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mathematics
practice of statistics

The Practice Of Statistics 6th Edition Daren S. Starnes, Josh Tabor - Solutions

Suppose a homeowner spends $300 for a home insurance policy that will pay out $200,000 if the home is destroyed by fire in a given year. Let P = the profit made by the company on a single policy. From previous data, the probability that a home in this area will be destroyed by fire is 0.0002.a.
In government data, a household consists of all occupants of a dwelling unit, while a family consists of two or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size
In a certain archery competition, each player continues to shoot until he or she misses the center of the target twice. Quinn is one of the archers in this competition. Based on past experience, she has a 0.60 probability of hitting the center of the target on each shot. We want to design a
A study sought to determine if the ancient Chinese art of acupuncture could help infertile women become pregnant. A total of 160 healthy women undergoing assisted reproductive therapy were recruited for the study. Half of the subjects were randomly assigned to receive acupuncture treatment 25
The ability to grow in shade may help pine trees found in the dry forests of Arizona to resist drought. How well do these pines grow in shade? Investigators planted pine seedlings in a greenhouse in either full light, light reduced to 25% of normal by shade cloth, or light reduced to 5% of normal.
A life insurance company sells a term insurance policy to 21-year-old males that pays $100,000 if the insured dies within the next 5 years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of $250 each year as payment
Exercise 10 described a large sample survey that asked a sample of people aged 19 to 25 years, “In the past seven days, how many times did you go to an exercise or fitness center or work out?” The response Y for a randomly selected survey respondent has the probability distribution shown here.
Exercise 9 described how the first digits of numbers in legitimate records often follow a model known as Benford’s law. Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit can’t be 0). From Exercise
Ana is a dedicated Skee Ball player (see photo in Exercise 4) who always rolls for the 50-point slot. The probability distribution of Ana’s score X on a randomly selected roll of the ball is shown here. From Exercise 8, μX = 23.8. Calculate and interpret the standard deviation of X.Exercise
A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected on a randomly selected ferry trip is shown here. From Exercise 7, μY=$19.35. Calculate and interpret the standard deviation of Y.Exercise 7.Get
Ana is a dedicated Skee Ball player (see photo in Exercise 4) who always rolls for the 50-point slot. The probability distribution of Ana’s score X on a randomly selected roll of the ball is shown here. From Exercise 8, μX = 23.8.a. Find the median of X.b. Compare the mean and median. Explain
A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected on a randomly selected ferry trip is shown here. From Exercise 7, μY = $19.35.a. Find the median of Y.b. Compare the mean and median. Explain why
Choose a person aged 19 to 25 years at random and ask, “In the past seven days, how many times did you go to an exercise or fitness center or work out?” Call the response Y for short. Based on a large sample survey, here is the probability distribution of Y.a. A histogram of the probability
Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren’t present in legitimate records. Some patterns, like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of
Refer to Exercise 4. Find the mean of X. Interpret this value.Exercise 4.Ana is a dedicated Skee Ball player (see photo) who always rolls for the 50-point slot. The probability distribution of Ana’s score X on a randomly selected roll of the ball is shown here. Score 10 20 30 40 50 Probability
Refer to Exercise 3. Find the mean of Y. Interpret this value.Exercise 3.Get on the boat! A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected (in dollars) on a randomly selected ferry trip is shown
Refer to Exercise 4. Make a histogram of the probability distribution. Describe its shape.Exercise 4.Ana is a dedicated Skee Ball player (see photo) who always rolls for the 50-point slot. The probability distribution of Ana’s score X on a randomly selected roll of the ball is shown here. Score
Refer to Exercise 3. Make a histogram of the probability distribution. Describe its shape.Exercise 3.Get on the boat! A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected (in dollars) on a randomly
Ana is a dedicated Skee Ball player (see photo) who always rolls for the 50-point slot. The probability distribution of Ana’s score X on a randomly selected roll of the ball is shown here.a. Find P(Y < 20). Interpret this result.b. Express the event “Anna scores at most 20” in terms of X.
