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mathematics
elementary statistics picturing
Elementary Statistics 11th Edition Mario F. Triola - Solutions
What is an unbiased estimator? Is the sample variance an unbiased estimator of the population variance? Is the sample standard deviation an unbiased estimator of the population standard deviation?
The Internet service provider AOL periodically conducts polls by posting a survey question on its Web site, and Internet users can respond if they choose to do so. Assume that a survey question asks whether the respondent has a high-definition television in the household and the results are used to
When predicting the chance that we will elect a Republican President in the year 2012, we could reason that there are two possible outcomes (Republican, not Republican), so the probability of a Republican President is 1/2 or 0.5. Is this reasoning correct? Why or why not?
In an America Online poll, Internet users were asked if they want to live to be 100. There were 3042 responses of “yes,” and 2184 responses of “no.”a. What percentage of responses were “yes”?b. Based on the poll results, what is the probability of randomly selecting someone who wants to
A new home owner is installing smoke detectors powered by the home’s electrical system. He reasons that he can make the smoke detectors independent by connecting them to separate circuits within the home. Would those smoke detectors be truly independent? Why or why not?
The typical combination lock uses three numbers between 0 and 49, and they must be selected in the correct sequence. Given the way that these locks work, is the name of “combination” lock correct? Why or why not?
Assume that you have access to a computer that can randomly generate whole numbers between any two values. Describe how this computer can be used to simulate the rolling of a pair of dice.
You want to find the probability of getting at least 1 defect when 10 heart pacemakers are randomly selected and tested. What do you know about the exact number of defects if “at least one” of the 10 pacemakers is defective?
Create your own example of two events that are independent, and create another example of two other events that are dependent. Do not use examples given in this section.
A single trial of some procedure is conducted and the resulting events are analyzed. In your own words, describe what it means for two events in a single trial to be disjoint.
Let a population consist of the values 1, 3, 14. (These are the same values used in Example 1, and they are the numbers of military intelligence satellites owned by India, Japan, and Russia.) Assume that samples of 2 values are randomly selected with replacement from this population. (That is, a
In a Gallup poll of 1236 adults, it was found that 5% of those polled said that bad luck occurs after breaking a mirror. Based on these results, such randomly selected groups of 1236 adults will have a mean of 61.8 people with that belief, and a standard deviation of 7.7 people. What is the
A Gallup poll of 1236 adults showed that 12% of the respondents believe that it is bad luck to walk under a ladder. Consider the probability that among 30 randomly selected people from the 1236 who were polled, there are at least 2 who have that belief. Given that the subjects surveyed were
The New York State Health Department reports a 10% rate of the HIV virus for the “at-risk” population. In one region, an intensive education program is used in an attempt to lower that 10% rate. After running the program, a follow-up study of 150 at-risk individuals is conducted.a. Assuming
Exercise 1 involves 8 randomly selected deaths during the time period spanning from the week before Thanksgiving to the week after Thanksgiving. Assume now that 20 deaths are randomly selected from that time period.a. Find the probability that exactly 14 of the deaths occur during the week before
In a binomial probability distribution, the symbols p and q are used to represent probabilities. What is the numerical relationship between p and q?
Assume that we have a binomial distribution with n = 100 and p = 0.1. It is impossible to get 101 successes in such a binomial distribution, but we can compute the probability that x = 101 if we use the Poisson distribution to approximate the binomial distribution, and the result is 4.82 × 10-64.
Excel is used to find the mean and standard deviation of a discrete probability distribution and the results are as follows: μ = 2.0 and σ = -3.5. Can these results be correct? Explain.
One of the requirements of a probability distribution is that the sum of the probabilities must be 1 (with a small discrepancy allowed for rounding errors). What is the justification for this requirement?
A researcher calculates the expected value for the number of girls in three births. He gets a result of 1.5. He then rounds the result to 2, saying that it is not possible to get 1.5 girls when three babies are born. Is this reasoning correct? Explain.
