Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions

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Radioactive Decay Radioactive atoms are unstable because they have too much energy.When they release their extra energy, they are said to decay. When studying cesium-137, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 977,287 radioactive atoms, so 22,713 atoms
Earthquakes in the World Various sources provide different earthquake data, but assume that for a recent 41-year period in the world, there were 5469 earthquakes measured at 6.0 or higher on the Richter scale (based on U.S. Geological Survey data).a. Find the mean number of earthquakes per year.b.
Earthquakes in the United States Various sources provide different earthquake data, but assume that for a recent 41-year period in the United States, there were 268 earthquakes measured at 6.0 or higher on the Richter scale (based on U.S. Geological Survey data).a. Find the mean number of
Find P(12), the probability that in a month, there will be 12 aircraft accidents. Is it unlikely to have a month with exactly 12 aircraft accidents?
Find P(10), the probability that in a month, there will be 10 aircraft accidents. Is it unlikely to have a month with exactly 10 aircraft accidents?
Find P(6), the probability that in a month, there will be 6 aircraft accidents. Is it unlikely to have a month with exactly 6 aircraft accidents?
Find P(0), the probability that in a month, there will be no aircraft accidents. Is it unlikely to have a month with no aircraft accidents?
Poisson Approximation to Binomial Assume that we plan to play the Texas Pick 3 lottery 100 times. For one bet, there is a 1>1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? If we use the Poisson distribution
Poisson Approximation to Binomial Assume that we want to find the probability of getting at least one win when playing the Texas Pick 3 lottery 50 times. For one bet, there is a 1>1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the
Tornadoes During a recent 46-year period, New York State had a total of 194 tornadoes that measured 1 or greater on the Fujita scale. Let the random variable x represent the number of such tornadoes to hit New York State in one year, and assume that it has a Poisson distribution. What is the mean
Notation In analyzing hits by V-1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In
Hypergeometric Distribution A statistics class consists of 10 females and 30 males, and each day, 12 of the students are randomly selected without replacement. Because the sampling is from a small finite population without replacement, the hypergeometric distribution applies.(See Exercise 47 in
Acceptable , Defective Products A new integrated circuit board is being developed for use in computers. In the early stages of development, a lack of quality control results in a 0.2 probability that a manufactured integrated circuit board has no defects. Engineers need 24 integrated circuit boards
Finding n, p, q In a survey of randomly selected adults, subjects were asked if they could identify at least one current member of the Supreme Court. After obtaining the results, the range rule of thumb was used to find that for randomly selected groups of the same size, the minimum usual number
Powerball Lottery As of this writing, the Powerball lottery is run in 42 states. If you buy one ticket, the probability of winning is 1/195,249,054. If you buy one ticket each week for 50 years, you play this lottery 2600 times.a. Find the mean and standard deviation for the number of wins for
Born on the 4th of July For the following questions, ignore leap years.a. For classes of 30 students, find the mean and standard deviation for the number born on the 4th of July. Express results using seven decimal places.b. For a class of 30 students, would 2 be an unusually high number who were
Roulette If you place a bet on the number 7 in roulette, you have a 1>38 probability of winning.a. Find the mean and standard deviation for the number of wins for people who bet on the number 7 fifty times.b. Would 0 wins in 50 bets be an unusually low number of wins?
Too Young to Tat Based on a Harris poll of 370 adults who regret getting tattoos, 20%say that they were too young when they got their tattoos.a. For randomly selected groups of 370 adults who regret getting tattoos, find the mean and standard deviation for the number who say that they were too
Deciphering Messages The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter e is used at a rate of 12.7%.a. Find the mean and standard
Deciphering Messages The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter r is used at a rate of 6%.a. Find the mean and standard
Test of Touch Therapy Nine-year-old Emily Rosa conducted this test: A professional touch therapist put both hands through a cardboard partition and Emily would use a coin flip to randomly select one of the hands. Emily would place her hand just above the hand of the therapist, who was then asked to
Cell Phones and Brain Cancer In a study of 420,095 cell phone users in Denmark, it was found that 135 developed cancer of the brain or nervous system. If we assume that the use of cell phones has no effect on developing such cancer, then the probability of a person having such a cancer is
Are 14% of M&M Candies Yellow? Mars, Inc. claims that 14% of its M&M plain candies are yellow, and a sample of 100 such candies is randomly selected.a. Find the mean and standard deviation for the number of yellow candies in such groups of 100.b. Data Set 20 in Appendix: Data Sets consists of a
Are 20% of M&M Candies Orange? Mars, Inc. claims that 20% of its M&M plain candies are orange, and a sample of 100 such candies is randomly selected.a. Find the mean and standard deviation for the number of orange candies in such groups of 100.b. Data Set 20 in Appendix: Data Sets consists of a
Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 580 peas, and Mendel theorized that 25% of them would be yellow peas.a. If Mendel’s theory is correct, find the mean and standard deviation for the numbers of yellow peas in
Gender Selection In a test of the YSORT method of gender selection, 291 babies are born to couples trying to have baby boys, and 239 of those babies are boys (based on data from the Genetics & IVF Institute).a. If the gender-selection method has no effect and boys and girls are equally likely, find
Clinical Trial In a clinical trial of the cholesterol drug Lipitor, 94 subjects were treated with 80 mg of Lipitor, and 6.4% of them developed headaches, so n = 94 and p = 0.064.