Get on the boat! A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected (in dollars) on a randomly selected ferry trip is shown here.a. Find P(X > 20). Interpret this result.b. Express the event
Spell-checking software catches “nonword errors,” which result in a string of letters that is not a word, as when “the” is typed as “teh.” When undergraduates are asked to write a 250-word essay (without spell checking), the number Y of nonword errors in a randomly selected essay has
In an experiment on the behavior of young children, each subject is placed in an area with five toys. Past experiments have shown that the probability distribution of the number X of toys played with by a randomly selected subject is as follows:a. Write the event “child plays with 5 toys” in
Matt and Diego suspect that people are more likely to agree to participate in a survey if the interviewers are dressed up. To test this idea, they went to the local grocery store to survey customers on two consecutive Saturday mornings at 10 A.M. On the first Saturday, they wore casual clothing
Your body mass index (BMI) is your weight in kilograms divided by the square of your height in meters. Online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a common but controversial indicator of being overweight or obese. A study by the National Center for
If P(A) = 0.24, P(B) = 0.52, and A and B are independent events, what is P(A or B)?a. 0.1248b. 0.28c. 0.6352d. 0.76e. The answer cannot be determined from the information given.Select the best answer.
Suppose a loaded die has the following probability model:If this die is thrown and the top face shows an odd number, what is the probability that the die shows a 1?a. 0.10b. 0.17c. 0.30d. 0.50e. 0.60Select the best answer. Outcome 1 4 5 Probability 0.3 0.1 0.1 0.1 0.1 0.3 3. 2.
In an effort to find the source of an outbreak of food poisoning at a conference, a team of medical detectives carried out a study. They examined all 50 people who had food poisoning and a random sample of 200 people attending the conference who didn’t get food poisoning. The detectives found
An athlete suspected of using steroids is given two tests that operate independently of each other. Test A has probability 0.9 of being positive if steroids have been used. Test B has probability 0.8 of being positive if steroids have been used. What is the probability that neither test is positive
A standard deck of playing cards consists of 52 cards with 13 cards in each of four suits: spades, diamonds, clubs, and hearts. Suppose you shuffle the deck thoroughly and deal 5 cards face-up onto a table.a. What is the probability of dealing five spades in a row?b. Find the probability that all 5
You are tossing a pair of fair, six-sided dice in a board game. Tosses are independent. You land in a danger zone that requires you to roll doubles (both faces showing the same number of spots) before you are allowed to play again.a. What is the probability of rolling doubles on a single toss of
Suppose C and D are two events such that P(C) = 0.6, P(D) = 0.45, and P(C ∩ D) = 0.3. Are events C and D independent? Justify your answer.
Suppose A and B are two events such that P(A) = 0.3, P(B) = 0.4, and P(A ∩ B) = 0.12. Are events A and B independent? Justify your answer.
The two-way table summarizes data from an experiment comparing the effectiveness of three different diets (A, B, and C) on weight loss. Researchers randomly assigned 300 volunteer subjects to the three diets. The response variable was whether each subject lost weight over a 1 year period.a. Suppose
The two-way table summarizes data on the gender and eye color of students in a college statistics class. Imagine choosing a student from the class at random. Define event A: student is male, and event B: student has blue eyes.a. Copy and complete the two-way table so that events A and B are
Internet sites often vanish or move so that references to them can’t be followed. In fact, 87% of Internet sites referred to in major scientific journals still work within two years of publication. Suppose we randomly select 7 Internet references from scientific journals.a. Find the probability
Many fire stations handle more emergency calls for medical help than for fires. At one fire station, 81% of incoming calls are for medical help. Suppose we choose 4 incoming calls to the station at random.a. Find the probability that all 4 calls are for medical help.b. What’s the probability that
An airline reports that 85% of its flights arrive on time. To find the probability that a random sample of 4 of this airline’s flights into LaGuardia Airport in New York City on the same night all arrive on time, can we multiply (0.85)(0.85)(0.85)(0.85)? Why or why not?
