: The Screamin’ Eagle, The Boss, River King Mine Train, Batman the Ride, Mr. Freeze, Ninja, Tony Hawk’s Big Spin, Evel Knievel, Xcalibur, and Sky Screamer. Of these, The Boss, The Screamin’ Eagle, and Ev

> John, Roberto, Clarice, Dominique, and Marco work for a publishing company. The company wants to send two employees to a statistics conference in Orlando. To be fair, the company decides that the two individuals who get to attend will have their names ra

> Which of the assignments of probabilities should be used if tails is twice as likely to occur as heads?

> Which of the assignments of probabilities should be used if the coin is known to always come up tails?

> A survey is conducted asking 400 people, “Do you prefer Coke or Pepsi?”

> Which of the assignments of probabilities should be used if the coin is known to be fair?

> Which of the assignments of probabilities are consistent with the definition of a probability model?

> On your drives to school each day you feel like there is a light that is always red when you reach it. You decide to record data to determine the likelihood of arriving at the light while it is red. Open the data set 5_1_38 at www.pearsonhighered.com/sul

> Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow. So, getting stopped by a train will likely make you late for work. You start recording data to determine the lik

> A survey was conducted by Wakefield Research in which participants were asked to disclose their favorite night to order takeout for dinner. The following data are based on their results. (a) Construct a probability model for favorite night to order takeo

> The table shows the movement of Walt Disney stock for 30 randomly selected trading days. “Up” means the stock price increased in value for the day. “Down” means the stock price decreased in value for the day, and “No Change” means the stock price closed

> The following data represent the number of live multiple-delivery births (three or more babies) in 2017 for women 15 to 54 years old. (a) Construct a probability model for number of multiple births. (b) In the sample space of all multiple births, are mul

> A police officer randomly selected 642 police records of larceny thefts. The following data represent the number of offenses for various types of larceny thefts. (a) Construct a probability model for type of larceny theft. (b) Are purse snatching larceni

> In a national survey conducted by the Centers for Disease Control to determine college students’ health-risk behaviors, college students were asked, “How often do you wear a seatbelt when driving a car?” The frequencies appear in the following table: (a)

> In a national survey conducted by the Centers for Disease Control to determine college students’ health-risk behaviors, college students were asked, “How often do you wear a seatbelt when riding in a car driven by someone else?” The frequencies appear in

> A study in which balding men were compared with non-balding men at one point in time found that balding men were 70% more likely to have heart disease. Source: USA Today, April 4, 2013.

> In Problem 29, we learned that for some diseases, such as sickle-cell anemia, an individual will get the disease only if he or she receives both recessive alleles. This is not always the case. For example, Huntington’s disease only requires one dominant

> A gene is composed of two alleles, either dominant or recessive. Suppose that a husband and wife, who are both carriers of the sickle-cell anemia allele but do not have the disease, decide to have a child. Because both parents are carriers of the disease

> Exclude leap years from the following calculations and assume each birthday is equally likely: (a) Determine the probability that a randomly selected person has a birthday on the 1st day of a month. Interpret this probability. (b) Determine the probabili

> In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, ……., 36. (See the photo.) To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. (a) Determine the sample space. (b) Deter

> The Chicago Tribune analyzed 17,713 complaints by citizens against Chicago police officers. Source: Chicago Tribune, June 14, 2015. (a) Of the 17,713 complaints against police officers, it was found that 7296 were accompanied by a signed affidavit, which

> The Wall Street Journal regularly publishes an article entitled “The Count.” In one article, The Count looked at 1000 randomly selected home runs in Major League Baseball. Source: Wall Street Journal, September 24, 2014. (a) Of the 1000 home runs, it was

> In a survey of 1100 female adults (18 years of age or older), it was determined that 341 volunteered at least once in the past year. (a) What is the probability that a randomly selected adult female volunteered at least once in the past year? (b) Interpr

> A survey of 500 randomly selected high school students determined that 288 played organized sports. (a) What is the probability that a randomly selected high school student plays organized sports? (b) Interpret this probability.

> Compute the probability of the event F = “an odd number.”

> Compute the probability of the event E = “an even number less than 9.”

