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mathematics
statistics

Questions and Answers of Statistics

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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,
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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.
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.
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
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
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
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,
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
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
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
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
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
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

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