According to the Current Population Survey (CPS), 27% of U.S. females are older than 55. The Centers for Disease Control and Prevention (CDC) report that 6% of all U.S. females are pregnant. Suppose that these results are accurate. If we randomly select a U.S. female, is P(pregnant and over 55) =
Suppose that you roll a fair, six-sided die 10 times. What’s the probability that you get at least one 6?
A shipping company claims that 90% of its shipments arrive on time. Suppose this claim is true. If we take a random sample of 20 shipments made by the company, what’s the probability that at least 1 of them arrives late?
Harris Interactive reported that 29% of all U.S. adults favor abolishing the penny. Assuming that responses from different individuals are independent, what is the probability of randomly selecting 3 U.S. adults who all say that they favor abolishing the penny?
A string of Christmas lights contains 20 lights. The lights are wired in series so that if any light fails, the whole string will go dark. Each light has probability 0.98 of working for a 3-year period. The lights fail independently of each other. Find the probability that the string of lights will
Refer to Exercise 85. Many of the positive results from EIA tests are false positives. It is therefore common practice to perform a second EIA test on another blood sample from a person whose initial specimen tests positive. Assume that the false positive and false negative rates remain the same
Tree diagrams can organize problems having more than two stages. The figure shows probabilities for a charity calling potential donors by telephone. Each person called is either a recent donor, a past donor, or a new prospect. At the next stage, the person called either does or does not pledge to
A boy uses a homemade metal detector to look for valuable metal objects on a beach. The machine isn’t perfect—it beeps for only 98% of the metal objects over which it passes, and it beeps for 4% of the nonmetallic objects over which it passes. Suppose that 25% of the objects that the machine
Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. A false positive occurs when the test gives a positive result but
Lactose intolerance causes difficulty in digesting dairy products that contain lactose (milk sugar). It is particularly common among people of African and Asian ancestry. In the United States (not including other groups and people who consider themselves to belong to more than one race), 82% of the
Tennis great Andy Murray made 60% of his first serves in a recent season. When Murray made his first serve, he won 76% of the points. When Murray missed his first serve and had to serve again, he won only 54% of the points. Suppose you randomly choose a point on which Murray served. You get
The Kaiser Family Foundation released a study about the influence of media in the lives of young people aged 8−18. In the study, 17% of the youth were classified as light media users, 62% were classified as moderate media users, and 21% were classified as heavy media users. Of the light users who
In a certain month, 88% of automobile drivers filled their vehicles with regular gasoline, 2% purchased midgrade gas, and 10% bought premium gas. Of those who bought regular gas, 28% paid with a credit card; of customers who bought midgrade and premium gas, 34% and 42%, respectively, paid with a
A statistics class with 30 students has 10 males and 20 females. Suppose you choose 3 of the students in the class at random. Find the probability that all three are female.
According to Forrest Gump, “Life is like a box of chocolates. You never know what you’re gonna get.” Suppose a candymaker offers a special “Gump box” with 20 chocolate candies that look alike. In fact, 14 of the candies have soft centers and 6 have hard centers. Suppose you choose 3 of
Suppose that 10% of adults belong to health clubs, and 40% of these health club members go to the club at least twice a week. Find the probability that a randomly selected adult belongs to a health club and goes there at least twice a week.
Illegal music downloading is a big problem: 29% of Internet users download music files, and 67% of downloaders say they don’t care if the music is copyrighted.18 Find the probability that a randomly selected Internet user downloads music and doesn’t care if it’s copyrighted.
Suppose you roll two fair, six-sided dice—one red and one green. Are the events “sum is 8” and “green die shows a 4” independent? Justify your answer. (See Figure 5.2 on page 314 for the sample space of this chance process.)Figure 5.2 ..
Suppose you roll two fair, six-sided dice—one red and one green. Are the events “sum is 7” and “green die shows a 4” independent? Justify your answer. (See Figure 5.2 on page 314 for the sample space of this chance process.)Figure 5.2 ..
Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.Suppose we select one of these students at random.a. Find
The Pew Research Center asked a random sample of 2024 adult cell phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including nonsmartphones). The two-way table summarizes the data.Suppose we select one of the survey respondents at
A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits—clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as “face cards.”
