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mathematics
statistics
Fundamentals Of Statistics 4th Edition Michael Sullivan III - Solutions
If a person rolls a six-sided die and then flips a coin, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the die outcomes and H, T for the coin outcomes.
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.
Compute the probability of the event E = {1, 2, 3}. Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Compute the probability of the event F = {3, 5, 9, 10}. Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Compute the probability of the event E =; an even number less than 9.” Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Compute the probability of the event F = ;an odd number.” Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
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.
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) Interpret this probability.
A bag of 100 tulip bulbs purchased from a nursery contains 40 red tulip bulbs, 35 yellow tulip bulbs, and 25 purple tulip bulbs. (a) What is the probability that a randomly selected tulip bulb is red? (b) What is the probability that a randomly selected tulip bulb is purple? (c) Interpret these two
The local golf store sells an “onion bag” that contains 80 “experienced” golf balls. Suppose the bag contains 35 Titleists, 25 Maxflis, and 20 Top-Flites. (a) What is the probability that a randomly selected golf ball is a Titleist? (b) What is the probability that a randomly selected golf
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) Determine the probability that the metal ball
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 probability that a randomly selected person has a
A gene is composed of two alleles. An allele can be 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, each has one dominant
In Problem 33, 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 gene for an individual to contract the
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 the following table:Response
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:Response ........FrequencyNever ........
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.Type of Larceny Theft ....Number of OffensesPocket picking ....... 4Purse snatching ....... 6Shoplifting .......133From motor vehicles
The following data represent the number of live multiple-delivery births (three or more babies) in 2007 for women 15 to 54 years old.Age ....Number of Multiple Births15–19 ..... 10020–24 ..... 46725–29 .....162030–34 .....226235–39 .....154540–44 ..... 32845–54 ..... 105(a) Construct
Which of the assignments of probabilities are consistent with the deï¬nition of a probability model? Use the given table, which lists six possible assignments of probabilities for tossing a coin twice, to answer the following questions.
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 randomly drawn from a hat. (a) Determine the
In 2011, Six Flags St. Louis had ten 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 Evel Knievel are wooden coasters. Ethan
On October 5, 2001, Barry Bonds broke Mark McGwire’s home-run record for a single season by hitting his 71st and 72nd home runs. Bonds went on to hit one more home run before the season ended, for a total of 73. Of the 73 home runs, 24 went to right field, 26 went to right center field, 11 went
Determine whether the probabilities on the following page are computed using classical methods, empirical methods, or subjective methods. (a) The probability of having eight girls in an eight-child family is 0.390625%. (b) On the basis of a survey of 1000 families with eight children, the
In 2006, the median income of families in the United States was $58,500. What is the probability that a randomly selected family has an income greater than $58,500?
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 in the next column summarizes reports of various side effects that were reported.(a) Is the variable
Explain the Law of Large Numbers. How does this law apply to gambling casinos?
Describe what an unusual event is. Should the same cutoff always be used to identify unusual events? Why or why not?
You are planning a trip to a water park tomorrow. The weather forecaster says there is a 70% chance of rain tomorrow. Explain what this result means.
Describe the difference between classical and empirical probability.
Ask Marilyn 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 discards two of the remaining
What does it mean when two events are complements?
A probability experiment is conducted in which the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let event E = {2, 3, 4, 5, 6, 7}, event F = {5, 6, 7, 8, 9}, event G = {9, 10, 11, 12}, and event H = {2, 3, 4}. Assume that each outcome is equally likely. List the
A probability experiment is conducted in which the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let event E = {2, 3, 4, 5, 6, 7}, event F = {5, 6, 7, 8, 9}, event G = {9, 10, 11, 12}, and event H = {2, 3, 4}. Assume that each outcome is equally likely. List the
A probability experiment is conducted in which the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let event E = {2, 3, 4, 5, 6, 7}, event F = {5, 6, 7, 8, 9}, event G = {9, 10, 11, 12}, and event H = {2, 3, 4}. Assume that each outcome is equally likely. List the
A probability experiment is conducted in which the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let event E = {2, 3, 4, 5, 6, 7}, event F = {5, 6, 7, 8, 9}, event G = {9, 10, 11, 12}, and event H = {2, 3, 4}. Assume that each outcome is equally likely. List the
Find P(E or F) if P(E and F) = 0.15. Find the probability of the indicated event if P(E) = 0.25 and P(F) = 0.45.