Among companies doing highway or bridge construction, 80% test employees for substance abuse (based on data from the Construction Financial Management Association). A study involves the random selection of 10 such companies.a. Find the probability that exactly 5 of the 10 companies test for
Last year, the author wrote 126 checks. Let the random variable x represent the number of checks he wrote in one day, and assume that it has a Poisson distribution. What is the mean number of checks written per day? What is the standard deviation? What is the variance?
Formula 5-8 shows that the standard deviation σ of values of the random variable x in a binomial probability distribution can be found by evaluating √npq. Some books give the expression √np(1 - p). Do these two expressions always give the same result? Explain.
In the United States, 35% of the population has blue eyes (based on data from Dr. P. Sorita Soni at Indiana State University). Suppose you want to find the probability of getting exactly 2 people with blue eyes when 5 people are randomly selected. Why can’t the answer be found as follows: Use the
It is common for professional auditors to analyze checking accounts with a randomly selected sample of checks. Given below are check amounts (in dollars) from a random sample of checks issued by the author.115.00 188.00 134.83 217.60 142.94a. Find the mean.b. Find the median.c. Find the range.d.
An interesting theory is that dying people have some ability to postpone their death to survive a major holiday. One study involved the analysis of deaths during the time period spanning from the week before Thanksgiving to the week after Thanksgiving. (See “Holidays, Birthdays, and the
What is a random variable? Is it possible for a discrete random variable to have an infinite number of possible values?
What are the conditions for using the Poisson distribution?
How many different ways can you make change for a dollar (including a one dollar coin)?
If the actual odds against event A are a:b, then Find the probability of the horse Cause to Believe winning the 132nd Kentucky Derby, given that the actual odds against his winning that race were 97:3.
When the horse Barbaro won the 132nd Kentucky Derby, a $2 bet that Barbaro would win resulted in a return of $14.20.a. How much net profit was made from a $2 win bet on Barbaro?b. What were the payoff odds against a Barbaro win?c. Based on preliminary wagering before the race, bettors collectively
A solitaire game was played 500 times. Among the 500 trials, the game was won 77 times. (The results are from the Microsoft solitaire game, and the Vegas rules of “draw 3” with $52 bet and a return of $5 per card are used.) Based on these results, find the odds against winning.
Each year, 64 college basketball teams compete in the NCAA tournament. Sandbox.com recently offered a prize of $10 million to anyone who could correctly pick the winner in each of the tournament games. (The president of that company also promised that, in addition to the cash prize, he would eat a
USA Today reporter Paul Wiseman described the old rules for the three-digit telephone area codes by writing about “possible area codes with 1 or 0 in the second digit. (Excluded: codes ending in 00 or 11, for toll-free calls, emergency services, and other special uses.)” Codes beginning with 0
This section included a table summarizing the gender outcomes for a couple planning to have three children.a. Construct a similar table for a couple planning to have four children.b. Assuming that the outcomes listed in part (a) are equally likely, find the probability of getting exactly two girls
As of this writing, the Mega Millions lottery is run in 12 states. Winning the jackpot requires that you select the correct five numbers between 1 and 56 and, in a separate drawing, you must also select the correct single number between 1 and 46. Find the probability of winning the jackpot.
A statistics professor tosses two coins that cannot be seen by any students. One student asks this question: “Did one of the coins turn up heads?” Given that the professor’s response is “yes,” find the probability that both coins turned up heads.
This section included a table summarizing the gender outcomes for a couple planning to have three children.a. Construct a similar table for a couple planning to have two children.b. Assuming that the outcomes listed in part (a) are equally likely, find the probability of getting two girls.c. Find
As of this writing, the Powerball lottery is run in 29 states. Winning the jackpot requires that you select the correct five numbers between 1 and 55 and, in a separate drawing, you must also select the correct single number between 1 and 42. Find the probability of winning the jackpot.