What is the relationship between educational achievement and home ownership? A random sample of 500 U.S. adults was selected. Each member of the sample was identified as a high school graduate (or not) and as a homeowner (or not). The two-way table summarizes the data.Are the events “homeowner”
A recent census at a major university revealed that 60% of its students mainly used Macs. The rest mainly used PCs. At the time of the census, 67% of the school’s students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students and used a Mac
In one large city, 40% of all households own a dog, 32% own a cat, and 18% own both. Suppose we randomly select a household and learn that the household owns a cat. Find the probability that the household owns a dog.
Select an adult at random. Define events D: person has earned a college degree, and T: person’s career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.P (D) P (T) P (D|T) P (T|D)
Select an adult at random. Define events T: person is over 6 feet tall, and B: person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your answer.P (T) P (B) P (T|B) P (B|T)
Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns in a recent year:a. What is the probability that a randomly chosen return shows an adjusted gross income of $50,000 or more?b. Given that a return shows an income of at
Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:a. What’s the probability that the student is studying a language other than English?b. What is the probability that a student is studying Spanish given
How is the hatching of water python eggs influenced by the temperature of a snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: cold, neutral, or hot. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the
A random sample of 1200 U.S. college students was asked, “What is your perception of your own body? Do you feel that you are overweight, underweight, or about right?” The two-way table below summarizes the data on perceived body image by gender.Suppose we randomly select one of the survey
A survey of 4826 randomly selected young adults (aged 19 to 25) asked, “What do you think are the chances you will have much more than a middle-class income at age 30?” The two-way table summarizes the responses.Choose a survey respondent at random. Define events G: a good chance, M: male, and
A random sample of 415 children from England and the United States who completed a survey in a recent year was selected. Each student’s country of origin was recorded along with which superpower they would most like to have: the ability to fly, ability to freeze time, invisibility, superstrength,
Fractures of the spine are common and serious among women with advanced osteoporosis (low mineral density in the bones). Can taking strontium ranelate help? A large medical trial was conducted to investigate this question. Researchers recruited 1649 women with osteoporosis who had previously had at
At what age do babies learn to crawl? Does it take longer to learn in the winter, when babies are often bundled in clothes that restrict their movement? Perhaps there might even be an association between babies’ crawling age and the average temperature during the month they first try to crawl
The most common bet in craps is the “pass line.” A pass line bettor wins immediately if either a 7 or an 11 comes up on the first roll.This is called a natural. What is the probability that a natural does not occur?a. 2/36b. 6/36c. 8/36d. 16/36e. 28/36The casino game craps is based on rolling
If a player rolls a 2, 3, or 12, it is called craps. What is the probability of getting craps or an even sum on one roll of the dice?a. 4/36b. 18/36c. 20/36d. 22/36e. 32/36The casino game craps is based on rolling two dice. Here is the assignment of probabilities to the sum of the numbers on the
In a sample of 275 students, 20 say they are vegetarians. Of the vegetarians, 9 eat both fish and eggs, 3 eat eggs but not fish, and 7 eat neither. Choose one of the vegetarians at random. What is the probability that the chosen student eats fish or eggs?a. 9/20b. 13/20c. 22/20d. 9/275e.
The partially completed table that follows shows the distribution of scores on the 2016 AP® Statistics exam.Suppose we randomly select a student who took this exam. What’s the probability that he or she earned a score of at least 3?a. 0.249b. 0.361c. 0.390d. 0.466e. 0.610Select the best answer.
Suppose C and D are two events such thatP(C) = 0.6, P(D) = 0.45, and P(C ∪ D) = 0.75. Find P(C ∩ D).
Suppose A and B are two events such thatP(A) = 0.3, P(B) = 0.4, and P(A ∪ B) = 0.58. Find P(A ∩ B).