Find P(E and F) if P(E or F) = 0.6. Find the probability of the indicated event if P(E) = 0.25 and P(F) = 0.45.
If P(E) = 0.60, P(E or F) = 0.85, and P(E and F) = 0.05, find P(F).
If P(F) = 0.30, P(E or F) = 0.65, and P(E and F) = 0.15, find P(E).
The following probability model shows the distribution of murders by type of weapon for murder cases in 2009. Weapon ...... Probability Handgun ....... 0.473 Rifle ....... 0.026 Shotgun ....... 0.031 Unknown firearm .... 0.141 Knives ....... 0.134 Hands, fists, etc. ... 0.059 Other
The following probability model shows the distribution of doctoral degrees from U.S. universities in 2009 by area of study. Area of Study ...... Probability Engineering ...... 0.154 Physical sciences ..... 0.087 Life sciences ..... 0.203 Mathematics ....... 0.031 Computer sciences
If events E and F are disjoint and the events F and G are disjoint, must the events E and G necessarily be disjoint? Give an example to illustrate your opinion.
Draw a Venn diagram like that in Figure 10 that expands the general addition rule to three events. Use the diagram to write the General Addition Rule for three events.
The following data represent the number of live multiple-delivery births (three or more babies) in 2007 for women 15 to 54 years old: Age ...... Number of Multiple Births 15–19 ...... 100 20–24 ...... 467 25–29 ...... 1620 30–34 ...... 2262 35–39 ...... 1545 40–44 ......
The following probability model shows the distribution for the number of rooms in U.S. housing units. Rooms .... Probability One ..... 0.005 Two ..... 0.011 Three ..... 0.088 Four ..... 0.183 Five ..... 0.230 Six ..... 0.204 Seven .... 0.123 Eight or more . 0.156 (a) Verify that this is a
A standard deck of cards contains 52 cards, as shown in Figur. One card is randomly selected from the deck.(a) Compute the probability of randomly selecting a heart or club from a deck of cards. (b) Compute the probability of randomly selecting a heart or club or diamond from a deck of cards. (c)
A standard deck of cards contains 52 cards, as shown in Figure. One card is randomly selected from the deck.(a) Compute the probability of randomly selecting a two or three from a deck of cards. (b) Compute the probability of randomly selecting a two or three or four from a deck of cards. (c)
Exclude leap years from the following calculations: (a) Compute the probability that a randomly selected person does not have a birthday on November 8. (b) Compute the probability that a randomly selected person does not have a birthday on the 1st day of a month. (c) Compute the probability that a
In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, . . . , 36. The odd-numbered slots are red, and the even-numbered slots are black. The numbers 0 and 00 are green. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered
According to the Centers for Disease Control, the probability that a randomly selected citizen of the United States has hearing problems is 0.151. The probability that a randomly selected citizen of the United States has vision problems is 0.093. Can we compute the probability of randomly selecting
A National Ambulatory Medical Care Survey administered by the Centers for Disease Control found that the probability a randomly selected patient visited the doctor for a blood pressure check is 0.593. The probability a randomly selected patient visited the doctor for urinalysis is 0.064. Can we
A social worker for a child advocacy center has a caseload of 24 children under the age of 18. Her caseload by age is as follows:What is the probability that one of her clients, selected at random, is: (a) Between 6 and10 years old? Is this unusual? (b) More than 5 years old? (c) Less than 1 year
Spoken at Home According to the U.S. Census Bureau, the probability that a randomly selected household speaks only English at home is 0.81. The probability that a randomly selected household speaks only Spanish at home is 0.12. (a) What is the probability that a randomly selected household speaks
According to the U.S. Census Bureau, the probability that a randomly selected worker primarily drives a car to work is 0.867. The probability that a randomly selected worker primarily takes public transportation to work is 0.048. (a) What is the probability that a randomly selected worker primarily
A guidance counselor at a middle school collected the following information regarding the employment status of married couples within his school€™s boundaries.(a) What is the probability that, for a married couple selected at random, both spouses work? (b) What is the probability that,
The data in the following table show the results of a national study of 137,243 U.S. men that investigated the association between cigar smoking and death from cancer.(a) If an individual is randomly selected from this study, what is the probability that he died from cancer? (b) If an individual is
The following table represents the employment status and gender of the civilian labor force ages 16 to 19 (in thousands).a) What is the probability that a randomly selected 16- to 19-year-old individual from the civilian labor force is employed? (b) What is the probability that a randomly selected
The following data represent the number of speeding tickets issued to individuals in the past year and the gender of the individuals. Determine the following probabilities based on the results of the survey.(a) Determine the probability a randomly selected driver is female. (b) Determine the
