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Statistical Reasoning For Everyday Life 4th Edition Jeff Bennett, Bill Briggs, Mario F. Triola - Solutions

Suppose you randomly select a family with four children. Assume that births of boys and girls are equally likely.a. How many birth orders are possible? List all of them.b. What is the probability that the family has four boys? Four girls?c. What is the probability that the family has a boy, a girl,
After recording the forecasts of your local weatherman for 30 days, you conclude that he gave a correct forecast 18 times. What is the probability that his next forecast will be correct?
In the year 2000, there were 34.7 million people over 65 years of age out of a U.S. population of 281 million. In the year 2050, it is estimated that there will be 78.9 million people over 65 years of age out of a U.S. population of 394 million. Would your chances of meeting a person over 65 at
The following table gives percentages of women and men married for the first time in several age categories (U.S. Census Bureau).a. What is the probability that a randomly encountered married woman was married, for the first time, between the ages of 35 and 44?b. What is the probability that a
a. Construct a table similar to Table 6.2, showing all possible outcomes of tossing four coins at once.b. Construct a table similar to Table 6.3, showing the probability distribution for the events 4 heads, 3 heads, 2 heads, 1 head, and 0 heads when you toss four coins at once.c. What is the
The histogram in Figure 6.7 shows the distribution of 5,964 Colorado lottery numbers (possible values range from 1 to 42). a. Assuming the lottery drawings are random, what would you expect the probability of any number to be? b. Based on the histogram, what is the relative frequency probability of
If there is a 0.9 probability that it will rain sometime today, then there is a probability of 0.1 that it will not rain sometime today.
An insurance company states that the probability that a particular car will be involved in a car crash this year is 0.6 and the probability that the car will not be involved in a car crash this year is 0.3.
Jack estimates that the subjective probability of his being struck by lightning sometime next year is 1/2.
In your own words, describe the law of large numbers.
A person who has a habit of driving fast has never had an accident or traffic citation. What does it mean to say that "the law of averages will catch up with him"? Is it true? Explain.
Suppose someone offers you this opportunity: You can place a bet of $ 10 and roll a single die once. You win twice the outcome of the die. For example, if you roll a 6, you win $12 for a net profit of $2. What is the expected value of this game? Should you play?
If you bet $1 I Kentucky's Pick 4 lottery game, you either lose $1 or gain $4,999. (The winning prize is $5,000, but your $1 bet is not returned, so the net gain is $4,999.) The game is played by selecting a four-digit number between 0000 and 9999. What is the probability of winning? If you bet $1
Football teams have the option of trying to score either 1 or 2 extra points after a touchdown. They get 1 point by kicking the ball through the goal posts or 2 points by running or passing the ball across the goal line. For a recent year in the NFL, 1 -point kicks were successful 94% of the time,
An actuary at an insurance company estimates from existing data that on a $1,000 policy, an average of 1 in 100 policyholders will file a $20,000 claim, an average of 1 in 200 policyholders will file a $50,000 claim, and an average of 1 in 500 policyholders will file a $100,000 claim.a. What is the
Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 30 minutes without delay (say, on the hour and on the half hour). What is the expected value of your waiting time? Explain how you got your answer.
The multi-state Powerball lottery advertises the following prizes and probabilities of winning for a single $1 ticket. Assume the jackpot has a value of $30 million one week. Note that there is more than one way to win some of the monetary prizes (for example, two ways to win $100), so the table
The Multi-State Big Game lottery advertises the following prizes and probabilities of winning for a single $l ticket. The jackpot is variable, but assume it has an average value of $3 million. Note that the same prize can be given to two outcomes with different probabilities. What is the expected
When you give the Venetian casino in Las Vegas $5 for a bet on the number 7 in roulette, you have a 37/38 probability of losing $5 and you have a 1/38 probability of making a net gain of $175. (The prize is $180, but your $5 bet is not returned, so the net gain is $175.) If you bet $5 that the
When you give a casino $5 for a bet on the "pass line" in a casino game of dice, there is a 251/495 probability that you will lose $5 and there is a 244/495 probability that you will make a net gain of $5. (If you win, the casino gives you $5 and you get to keep your $5 bet, so the net gain is $5.)
A geneticist computes the expected number of girls in 5 births and obtains the result of 2.5 girls. He rounds the result to 3 girls, reasoning that it is impossible to get 2.5 girls in 5 births. Is that reasoning correct? Why or why not?
