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Elementary Statistics 12th Edition Mario F. Triola - Solutions
Using the same events A and B described in Exercise 3, what is confusion of the inverse? (Express the answer in both words and symbols.)
If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of getting at least 1 correct? If a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by
A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates that there is 0.92 probability that the calculator will work on any given day. Because the final exam is so important, she plans to use redundancy by bringing in two TI-84 Plus
In China, the probability of a baby being a boy is 0.545. Many couples are allowed to have only one child. Among the next five randomly selected births in China, what is the probability that at least one of them is a girl? Can this system continue to work indefinitely?
The probability of a randomly selected car crashing during a year is 0.0423 (based on data from the Statistical Abstract of the United States). If a family has three cars, find the probability that at least one of them has a crash during the year. Is there any reason why this probability might be
According to FBI data, 12.4% of burglaries are cleared with arrests. A new detective is assigned to five different burglaries.a.What is the probability that at least one of them is cleared with an arrest?b.What is the probability that the detective clears five burglaries with arrests?c.What should
Based on a poll conducted through the e-edition of USA Today, 67% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among four randomly selected Internet users, at least one is more careful about personal information
Based on a poll conducted through e-mail by USA Today, 41% of survey respondents most liked to get compliments at work from their co-workers. Among 12 randomly selected workers, what is the probability of getting at least 1 who most likes to get compliments from co-workers? How is the result
Find the probability of selecting a subject with a positive test result, given that the subject does not use drugs. Why is this particular case problematic for test subjects?
Find the probability of selecting a subject with a negative test result, given that the subject uses drugs. Who would suffer from this type of error?
Find P’(subject uses drugs | negative test result). Compare this result to the result found in Exercise 20. Are /’(subject uses drugs | negative test result) and /(negative test result | subject uses drugs) equal?
a.Find P (negative test result | subject does not use drugs).b.Find P(subject does not use drugs | negative test result).c.Compare the results from parts(a) and (b). Are they equal?
Hard Drives Assume that there is a 2% rate of disk drive failure in a year (based on data from various sources, including “Failure Trends in Large Disk Drive Population,” by Pinhero et al. of Google, Inc.).a.If all of your computer data is stored on a hard disk drive with a copy stored on a
The FAA requires that commercial aircraft used for flying in instrument conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.0035. What is the probability that a particular flight will be safe with at least one working
Based on the data in Table 4-1, assume that the probability of a randomly selected person testing positive for drug use is 0.134. If drug screening samples are collected from 8 random subjects and combined, find the probability that the combined sample will reveal a positive result. Is that
The Fairfield County Department of Public Health tests water for contamination due to the presence of E. coli (Escherichia colt) bacteria. To reduce laboratory costs, water samples from five public swimming areas are combined for one test, and further testing is done only if the combined sample
Find the probability that of 25 randomly selected people,a. No 2 share the same birthday.b. At least 2 share the same birthday.
In one study, physicians were asked to estimate the probability of a malignant cancer given that a test showed a positive result. They were told that the cancer had a prevalence rate of 1%, the test has a false positive rate of 10%, and the test is 80% accurate in correctly identifying a malignancy
What does the symbol ! represent? Four different people can stand in a line 4! different ways. What is the actual number of ways that four people can stand in a line?
The winning numbers for the current California Daily 4 lottery are 5, 0, 0, and 4 in that exact order. Because order counts, do calculations for this lottery involve either of the two permutation rules presented in this section? Why or why not? If not, what rule does apply?
A thief steals an ATM card and must randomly guess the correct pin code that consists of four digits (0 through 9) that must be entered in the correct order. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
A fan of Lady Antebellum music plans to make a custom CD with 12 of her 27 songs. How many different combinations of 12 songs are possible? Is it practical to make a different CD for each possible combination?
Winning the jackpot in the Connecticut Classic Lotto requires that you choose six different numbers from 1 to 44, and your numbers must match the same six numbers that are later drawn. The order of the selected numbers does not matter. If you buy one ticket, what is the probability of winning the
Winning the jackpot in the Florida Lotto requires that you choose six different numbers from 1 to 53, and your numbers must match the same six numbers that are later drawn. The order of the selected numbers does not matter. If you buy one ticket, what is the probability of winning the jackpot?
a.In the Maine Megabucks game, you win the jackpot by selecting five different whole numbers from 1 through 41 and getting the same five numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game?b.In the Maine Pick 4 game, you win a straight bet by
a. In the Illinois Little Lotto game, you win the jackpot by selecting five different whole numbers from 1 through 39 and getting the same five numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game?b. In the Illinois Pick 3 game, you win a bet by
The Teknomill Corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a Planning Committee with four different members. There are 12 qualified candidates, and officers can also serve on the
Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we
The typical combination lock uses three numbers between 0 and 49, and they must be selected in the correct sequence. How many different “combinations” are possible? Which of the five rules of this section is used to find that number? Is the name of “combination lock” appropriate? If not,
Credit card numbers typically have 16 digits, but not all of them are random. Answer the following and express probabilities as fractions.a.What is the probability of randomly generating 16 digits and getting your MasterCard number?b.Receipts often show the last four digits of a credit card number.