> Seventh-grade students are randomly divided into two groups. One group is taught math using traditional techniques; the other is taught math using a reform method. After 1 year, each group is given an achievement test to compare proficiency.

> Compute the probability of the event F = {3, 5, 9, 10}

> Compute the probability of the event E = {1, 2, 3}.

> According to the American Veterinary Medical Association, the proportion of households owning a dog is 0.372. What is the probability that a randomly selected household owns a dog?

> According to the U.S. Department of Education, 42.8% of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?

> If a basketball player shoots three free throws, describe the sample space of possible outcomes using S for a made free throw and F for a missed free throw.

> A person can have one of four blood types: A, B, AB, or O. If a person is randomly selected, is the probability they have blood type A equal to 1/4? Why or why not?

> Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes as 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Because there are 11 outcomes, he reasoned the probability of rolling a two must be 1/11 . What is wrong with Bob’

> Suppose that you roll a die 100 times and get six 80 times. Based on these results, what is the estimated probability that the next roll results in six?

> Suppose that you toss a coin 100 times and get 95 heads and five tails. Based on these results, what is the estimated probability that the next flip results in a head?

> Rats with cancer are divided into two groups. One group receives 5 milligrams (mg) of a medication that is thought to fight cancer, and the other receives 10 mg. After 2 years, the spread of the cancer is measured.

> In seven-card stud poker, a player is dealt seven cards. The probability that the player is dealt two cards of the same value and five other cards of different value so that the player has a pair is 0.44. Explain what this probability means. If you play

> According to Nate Silver, the probability of a senate candidate winning his/her election with a 5% lead in an average of polls with a week until the election is 0.89. Interpret this probability. Source: fivethirtyeight.com

> Which of the following numbers could be the probability of an event?

> Which of the following numbers could be the probability of an event? 0, 0.01, 0.35, -0.4, 1, 1.4

> Why is the following not a probability model?

> Refer to Table 8. Is constructing a conditional distribution by level of education different from constructing a conditional distribution by employment status? If they are different, explain the difference.

> What is meant by a marginal distribution? What is meant by a conditional distribution?

> Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanStatsSurveyII. (a) Create a relative frequency distribution for political philosophy. What percent of the respondents are moderate? (b) Draw a relative frequency bar graph for po

> The following data represent the sentences imposed on offenders convicted of murder by race. (a) Which race appears to get a death sentence more frequently? Why? The data in the table above do not consider the race of the victim. The data below show the

> Could it be that smoking actually increases survival rates among women? The following data represent the 20-year survival status and smoking status of 1314 English women who participated in a cohort study from 1972 to 1992. (a) What proportion of the smo

> The American Cancer Society is beginning a study to learn why some people never get cancer. To take part in the study, a person must be 30–65 years of age and never had cancer. The study requires that the participants fill out surveys about their health

> The General Social Survey asks questions about one’s happiness in marriage. Is there an association between gender and happiness in marriage? Use the data in the table to determine if gender is associated with happiness in marriage. Treat gender as the e

> The General Social Survey asks questions about one’s happiness and health. One would think that health plays a role in one’s happiness. Use the data in the table to determine whether healthier people tend to also be happier. Treat level of health as the

> The Pew Research Center for the People and the Press conducted a poll in which it asked individuals to disclose their level of education and feelings about the availability of abortion. The table is based on the results of the survey. (a) Construct a fre

> A college education is certainly a factor in determining one’s income. Researchers at payscale.com wanted to determine if there was an association between mid- career income and household income while an individual is in college. The idea was to determin

> In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “Given a choice of the following, which one would you most want to be?” Results of the survey, by gender, are given in the contingency table. (a) How many adult A

> In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “When you see an ad emphasizing that a product is ‘Made in America,’ are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy

>

>

> Explain the idea behind Simpson’s Paradox.

> Explain why we use the term association rather than correlation when describing the relation between two qualitative variables.

> What does it mean when an observational study is retrospective? What does it mean when an observational study is prospective?