In New Jersey's Pick 4 lottery game, you pay 500 to select a sequence of four digits, such as 2273, from the 10,000 different possible four-digit sequences. If you select the same sequence of four digits that are drawn, you win and collect $2788. What is your expected value? In the long run, how
In 1953, a French economist named Maurice Allais conducted a survey of how people assess risk. Here are two scenarios that he used, each of which required people to choose between two options.Decision 1:Option A: 100% chance of gaining $1,000,000Option B: 10% chance of gaining $2,500,000; 89%
Reader's Digest ran a sweepstakes in which prizes were listed along with the chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5,000 (1 chance in 36,667,000), and $2,500 (1 chance in 27,500,000).a. Assuming that there is
Suppose you roll a die with a friend, with the following rules: For every even number you roll, you win $1 from your friend; for every odd number you roll, you pay $1 to your friend.a. What are the chances of rolling an even number on one roll of a fair die? An odd number?b. Suppose that on the
Suppose that you toss a fair coin 100 times, getting 38 heads and 62 tails, which is 24 more tails than heads.a. Explain why, on your next toss, the difference in the numbers of heads and tails is as likely to grow to 25 as it is to shrink to 23.b. Extend your explanation from part a to explain
A professional gambler playing black jack in the Venetian casino has lost each of his first 10 bets. He begins to place larger bets, reasoning that his current proportion of wins (which is 0) will increase to get closer to the average number of wins. Is his betting strategy sound? Is his reasoning
Steve learns that for a $5 bet on a number in roulette, the expected return is $4.74, but for a $5 bet on the pass line in the game of craps, the expected return is $4.93, so it is better to play this particular craps bet than the roulette bet.
Jennifer purchases a state lottery ticket and she avoids the combination of 1, 2, 3, 4, 5, and 6. She reasons that this combination has the same chance as any other combination, but the jackpot is divided among the winners, and many people are likely to select 1, 2, 3, 4, 5, and 6, so the jackpot
In planning an experiment designed to test the effectiveness of a gender selection method, assume that boys and girls are equally likely to be born. Among 500 births, should we expect to get exactly 250 boys and 250 girls? As the number of births increases, what does the law of large numbers tell
The current U.S. birth rate is given as 13.5 per 1,000 population. When comparing population growth in different countries, why is it better to use birth rates instead of the actual numbers of births?
For each of the three years, find the fatality rate in deaths per billion passenger miles. On the basis of those rates, which year was the safest? Why?
For each of the three years, find the fatality rate in deaths per million passengers. On the basis of those rates, which year was the safest? Why?
For the year 2008, find the fatality rate in deaths per pas¬senger mile. Why don't we report the fatality rate in units of deaths per passenger mile?
Life insurance companies must carefully monitor death rates. Before issuing a life insurance policy for a 19-year-old, the company needs to know the death rate for that age group. Find the death rate per 10,000 for people during their 20th year (age 19-20).
Find the death rate per 10,000 for people during their 17th year (age 16-17).
The highest and lowest birth rates in the United States in 2008 were in Utah and Maine, respectively. Utah reported 55,633 births with a population of 2,736,424 people. Maine reported 13,610 births with a population of 1,316,456 people. Use these data to find the birth rate in births per 1,000
In a recent year, there were 235,000 deaths in California, the highest number in the United States. The state with the lowest number of deaths was Alaska, with 3,000 deaths. The populations of California and Alaska were approximately 35,463,000 and 648,000, respectively.a. Compute the death rates
In 2011, the estimated U.S. population reached 313 million. The overall birth rate was estimated to be 13.8 births per 1,000, and the overall death rate was estimated to be 8.4 deaths per 1,000.a. Approximately how many births were there in the United States?b. About how many deaths were there in
These estimated 2011 values are for China: population = 1,336,718,015; birth rate = 12.3 per 1,000; death rate = 7.0 per 1,000.a. Approximately how many births were there in China?b. About how many deaths were there in China?c. Based on births and deaths alone (i.e., not counting immigration and
What is life expectancy? Does a 30-year-old person have the same life expectancy as a 20-year-old person? Why or why not?
Based on recent data, a 20-year-old person in the United States has a life expectancy of 58.8 years. What does that mean?
As you become older, your expected age at death increases
In a recent year, the total numbers of deaths in the United States due to either accidents or pneumonia were approximately equal. Therefore, the risks of death by accident and pneumonia per 100,000 people are approximately equal.Commercial Aviation Fatality Rates. For Exercises 9-12, use the
For each of the three years, find the fatality rate in deaths per 1,000 departures. On the basis of those rates, which year was the safest? Why?
Let A denote the event of turning on your cell phone and finding that it works, and let B denote the event of turning on your car radio and finding that it works. Are events A and B independent or are they dependent?