The Rock ’n’ Roller Coaster at Disney–MGM Studios in Orlando has 2 seats in each of 12 rows. Riders are assigned to seats in the order that they arrive. If you ride this roller coaster once, what is the probability of getting the coveted first row? How many times must you ride in order to
USA Today reported on a survey of office workers who were asked how much time they spend on personal phone calls per day. Among the responses, 1065 reported times between 1 and 10 minutes, 240 reported times between 11 and 30 minutes, 14 reported times between 31 and 60 minutes, and 66 said that
The Atlanta plant of the Medassist Pharmaceutical Company manufactures 400 heart pacemakers, of which 3 are defective. The Baltimore plant of the same company manufactures 800 pacemakers, of which 2 are defective. If 1 of the 1200 pacemakers is randomly selected and is found to be defective, what
In a survey of consumers aged 12 and older conducted by Frank N. Magid Associates, respondents were asked how many cell phones were in use by the household. Among the respondents, 211 answered “none,” 288 said “one,” 366 said “two,” 144 said “three,” and 89 responded with four or
A quality control analyst randomly selects 3 different car ignition systems from a manufacturing process that has just produced 200 systems, including 5 that are defective.a. Does this selection process involve independent events?b. What is the probability that all 3 ignition systems are good? (Do
Adults were randomly selected for a Newsweek poll, and they were asked if they “favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos.” Of the adults selected, 481 were in favor, 401 were opposed, and 120 were unsure. Based on these
The Orange County Department of Public Health tests water for contamination due to the presence of E. coli (Escherichia coli) bacteria. To reduce laboratory costs, water samples from six public swimming areas are combined for one test, and further testing is done only if the combined sample fails.
The Wheeling Tire Company produced a batch of 5000 tires that includes exactly 200 that are defective.a. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good?b. If 100 tires are randomly selected for shipment to an outlet, what is the
In the last 30 years, death sentence executions in the United States included 795 men and 10 women (based on data from the Associated Press). If an execution is randomly selected, find the probability that the person executed is a woman. Is it unusual for a woman to be executed? How might the
In a preliminary test of the MicroSort gender-selection method, 14 babies were born and 13 of them were girls.a. Find the number of different possible sequences of genders that are possible when 14 babies are born.b. How many ways can 13 girls and 1 boy be arranged in a sequence?c. If 14 babies are
When testing blood samples for HIV infections, the procedure can be made more efficient and less expensive by combining samples of blood specimens. If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability
Among 15,378 Delta airline passengers randomly selected, 3 were bumped from a flight against their wishes (based on data from the U.S. Department of Transportation). Find the probability that a randomly selected passenger is involuntarily bumped. Is such bumping unusual? Does such bumping pose a
With one method of the procedure called acceptance sampling, a sample of items is randomly selected without replacement, and the entire batch is rejected if there is at least one defect. The Newport Gauge Company has just manufactured a batch of aircraft altimeters, and 3% are defective.a. If the
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that your alarm clock has a 0.9 probability of working on any given morning.a. What is the probability that your alarm clock will not work on the morning of an important final
There are 11 members on the board of directors for the Coca Cola Company.a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?b. If they must form an ethics subcommittee of four members, how many
A statistics student wants to ensure that she is not late for an early statistics class because of a malfunctioning alarm clock. Instead of using one alarm clock, she decides to use three. What is the probability that at least one of her alarm clocks works correctly if each individual alarm clock
Find P(challenge was made by a woman or was not successful).Use the data in the accompanying table, which summarizes challenges by tennis players (based on data reported in USA Today). The results are from the first U.S. Open that used the Hawk-Eye electronic system for displaying an instant replay
When the drug Viagra was clinically tested, 117 patients reported headaches and 617 did not (based on data from Pfizer, Inc.). Use this sample to estimate the probability that a Viagra user will experience a headache. Is it unusual for a Viagra user to experience headaches? Is the probability high
An experiment involves rolling a die 6 times and counting the number of 2s that occur. If we calculate the probability of x = 0 occurrences of 2 using the Poisson distribution, we get 0.368, but we get 0.335 if we use the binomial distribution. Which is the correct probability of getting no 2s when
This chapter described the concept of a discrete probability distribution, and then described the binomial and Poisson probability distributions. Are all discrete probability distributions either binomial or Poisson? Why or why not?
