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statistics

Questions and Answers of Statistics

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
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
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
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
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
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.
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,
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
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 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 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
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 .....
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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)
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
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
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
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
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,
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
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
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
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
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
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
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
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 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
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)
The following data represent the homework scores for the material on Polynomial and Rational Functions in Sullivanâ€™s College Algebra course.(a) Construct a relative frequency distribution with
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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