A couple plans to have four children. Find the probability that the first two children are girls and the last two children are boys.
A new computer owner creates a password consisting of five characters. She randomly selects a letter of the alphabet for the first character and a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for each of the other four characters; the digits may be reused, so there are 10 possibilities for each of the four
A study of hunting injuries and the wearing of hunter orange clothing showed that among 123 hunters injured when mistaken for game, 6 were wearing orange (based on data from the Centers for Disease Control and Prevention). If a follow-up study begins with the random selection of hunters from this
An MP3 player is loaded with 60 musical selections: 30 rock selections, 15 jazz selections, and 15 blues selections. The player is set on "random play," so selections are played randomly and can be repeated. What is the probability of each of the following events?a. The first four selections are
A telephone pollster has names and telephone numbers for 45 voters, 20 of whom are registered Democrats and 25 of whom are registered Republicans. Calls are made in random order. Suppose you want to find the probability that the first two calls are to Republicans.a. Are these independent or
What is the probability that a randomly selected defendant either pled guilty or was sent to prison?
What is the probability that a randomly selected defendant either pled not guilty or was not sent to prison?
If two different defendants are randomly selected, what is the probability that they both entered guilty pleas?
If two different defendants are randomly selected, what is the probability that they both were sentenced to prison?
If a defendant is randomly selected, what is the probability that the defendant entered a guilty plea and was sent to prison?
If a defendant is randomly selected, what is the probability that the defendant entered a guilty plea and was not sent to prison? Pedestrian deaths. For Exercises 21-26, use the following table, which summarizes data on 985 pedestrian deaths that were caused by accidents (based on data from the
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated.
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated.
If one of the pedestrian deaths is randomly selected, find the probability that the driver was intoxicated or the pedestrian was not intoxicated.
If two different pedestrian deaths are randomly selected, find the probability that they both involved intoxicated drivers.
If two different pedestrian deaths are randomly selected, find the probability that in both cases the pedestrians were intoxicated.
An allergy drug is tested by giving 120 people the drug and 100 people a placebo. A control group consists of 80 people who were given no treatment. The number of people in each group who showed improvement appears in the table below.a. What is the probability that a randomly selected person in the
Refer to the following table summarizing results from a study of people who refused to answer survey questions (based on data from "I Hear You Knocking but You Can't Come In," by Fitzgerald and Fuller, Sociological Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects
a. What is the probability that a child receive an A gene from both parents?b. What is the probability that a child receives an A gene from one parent and an a gene from the other parent? Note that this can occur in two ways.c. What is the probability that a child receives an a gene from both
The game of BINGO involves drawing numbered and lettered buttons at random from a barrel. The B numbers are 1-15, the I numbers are 16-30, the N numbers are 31-45, the G numbers are 46-60, and the O numbers are 61-75. Buttons are not replaced after they have been selected. What is the probability
It is said that probability theory was invented in the 17th century to explain the gambling of a nobleman named the Chevalier de Mere.a. In his first game, the Chevalier bet on rolling at least one 6 with four rolls of a fair die. If played repeatedly, is this a game he should expect to win?b. In
Suppose that 3% of the students at a particular college are known to carry HIV.a. If a student has 6 sexual partners during the course of a year, what is the probability that at least one of them carries HIV?b. If a student has 12 sexual partners during the course of a year, what is the probability
The numbers 5, 17, 18, 27, 36, and 41 were drawn in the last lottery; they should not be bet on in the next lottery because they are now less likely to occur.
The probability of flipping a coin and getting heads is 0.5. The probability of selecting a red card when one card is drawn from a shuffled deck is also 0.5. When flipping a coin and drawing a card, the probability of getting heads or a red card is 0.5 + 0.5 = 1.
Either/Or Probability. P(A) = 0.5 and P(A or B) = 0.8.
The probability of your winning the state lottery this week is not affected by whether you won that same lottery last week.
Refer to the combined city-highway fuel economy ratings (mi/gal) for different cars. The old ratings are based on tests used before 2008 and the new ratings are based on tests that went into effect in 2008.Construct a scatterplot. What does the result suggest?
Examine the scatterplot in Figure 7.22 and estimate the value of the correlation coefficient.
Refer to the combined city-highway fuel economy ratings (mi/gal) for different cars. The old ratings are based on tests used before 2008 and the new ratings are based on tests that went into effect in 2008.Estimate the value of the correlation coefficient. What does that value suggest?