You want to obtain cash by using an ATM machine, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.a. What is the probability of selecting a random position
Clinical trials of Nasonex involved a group given placebos and another group given treatments of Nasonex. Assume that a preliminary phase I trial is to be conducted with 10 subjects, including 5 men and 5 women. If 5 of the 10 subjects are randomly selected for the treatment group, find the
Names A common computer programming rule is that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names are A, BBB,
a. Five managers gather for a meeting. If each manager shakes hands with each other manager exactly once, what is the total number of handshakes?b. If n managers shake hands with each other exactly once, what is the total number of handshakes?c. How many different ways can five managers be seated
How many different ways can you make change for a quarter? (Dif-ferent arrangements of the same coins are not counted separately.)
About 35% of the population has blue eyes (based on a study by Dr. P. Sorita Soni at Indiana University). a. If someone is randomly selected, what is the probability that he or she does not have blue eyes? b. If four different people are randomly selected, what is the probability that they all have
a. If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in Japan. Ignore leap years. b. If a person is randomly selected, find the probability that his or her birthday is in October. Ignore leap years. c. Estimate a
Currently, the rate for sexually transmitted diseases (STDs) is 213 per 100,000 (based on data from the Centers for Disease Control and Prevention). When testing for the presence of STDs, the Acton Medical Testing Company saves money by combining blood samples for tests. The combined sample tests
Listed below are the differences (in years) between the ages of actresses and actors when they won Oscars. The differences are found by subtracting the age of the male winner from the age of the female winner: (actress age) — (actor age). The differences are found using results from the last 12
a. The mean pulse rate for adult women is 77.5 beats per minute, with a standard deviation of 11.6 beats per minute (based on Data Set 1 in Appendix B). Using the range rule of thumb, would a pulse rate of 100 beats per minute be considered unusual? Explain. b. For the pulse rates of adult women
USA Today provided information about a survey of 5100 adult Internet users. Of the respondents, 2346 said they are willing to donate organs after death. In this survey conducted for Donate Life America, 100 adults were surveyed in each state and the District of Columbia, and results were weighted
In a survey of Americans age 16 years or older, respondents were asked if they texted or e-mailed while driving during the previous 30 days. The results are summarized in the accompanying graph (based on data from AAA Foundation for Traffic Safety). What is wrong with this graph?
Based on a study by Dr. P. Sorita Soni at Indiana University, we know that eye colors in the United States are distributed as follows: 40% brown, 35% blue, 12% green, 7% gray, 6% hazel.a. A statistics instructor collects eye color data from her students. What is the name for this type of sample?b.
Given below are the chest sizes (inches) and weights (pounds) of 10 bears taken from Data Set 7 in Appendix B. Construct a scatter plot. Based on the scatter plot, does there appear to be a correlation between the chest sizes of bears and their weights?
Winning the jackpot in the Vermont Hot Lotto game requires that you select five numbers between 1 and 39 and another number between 1 and 19. The first five numbers must match (in any order) the same five numbers that are later drawn, and the sixth number must also match the sixth number that is
Is the random variable given in Table 5-7 discrete or continuous? Explain.
Does Table describe a probability distribution? Show how the requirements are satisfied or are not satisfied.
For 200 births, the probability of exactly 90 girls is 0.0208 and the probability of 90 or fewer girls is 0.089.a. Is exactly 90 girls in 200 births unlikely?b. Among 200 births, is 90 girls an unusually low number of girls?
a. Exact weights of quarters now in circulation in the United States b. Numbers of tosses of quarters required to get heads c. Responses to the survey question “Did you smoke at least one cigarette in the last week?” d. Numbers of spins of roulette wheels required to get the number 7 e. Exact
a. Eye colors of humans on commercial aircraft flights b. Weights of humans on commercial aircraft flights c. Numbers of passengers on commercial aircraft flights d. Numbers of randomly generated digits before getting the digit 3 e. Political party affiliations of adults in the United States f.
Genetic Disorder Four males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the four who inherit the X-linked genetic disorder.In determine whether a probability distribution is given. If a probability distribution is given, find its mean
Male Color Blindness When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness (based on data from the National Institutes of Health).In determine
A sociologist randomly selects single adults for different groups of four, and the random variable x is the number in the group who say that the most fun way to flirt is in person (based on a Microsoft Instant Messaging survey).In determine whether a probability distribution is given. If a
Groups of people aged 15€“65 are randomly selected and arranged in groups of six. The random variable x is the number in the group who say that their family and/or partner contribute most to their happiness (based on a Coca-Cola survey).In determine whether a probability distribution is
Find the mean and standard deviation for the numbers of girls in 10 births.