A company is testing a new medicine for migraine headaches. In the study, 150 women were given the new medicine and an additional 100 women were given a placebo. Each participant was directed to take the medicine when the ï¬rst symptoms of a migraine occurred and then to record
Harris Interactive conducted a survey in which they asked adult Americans (18 years or older) whether they used social media (Facebook, Twitter, and so on) regularly. The following table is based on the results of the survey.(a) If an adult American is randomly selected, what is the probability he
The following data represent the number of drivers involved in fatal crashes in the United States in 2009 by day of the week and gender.(a) Determine the probability that a randomly selected fatal crash involved a male. (b) Determine the probability that a randomly selected fatal crash occurred on
In a study of the feasibility of a red-light camera program in the city ofMilwaukee, the data above summarize the projected number of crashes at 13 selected intersections over a 5-year period.(a) Identify the variables presented in the table.(b) State whether each variable is qualitative or
The following data represent the homework scores for the material on Polynomial and Rational Functions in Sullivan’s College Algebra course.(a) Construct a relative frequency distribution with a lower class limit of the ï¬rst class equal to 30 and a class width of 10.(b) Draw a relative
When two events are disjoint, they are also independent.
Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: Speeding on the interstate. F: Being pulled over by a police officer. (b) E: You gain weight. F: You eat fast food for dinner every night. (c) E: You get a high score on a statistics exam. F: The Boston
Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: The battery in your cell phone is dead. F: The batteries in your calculator are dead. (b) E: Your favorite color is blue. F: Your friend’s favorite hobby is fishing. (c) E: You are late for school. F:
Suppose that events E and F are independent, P(E) = 0.3 and P(F ) = 0.6. What is the P(E and F )?
Suppose that events E and F are independent, P(E) = 0.7 and P(F ) = 0.9. What is the P(E and F )?
What is the probability of obtaining five heads in a row when flipping a fair coin? Interpret this probability.
What is the probability of obtaining 4 ones in a row when rolling a fair, six-sided die? Interpret this probability.
About 13% of the population is left-handed. If two people are randomly selected, what is the probability that both are left-handed? What is the probability that at least one is right-handed?
Shawn lives near the border of Illinois and Missouri. One weekend he decides to play $1 in both state lotteries in hopes of hitting two jackpots. The probability of winning the Missouri Lotto is about 0.00000028357 and the probability of winning the Illinois Lotto is about 0.000000098239. (a)
The ELISA is a test to determine whether the HIV antibody is present. The test is 99.5% effective, which means that the test will come back negative if the HIV antibody is not present 99.5% of the time. The probability of a test coming back positive when the antibody is not present (a false
Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose that the lights are designed so that the probability a bulb will last 2 years is 0.995. The success or failure of a bulb is independent of the success
The probability that a randomly selected 40-year-old male will live to be 41 years old is 0.99757, according to the National Vital Statistics Report, Vol. 56, No. 9. (a) What is the probability that two randomly selected 40-year-old males will live to be 41 years old? (b) What is the probability
The probability that a randomly selected 40-year-old female will live to be 41 years old is 0.99855 according to the National Vital Statistics Report, Vol. 56, No. 9. (a) What is the probability that two randomly selected 40-year-old females will live to be 41 years old? (b) What is the probability
According to the Department of Health and Human Services, 30% of 18- to 25-year-olds have some form of mental illness. (a) What is the probability two randomly selected 18- to 25-year-olds have some form of mental illness? (b) What is the probability six randomly selected 18- to 25-year-olds have
Suppose that a company selects two people who work independently inspecting two-by-four timbers. Their job is to identify low-quality timbers. Suppose that the probability that an inspector does not identify a low-quality timber is 0.20. (a) What is the probability that both inspectors do not
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.15 probability of failure. (a) Would it be unusual to observe one component fail? Two
The packaging of an E.P.T. Pregnancy Test states that the test is “99% accurate at detecting typical pregnancy hormone levels.” Assume that the probability that a test will correctly identify a pregnancy is 0.99 and that 12 randomly selected pregnant women with typical hormone levels are each
Players in sports are said to have “hot streaks” and “cold streaks.” For example, a batter in baseball might be considered to be in a slump, or cold streak, if he has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 30% of the time he comes to the
In a recent basketball game, a player who makes 65% of his free throws made eight consecutive free throws. Assuming that free-throw shots are independent, determine whether this feat was unusual.