Of the 2223 passengers on board the Titanic, 706 survived.a. If one of the passengers is randomly selected, find the probability that the passenger survived.b. If two different passengers are randomly selected, find the probability that they both survived.c. If two different passengers are randomly
A professional gambler claims that he has loaded a die so that the outcomes of 1, 2, 3, 4, 5, 6 have corresponding probabilities of 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6. Can he actually do what he has claimed? Is a probability distribution described by listing the outcomes along with their
When using Table A-1 to find the probability of guessing and getting exactly 8 correct answers on a multiple choice test with 10 questions, the result is found to be 0+. What does 0+ indicate? Does 0+ indicate that it is it impossible to get exactly 8 correct answers? TABLE A-1 Binomial
A statistics class consists of 10 females and 30 males. Each day, 12 of the students are randomly selected without replacement, and the number of females is counted. Using the methods of this section we get μ = 3.0 females and σ = 1.5 females, but the value of the standard deviation is wrong. Why
A newborn baby is considered to have a low birth weight if it weighs less than 2500 grams. Such babies often require extra care. Dutchess County, New York, has been experiencing a mean of 210.0 cases of low birth weight each year.a. Find the mean number of low birth weight babies born each day.b.
Assume that the Poisson distribution applies, and proceed to use the given mean to find the indicated probability.If μ = 2, find P (3).
When we refer to a “normal” distribution, does the word “normal” have the same meaning as in ordinary language, or does it have a special meaning in statistics? What exactly is a normal distribution?
Each year, the U.S. Department of Energy publishes an Annual Energy Review that includes per capita energy consumption (in millions of Btu) for each of the 50 states. If you calculate the mean of these 50 values, is the result the mean per capita energy consumption for the total population from all
a. The number of people now driving a car in the United Statesb. The weight of the gold stored in Fort Knoxc. The height of the last airplane that departed from JFK Airport in New York Cityd. The number of cars in San Francisco that crashed last yeare. The time required to fly from Los Angeles to
Treating 863 subjects with Lipitor (Atorvastatin) and recording whether there is a “yes” response when they are each asked if they experienced a headache (based on data from Pfizer, Inc.).Determine whether or not the given procedure results in a binomial distribution. For those that are not
Random guesses are made for 50 SAT multiple choice questions, so n = 50 and p = 0.2.Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean μ and standard deviation σ. Also, use the
Assume that the Poisson distribution applies, and proceed to use the given mean to find the indicated probability.If μ = 0.3, find P (1).
a. The total amount (in ounces) of soft drinks that you consumed in the past yearb. The number of cans of soft drinks that you consumed in the past yearc. The number of movies currently playing in U.S. theatersd. The running time of a randomly selected moviee. The cost of making a randomly selected
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use Table A-1 to find the probability of x successes given the probability p of success on a given trial.n = 15 x = 11 p = 0.99
Treating 863 subjects with Lipitor (Atorvastatin) and asking each subject “How does your head feel?” (based on data from Pfizer, Inc.).Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at least one requirement that is not
In an analysis of test results from the YSORT gender selection method, 152 babies are born and it is assumed that boys and girls are equally likely, so n = 152 and p = 0.5.Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the
Assume that the Poisson distribution applies, and proceed to use the given mean to find the indicated probability.If μ = 3/4, find P(3).
In Kentucky’s Pick 4 game, you pay $1 to select a sequence of four digits, such as 2283. If you buy only one ticket and win, your prize is $5000 and your net gain is $4999.a. If you buy one ticket, what is the probability of winning?b. Construct a table describing the probability distribution
Three males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the three who inherit the X-linked genetic disorder.x P
Treating 152 couples with the YSORT gender selection method developed by the Genetics & IVF Institute and recording the ages of the parents.Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at least one requirement that is
In an analysis of the 1-Panel TCH test for marijuana usage, 300 subjects are tested and the probability of a positive result is 0.48, so n = 300 and p = 0.48.Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values
Assume that the Poisson distribution applies, and proceed to use the given mean to find the indicated probability.If μ = 1/6, find P (0).