Use the range rule of thumb to identify a range of values containing the usual numbers of girls in 10 births. Based on the result, is 1 girl in 10 births an unusually low number of girls? Explain.
a. Find the probability of getting exactly 8 girls in 10 births.b. Find the probability of getting 8 or more girls in 10 births.c. Which probability is relevant for determining whether 8 is an unusually high number of girls in 10 births: the result from part (a) or part (b)?d. Is 8 an unusually
a. Find the probability of getting exactly 1 girl in 10 births.b. Find the probability of getting 1 or fewer girls in 10 births.c. Which probability is relevant for determining whether 1 is an unusually low number of girls in 10 births: the result from part (a) or part (b)?d. Is 1 an unusually low
Find the mean and standard deviation for the numbers of cars that failed among the six cars that are tested.
Range Rule of Thumb for Unusual Events Use the range rule of thumb with the results from Exercise 19 to identify a range of values containing the usual numbers of car failures among six cars tested. Based on the result, is three an unusually high number of failures among six cars tested? Explain.
Using Probabilities for Unusual Eventsa. Find the probability of getting exactly three cars that fail among six cars tested.b. Find the probability of getting three or more cars that fail among six cars tested.c. Which probability is relevant for determining whether three is an unusually high
a. Find the probability of getting exactly one car that fails among six cars tested.b. Find the probability of getting one or fewer cars that fail among six cars tested.c. Which probability is relevant for determining whether one is an unusually low number of cars that fail among six cars tested:
Expected Value for the Texas Pick 3 Game In the Texas Pick 3 lottery, you can bet $1 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect $500. a. How many different selections are possible? b. What is the
In Maine’s Pick 4 lottery game, you can pay $1 to select a sequence of four digits, such as 1332. If you select the same sequence of four digits that are drawn, you win and collect $5000. a. How many different selections are possible? b. What is the probability of winning? c. If you win, what is
When playing roulette at the Venetian casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 27 or to bet $5 that the outcome is any one of these five possibilities: 0, 00, 1, 2, 3. From Example 8, we know that the expected value of the $5 bet for a single number is
The television game show Deal or No Deal begins with individual suitcases containing the amounts of 1c, $1, $5, $10, $25, $50, $75, $100, $200, $300, $400, $500, $750, $1000, $5000, $10,000, $25,000, $50,000, $75,000, $100,000, $200,000, $300,000, $400,000, $500,000, $750,000, and $1,000,000. If a
Based on a Saint Index survey, assume that when adults are asked to identify the most unpopular projects for their hometown, 54% include Wal-Mart among their choices. Suppose we want to find the probability that when five adults are randomly selected, exactly two of them include Wal-Mart. What is
If we use the binomial probability formula (Formula 5-5) for finding the probability described in Exercise 1, what is wrong with letting p denote the probability of getting an adult who includes Wal-Mart while x counts the number of adults who do not include Wal-Mart?
Based on a Saint Index survey, when 1000 adults were asked to identify the most unpopular projects for their hometown, 54% included Wal-Mart among their choices. Consider the probability that among 30 different adults randomly selected from the 1000 who were surveyed, there are at least 18 who
The current Senate consists of 83 males and 17 females. Forty different senators are randomly selected without replacement, and the gender of each selected senator is recorded. Determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as
Surveying Senators Ten different senators are randomly selected without replacement, and the numbers of terms that they have served are recorded.Determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not
In a RingCentral survey, 380 different smartphone users are randomly selected without replacement. Respondents were asked to identify the only thing that they can’t live without. Responses consist of whether a smartphone was identified. Determine whether the given procedure results in a binomial
In a Consumer Reports survey, 427 different women are randomly selected without replacement, and each woman is asked what she purchases online. Responses consist of whether clothing was identified. Determine whether the given procedure results in a binomial distribution (or a distribution that can
The math portion of the ACT test consists of 60 multiple-choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions. a. Use the multiplication rule to find the probability that the first two guesses are
In the New York State Win 4 lottery, you place a bet by selecting four digits. Repetition is allowed, and winning requires that your sequence of four digits matches the four digits that are later drawn. Assume that you place one bet with a sequence of four digits. a. Use the multiplication rule to
Find the probability that the number x of correct answers is at least 3. Assume that random guesses are made for five multiple-choice questions on an ACT test, so that there are n = 5 trials, each with probability of success (correct) given by p = 0.20. Use the Binomial Probability table (Table
Find the probability that the number x of correct answers is more than 2. Assume that random guesses are made for five multiple-choice questions on an ACT test, so that there are n = 5 trials, each with probability of success (correct) given by p = 0.20. Use the Binomial Probability table(Table
Find the probability that the number x of correct answers is fewer than 3. Assume that random guesses are made for five multiple-choice questions on an ACT test, so that there are n = 5 trials, each with probability of success (correct) given by p = 0.20. Use the Binomial Probability table (Table
Find the probability that at least two of the six offspring peas have green pods. If at least two offspring peas with green pods are required for further experimentation, is it reasonable to expect that at least two will be obtained?