Suppose that Ralph gets a strike when bowling 30% of the time. (a) What is the probability that Ralph gets two strikes in a row? (b) What is the probability that Ralph gets a turkey (three strikes in a row)? (c) When events are independent, their complements are independent as well. Use this result
Among Americans who consider themselves auto racing fans, 59% identify NASCAR stock cars as their favorite type of racing. Suppose that four auto racing fans are randomly selected. Source: ESPN/TNS Sports, reported in USA Today (a) What is the probability that all four will identify NASCAR stock
Among 21- to 25-year-olds, 29% say they have driven while under the influence of alcohol. Suppose that three 21- to 25-year-olds are selected at random. (a) What is the probability that all three have driven while under the influence of alcohol? (b) What is the probability that at least one has
Suppose that a satellite defense system is established in which four satellites acting independently have a 0.9 probability of detecting an incoming ballistic missile. What is the probability that at least one of the four satellites detects an incoming ballistic missile? Would you feel safe with
According to Internal Revenue Service records, 6.42% of all household tax returns are audited. According to the Humane Society, 39% of all households own a dog. Assuming dog ownership and audits are independent events, what is the probability a randomly selected household is audited and owns a dog?
According to the National Vital Statistics Report, 20.1% of all pregnancies result in weight gain in excess of 40 pounds (for singleton births). In addition, 49.5% of all pregnancies result in the birth of a baby girl. Assuming gender and weight gain are independent, what is the probability a
Suppose your financial advisor recommends three stocks to you. He claims the likelihood that the first stock will increase in value at least 10% within the next year is 0.7, the likelihood the second stock will increase in value at least 10% within the next year is 0.55, and the likelihood the
According to a Gallup Poll, about 17% of adult Americans bet on professional sports. Census data indicate that 48.4% of the adult population in the United States is male. (a) Assuming that betting is independent of gender, compute the probability that an American adult selected at random is a male
Fingerprints are now widely accepted as a form of identification. In fact, many computers today use fingerprint identification to link the owner to the computer. In 1892, Sir Francis Galton explored the use of fingerprints to uniquely identify an individual. A fingerprint consists of
Suppose that E and F are two events and that P(E) = 0.8 and P(F|E) = 0.4. What is P(E and F )?
Suppose that E and F are two events and that P(E) = 0.4 and P(F|E) = 0.6. What is P(E and F )?
Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a club? Now suppose that a single card is drawn from a standard 52-card deck, but we are told that the card is black. What is the probability that the card drawn is a club?
Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a king? Now suppose that a single card is drawn from a standard 52-card deck, but we are told that the card is a heart. What is the probability that the card drawn is a king? Did the
For the month of June in the city of Chicago, 37% of the days are cloudy. Also in the month of June in the city of Chicago, 21% of the days are cloudy and rainy. What is the probability that a randomly selected day in June will be rainy if it is cloudy?
According to the U.S. National Center for Health Statistics, 0.15% of deaths in the United States are 25- to 34-year-olds whose cause of death is cancer. In addition, 1.71% of all those who die are 25 to 34 years old. What is the probability that a randomly selected death is the result of cancer if
According to the U.S. Census Bureau, 8.0% of 16- to 24-year-olds are high school dropouts. In addition, 2.1% of 16- to 24-year-olds are high school dropouts and unemployed. What is the probability that a randomly selected 16-to 24-year-old is unemployed, given he or she is a dropout?
According to the U.S. Census Bureau, 17.9% of U.S. households are in the Northeast. In addition, 5.4% of U.S. households earn $100,000 per year or more and are located in the Northeast. Determine the probability that a randomly selected U.S. household earns more than $100,000 per year, given that
In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, €œWhen 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
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