In a study of randomly selected subjects, it is found that there is a strong correlation between household income and number of visits to dentists. Is it valid to conclude that higher incomes cause people to visit dentists more often? Is it valid to conclude that more visits to dentists cause
You are considering the most expensive purchase that you are likely to make: the purchase of a home. Identify at least five different variables that are likely to affect the actual value of a home. Among the variables that you have identified, which single variable is likely to have the greatest
A researcher collects paired sample data and computes the value of the linear correlation coefficient to be 0. Based on that value, he concludes that there is no relationship between the two variables. What is wrong with this conclusion?
Figure 7.8 shows a scatterplot in which theActual high temperature for the day is compared with a forecast made two days in advance. Estimate the correlation coefficient and discuss what these data imply about weather forecasts. Do you think you would get similar results if you made similar
Consider the following table showing speed limits and death rates from automobile accidents in selected countries.a. Construct a scatterplot of the data. b. Briefly characterize the correlation in words (for example, strong positive correlation, weak negative correlation) and estimate the
What is a scatterplot, and how does it help us investigate correlation?
Population Growth. Consider the following table showing percentage change in population and birth rate (per 1,000 of population) for 10 states over a period of 10 years.a. Construct a scatterplot for the data. b. Briefly characterize the correlation in words and estimate the correlation
Brain Size and Intelligence. The table below lists brain sizes (in cm3) and Wechsler IQ scores of subjects (based on data from "Brain Size, Head Size, and Intelligence Quotient in Monozygatic Twins," by Tramo et al, Neurology, Vol. 50, No. 5). Is there sufficient evidence to conclude that there is
Consider the following table showing total box office receipts and total attendance for all American films.a. Construct a scatterplot of the data. b. Briefly characterize the correlation in words and estimate the correlation coefficient.
Consider the following table showing the average hours of television watched in households in five categories of annual income.a. Construct a scatterplot for the data. To locate the dots, use the midpoint of each income category. Use a value of $25,000 for the category "less than $30,000," and use
Consider the following table showing January mean monthly precipitation and mean daily high temperature for ten Northern Hemisphere cities (National Oceanic and Atmospheric Administration).a. Construct a scatterplot of the data. b. Briefly characterize the correlation in words and estimate the
Consider the following table showing one year's total sales (revenue) and profits for eight large retailers in the United States.a. Construct a scatterplot for the data. b. Briefly characterize the correlation in words and estimate the correlation coefficient. c. Discuss your observations. Does
Consider the following table showing mean daily caloric intake (all residents) and infant mortality rate (per 1,000 births) for 10 countries.a. Construct a scatterplot for the data. b. Briefly characterize the correlation in words and estimate the correlation coefficient. c. Discuss any patterns
The correlation coefficient remains unchanged if we interchange the variables x and y. Determine whether the given property is true, and explain your answer.
The correlation coefficient remains unchanged if we change the units used to measure x, y, or both. Determine whether the given property is true, and explain your answer.
One set of paired data results in r = 1 and a second set of paired data results in r = — 1. How do the corresponding scatterplots differ?
A study showed that for one town, as the stork population increased, the number of births in the town also increased. It therefore follows that the increase in the stork population caused the number of births to increase. Decide whether the statement make sense or not? Explain clearly.
An engineer for a car company finds that by reducing the weights of various cars, mileage (mi/gal) increases. Because this is a positive result, we say that there is a positive correlation. Decide whether the statement make sense or not? Explain clearly.
Two studies both found a correlation between low birth weight and weakened immune systems. The second study had a much larger sample size, so the correlation it found must be stronger. Decide whether the statement make sense or not? Explain clearly.
In clinical trials of the drug Lisinopril, it is found that increased dosages of the drug correlated with lower blood pressure levels. Based on the correlation, can we conclude that Lisinopril treatments cause lower blood pressure? Why or why not?
It has been found that people who exercise regularly by running tend to weigh less than those who do not run, and those who run longer distances tend to weigh less than those who run shorter distances. State the correlation clearly. Then state whether the correlation is most likely due to
It has been found that as the number of registered vehicles increases, the time drivers spend sitting in traffic also increases. State the correlation clearly. Then state whether the correlation is most likely due to coincidence, a common underlying cause or a direct cause? Explain your answer.
It has been found that as the number of traffic lights increases, the number of car crashes also increases. State the correlation clearly. Then state whether the correlation is most likely due to coincidence, a common underlying cause or a direct cause? Explain your answer.
It has been found that as gas prices increase, the distances vehicles are driven tend to get shorter. State the correlation clearly. Then state whether the correlation is most likely due to coincidence, a common underlying cause or a direct cause? Explain your answer.

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