Refer to Exercise 48.a. Make a Venn diagram to display the outcomes of this chance process using events L: reads the Los Angeles Times and W: reads the Wall Street Journal.b. Find P(LC ∩ W).Exercise 48.In a large business hotel, 40% of guests read the Los Angeles Times. Only 25% read the Wall
Refer to Exercise 47.a. Make a Venn diagram to display the outcomes of this chance process using events D: owns a dog and C: owns a cat.b. Find P(D ∩ CC).Exercise 47.In one large city, 40% of all households own a dog, 32% own a cat, and 18% own both. Suppose we randomly select a household.
In January 2017, 52% of U.S. senators were Republicans and the rest were Democrats or Independents.Twenty-one percent of the senators were females, and 47% of the senators were male Republicans. Suppose we select one of these senators at random. Define events R: is a Republican and M: is male.a.
A recent census at a major university revealed that 60% of its students mainly used Macs. The rest mainly used PCs. At the time of the census, 67% of the school’s students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students and used a Mac
In a large business hotel, 40% of guests read the Los Angeles Times. Only 25% read the Wall Street Journal. Five percent of guests read both papers. Suppose we select a hotel guest at random and record which of the two papers the person reads, if either. What’s the probability that the person
A jar contains 36 disks: 9 each of four colors—red, green, blue, and yellow. Each set of disks of the same color is numbered from 1 to 9. Suppose you draw one disk at random from the jar. Define events R: get a red disk, and N: get a disk with the number 9.a. Make a two-way table that describes
In one large city, 40% of all households own a dog, 32% own a cat, and 18% own both. Suppose we randomly select a household. What’s the probability that the household owns a dog or a cat?
An American roulette wheel has 38 slots with numbers 1 through 36, 0, and 00, as shown in the figure. Of the numbered slots, 18 are red, 18 are black, and 2—the 0 and 00—are green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced, the ball
Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.Suppose we select one of these students at random. What’s
A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits—clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as “face cards.”
The Pew Research Center asked a random sample of 2024 adult cell phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). The two-way table summarizes the data.Suppose we select one of the survey respondents at
Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, “Do you eat breakfast on a regular basis?” All 595 students in the school responded to the survey. The resulting data are shown in the two-way table.Suppose we select a
A company that offers courses to prepare students for the Graduate Management Admission Test (GMAT) has collected the following information about its customers: 20% are undergraduate students in business, 15% are undergraduate students in other fields of study, and 60% are college graduates who are
Choose a young adult (aged 25 to 29) at random. The probability is 0.13 that the person chosen did not complete high school, 0.29 that the person has a high school diploma but no further education, and 0.30 that the person has at least a bachelor’s degree.a. What must be the probability that a
The National Household Travel Survey gathers data on the time of day when people begin a trip in their car or other vehicle. Choose a trip at random and record the time at which the trip started. Here is an assignment of probabilities for the outcomes:a. What probability should replace “?” in
In government data, a household consists of all occupants of a dwelling unit. Choose an American household at random and count the number of people it contains. Here is the assignment of probabilities for the outcome. The probability of finding 3 people in a household is the same as the probability
Canada has two official languages, English and French. Choose a Canadian at random and ask, “What is your mother tongue?” Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region:a. Explain why this is a valid probability model.b. What is the
Ms. Tyson keeps a Mystery Box in her classroom. If a student meets expectations for behavior, she or he is allowed to draw a slip of paper without looking. The slips are all of equal size, are well mixed, and have the name of a prize written on them. One of the “prizes”—extra
Abigail, Bobby, Carlos, DeAnna, and Emily go to the bagel shop for lunch every Thursday. Each time, they randomly pick 2 of the group to pay for lunch by drawing names from a hat.a. Give a probability model for this chance process.b. Find the probability that Carlos or DeAnna (or both) ends up
Imagine tossing a fair coin 3 times.a. Give a probability model for this chance process.b. Define event B as getting more heads than tails. Find P(B).
Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them.a. Give a probability model for this chance process.b. Find the probability that at
A four-sided die is a pyramid whose four faces are labeled with the numbers 1, 2, 3, and 4 (see image). Imagine rolling two fair, four-sided dice and recording the number that is showing at the base of each pyramid. For instance, you would record a 4 if the die landed as shown in the figure.a. Give

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