Find the probability that at most five of the six offspring peas have green pods.
Find the probability that at most two of the six offspring peas have green pods. Is two an unusually low number of peas with green pods (among six)? Why or why not?
Find the probability that five or more of the six offspring peas will have green pods. Is five an unusually high number of offspring peas with green pods? Why or why not?
Based on a Harris Interactive poll, 20% of adults believe in reincarnation. Assume that six adults are randomly selected, and find the indicated probability. a. What is the probability that exactly five of the selected adults believe in reincarnation? b. What is the probability that all of the
Based on a Comcast survey, there is a 0.8 probability that a randomly selected adult will watch prime-time TV live, instead of online, on DVR, etc. Assume that seven adults are randomly selected, and find the indicated probability. a. Find the probability that exactly two of the selected adults
Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability. a. Find the probability that none of the selected adults say
Based on the American Chemical Society, there is a 0.9 probability that in the United States, a randomly selected dollar bill is tainted with traces of cocaine. Assume that eight dollar bills are randomly selected. a. Find the probability that all of them have traces of cocaine. b. Find the
Based on a Bellowes survey of adults, there is a 0.48 probability that a randomly selected adult uses a tax preparer to file taxes. Find the probability that among 20 randomly selected adults, exactly 12 use tax preparers to file their taxes. Among 20 random adults, is 12 an unusually high number
Based on a Ridgid survey of high school students, 25% of high school students plan to choose a career in information technology. Find the probability that among 24 randomly selected high school students, exactly 6 plan to choose a career in information technology. Is it unlikely to find that
The U.S. Department of Transportation recently reported that 80.5% of U.S. airline flights arrived on time. Find the probability that among 12 randomly selected flights, exactly 10 arrive on time. Does that probability apply to the author, who must make 12 flights originating in New York?
Based on data from a USA Today Snapshot, 72% of adults have security concerns about online banking. Find the probability that among 30 randomly selected adults, exactly 20 have security concerns. Among 30 random adults, is 20 an unusually low number for those who have security concerns?
CBS televised a recent Super Bowl football game between the New Orleans Saints and the Indianapolis Colts. That game received a rating of 45, indicating that among all U.S. households, 45% were tuned to the game (based on data from Nielsen Media Research). An advertiser wants to obtain a second
When someone buys a ticket for an airline flight, there is a 0.0995 probability that the person will not show up for the flight (based on data from an IBM research paper by Lawrence, Hong, and Cherrier). The Beechcraft 1900C jet can seat 19 passengers. Is it wise to book 21 passengers for a flight
When testing a method of gender selection, we assume that the rate of female births is 50%, and we reject that assumption if we get results that are unusual in the sense that they are very unlikely to occur with the 50% rate. In a preliminary test of the XSORT method of gender selection, 14 births
In a recent U.S. Open tennis tournament, among 20 of the calls challenged by players, 8 were overturned after a review using the Hawk-Eye electronic system. Assume that when players challenge calls, they are successful in having them overturned 50% of the time. a. Find the probability that among
The probability of a randomly selected adult in the United States being infected with the human immunodeficiency virus (HIV) is 0.006 (based on data from the Kaiser Family Foundation). In tests for HIV, blood samples from 24 people are combined. What is the probability that the combined sample
Based on data from the Centers for Disease Control, the probability of a randomly selected person having gonorrhea is 0.00114. In tests for gonorrhea, blood samples from 16 people are combined. What is the probability that the combined sample tests positive for gonorrhea? Is it unlikely for such a
The Medassist Pharmaceutical Company receives large shipments of aspirin tablets and uses this acceptance sampling plan: Randomly select and test 40 tablets, then accept the whole batch if there is only one or none that doesn’t meet the required specifications. If one shipment of 5000 aspirin
The Killington Market chain uses this acceptance sampling plan for large shipments of packages of its generic chocolate chip cookies: Randomly select 30 packages and determine whether each is within specifications (not too many broken cookies, acceptable taste, distribution of chocolate chips, and
If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use the hyper geometric distribution. If a population has
For the binomial distribution described by the conditions in Exercise, find the standard deviation by evaluating 1npq. Some books use the expression 1np(1 p) for the standard deviation. Will that expression always yield the same result? In exercise In a clinical trial of the cholesterol drug
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