> Match the coefficient of determination to the scatter diagram. The scales on the horizontal and vertical axis are the same for each scatter diagram. (a) R2 = 0.58 (b) R2 = 0.90 (c) R2 = 1 (d) R2 = 0.12

> Total deviation ______ deviation ______ deviation

> The_____, R2, measures the proportion of total variation in the response variable that is explained by the least- squares regression line.

> Go to www.pearsonhighered.com/ sullivanstats to obtain the data file SullivanStatsSurveyII using the file format of your choice for the version of the text you are using. One question asked in this survey is, “What percent of income do you believe indivi

> Go to www.pearsonhighered.com/sullivanstats to obtain the data file 4_3_17. The data represent the 2015 tax rate per pack of cigarettes and the percent of cigarettes smuggled as a percentage of total consumption. A negative value of consumption represent

> The data on the next page represent scores earned by students in Sullivan’s Elementary Algebra course for Chapter 2 (Linear Equations and Inequalities in One Variable) and Chapter 3 (Linear Equations and Inequalities in Two Variables). Completely summari

> Is the width of a tornado related to the amount of distance for which the tornado is on the ground? Go to www.pearsonhighered.com/sullivanstats to obtain the data file 4_3_15. The data represent the width (in yards) and length (in miles) for tornadoes in

> Suppose that we find a bear that is 205 cm long and weighs 187 kg and add the bear to the data in Problem 20 from Section 4.2. Compute the coefficient of determination of the expanded data set. What effect does the additional bear have on R2?

> Suppose that we add the Dodge Viper to the data in Problem 24 in Section 4.2. A Dodge Viper weighs 3425 pounds and gets 11 miles per gallon. Compute the coefficient of determination of the expanded data set. What effect does the addition of the Viper to

> Use the results from Problem 32 in Section 4.1 and Problem 22 in Section 4.2. (a) What proportion of the variability in the wind speed is explained by the relation between the atmospheric pressure and wind speed? (b) Interpret the coefficient of determin

> Explain why it would be unlikely to use a designed experiment to answer the research question posed in Example 3.

> Use the results from Problem 31 in Section 4.1 and Problem 21 in Section 4.2. (a) What proportion of the variability in distance is explained by the relation between speed at which the ball is hit and distance? (b) Interpret the coefficient of determinat

> Use the results from Problem 30 in Section 4.1 and Problem 20 in Section 4.2 to: (a) Compute the coefficient of determination, R2. (b) Interpret the coefficient of determination and comment on the adequacy of the linear model.

> Use the results from Problem 29 in Section 4.1 and Problem 19 in Section 4.2 to: (a) Compute the coefficient of determination, R2. (b) Interpret the coefficient of determination and comment on the adequacy of the linear model.

> Use the results from Problem 28 in Section 4.1 and Problem 18 in Section 4.2 to: (a) Determine the coefficient of determination, R2. (b) Interpret the coefficient of determination and comment on the adequacy of the linear model.

> Use the results from Problem 27 in Section 4.1 and Problem 17 in Section 4.2 to: (a) Determine the coefficient of determination, R2. (b) Interpret the coefficient of determination and comment on the adequacy of the linear model.

> As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength (in pounds per square inch) of a certain type of concrete. The coefficient of determination is 57.5%. Provide an interpretation of this value.

> Perhaps you are familiar with the famous Old Faithful geyser in Yellowstone National Park. Another Old Faithful geyser is located in Calistoga in California’s Napa Valley. The following data represent the time (in minutes) between eruptions and the lengt

> Use the linear correlation coefficient given to determine the coefficient of determination, R2. Interpret each R2. (a) r = -0.32 (b) r = 0.13 (c) r = 0.40 (d) r = 0.93

> If the linear correlation between two variables is negative, what can be said about the slope of the regression line?

> The difference between the observed and predicted value of y is the error, or______ .

> The data used in the influenza study presented in Example 3 were obtained from a cohort study. What does this mean? Why is a cohort study superior to a case-control study?

> Only 12 men have walked on the moon. The average time these men spent on the moon was 43.92 hours. Source: www.theguardian.com

> Mark Twain, in his book Life on the Mississippi (1884), makes the following observation: Therefore, the Mississippi between Cairo and New Orleans was twelve hundred and fifteen miles long one hundred and seventy-six years ago. It was eleven hundred and e