“Inability to get along with others” is the reason cited in 17% of worker firings (based on data from Robert Half International, Inc.). Concerned about her company’s working conditions, the personnel manager at the Boston Finance Company plans to investigate the five employee firings that
In the accompanying table, the random variable x represents the number of cups or cans of caffeinated beverages consumed by Americans each day (based on data from the National Sleep Foundation).x P
Treating 152 couples with the YSORT gender selection method developed by the Genetics & IVF Institute and recording the gender of each of the 152 babies that are born.Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at
A Gallup poll of 1236 adults showed that 14% believe that bad luck follows if your path is crossed by a black cat, so n = 1236 and p = 0.14.Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find
Dutchess County, New York, has been experiencing a mean of 35.4 motor vehicle deaths each year.a. Find the mean number of deaths per day.b. Find the probability that on a given day, there are more than 2 motor vehicle deaths.c. Is it unusual to have more than 2 motor vehicle deaths on the same day?
Air America has a policy of routinely overbooking flights. The random variable x represents the number of passengers who cannot be boarded because there are more passengers than seats (based on data from an IBM research paper by Lawrence, Hong, and Cherrier).x
Twenty different Senators are randomly selected from the 100 Senators in the current Congress, and each was asked whether he or she is in favor of abolishing estate taxes.Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at
The midterm exam in a nursing course consists of 75 true/false questions. Assume that an unprepared student makes random guesses for each of the answers.a. Find the mean and standard deviation for the number of correct answers for such students.b. Would it be unusual for a student to pass this exam
In analyzing hits by V-1 buzz bombs in World War II, South London was subdivided into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions.a. What is the mean number of hits per region?b. If a region is randomly selected, find the probability that it
Fifteen different Governors are randomly selected from the 50 Governors currently in office and the sex of each Governor is recorded.Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at least one requirement that is not
The final exam in a sociology course consists of 100 multiple-choice questions. Each question has 5 possible answers, and only 1 of them is correct. An unprepared student makes random guesses for all of the answers.a. Find the mean and standard deviation for the number of correct answers for such
In the accompanying table, the random variable x represents the number of televisions in a household in the United States (based on data from Frank N. Magid Associates).x P
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use Table A-1 to find the probability of x successes given the probability p of success on a given trial.n = 5 x = 1 p = 0.95
Five hundred different New York City voters are randomly selected from the population of 2.8 million registered voters, and each is asked if he or she is a Democrat.Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at least
Mars, Inc. claims that 16% of its M&M plain candies are green. A sample of 100 M&Ms is randomly selected.a. Find the mean and standard deviation for the numbers of green M&Ms in such groups of 100.b. Data Set 18 in Appendix B consists of a random sample of 100 M&Ms in which 19 are
In a study of television ratings, groups of 6 U.S. households are randomly selected. In the accompanying table, the random variable x represents the number of households among 6 that are tuned to 60 Minutes during the time that the show is broadcast (based on data from Nielsen Media Research).x
A psychology test consists of multiple-choice questions, each having 4 possible answers (a, b, c, d), 1 of which is correct. Assume that you guess the answers to 6 such questions.a. Use the multiplication rule to find the probability that the first 2 guesses are wrong and the last 4 guesses are
Two hundred statistics students are randomly selected and each is asked if he or she owns a TI-84 Plus calculator.Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at least one requirement that is not satisfied.
In one year, there were 116 homicide deaths in Richmond, Virginia (based on “A Classroom Note on the Poisson Distribution: A Model for Homicidal Deaths in Richmond, VA for 1991,” by Winston A. Richards in Mathematics and Computer Education). For a randomly selected day, find the probability
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