Identity Theft In a Gallup poll of 1013 randomly selected adults, 66% said that they worry about identity theft, so n = 1013 and p = 0.66.
Gender Selection In an analysis of preliminary test results from the XSORT genderselection method, 14 babies are born and it is assumed that 50% of babies are girls, so n = 14 and p = 0.5.
Guessing on ACT Random guesses are made for the 60 multiple-choice questions on the math portion of the ACT test, so n = 60 and p = 1>5 (because each question has possible answers ofa, b,c, d,e, and only one of them is correct).
Why a Parameter? Given the results described in Exercise 3, is the mean of 140.0 executives expressed with m or x? Explain why the mean of 140.0 executives is a parameter instead of a statistic.
Variance An Office Team survey of 150 executives found that 93.3% of them said that they would be concerned about gaps in a résumé of a job applicant. Based on these results, such randomly selected groups of 150 executives have a mean of 140.0 executives and a standard deviation of 3.1
Standard Deviation For the binomial distribution described by the conditions in Exercise 1, 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?
Notation In a clinical trial of the cholesterol drug Lipitor, 270 subjects were given a placebo, and 7% of them developed headaches. For such randomly selected groups of 270 subjects given a placebo, identify the values of n, p, and q that would be used for finding the mean and standard deviation
Geometric Distribution If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used.The probability of getting the first success on the xth trial is given by P (x) = p(1 - p)x-1, where p is the
Chocolate Chip Cookies 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
Aspirin 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
STD 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
HIV 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
Challenged Calls in Tennis 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
XSORT Method of Gender Selection 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
Overbooking Flights 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
Nielsen Rating 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
Online Banking 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
On-Time Flights 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
Career Choice 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
Death of Taxes 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
Tainted Currency 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.
Too Young to Tat 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
Live TV 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
See You Later 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
Genetics 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?
Genetics 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?
Genetics Find the probability that at most five of the six offspring peas have green pods.
Genetics 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?
If the number of blood donors is n = 11, find the probability that the number with Group O blood is x = 9.
If the number of blood donors is n = 20, find the probability that the number with Group O blood is x = 16.
If the number of blood donors is n = 16, find the probability that the number with Group O blood is x = 6.
If the number of blood donors is n = 8, find the probability that the number with Group O blood is x = 3.
Find the probability that all answers are correct.
Find the probability of no correct answers.
Find the probability that the number x of correct answers is fewer than 3.
Find the probability that the number x of correct answers is more than 2.
Find the probability that the number x of correct answers is at least 3.
Find the probability that the number x of correct answers is exactly 3.
Win 4 Lottery 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
Guessing Answers 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
Online Shopping 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.
Smartphone Survey 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.
Surveying Senators Ten different senators are randomly selected without replacement, and the numbers of terms that they have served are recorded.
Surveying Senators 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.
Veggie Survey In an Idaho Potato Commission survey of 1000 adults, subjects are asked to select their favorite vegetables, and responses of potatoes, corn, broccoli, tomatoes, or“other” were recorded.
Veggie Survey In an Idaho Potato Commission survey of 1000 adults, subjects are asked to select their favorite vegetables, and each response was recorded as “potatoes” or “other.”
Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, is designed to increase the likelihood that a baby will be a boy.When 291 couples use the YSORT method and give birth to 291 babies, the genders of the babies are recorded.
Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, is designed to increase the likelihood that a baby will be a boy.When 291 couples use the YSORT method and give birth to 291 babies, the weights of the babies are recorded.
Notation of 0+ Using the same survey from Exercise 3, the probability of randomly selecting 30 of the 1000 adults and getting exactly 28 who include Wal-Mart is represented as 0+. What does 0+ indicate? Does 0+ indicate that it is it impossible to get exactly 28 adults who include Wal-Mart?
Independent Events 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
Consistent Notation If we use the binomial probability formula (Formula 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?
Calculating Probabilities 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
Expected Value for Deal or No Deal 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,
From Example 8, we know that the expected value of the $5 bet for a single number is -26c. For the $5 bet that the outcome is 0, 00, 1, 2, or 3, there is a probability of 5/38 of making a net profit of $30 and a 33/38 probability of losing $5.a. Find the expected value for the $5 bet that the
Expected Value in Roulette 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,
Expected Value in Maine’s Pick 4 Game 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
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 probability of
Using Probabilities for Unusual Eventsa. 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
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
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.
Mean and Standard Deviation Find the mean and standard deviation for the numbers of cars that failed among the six cars that are tested.
Using Probabilities for Unusual Eventsa. 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)
Using Probabilities for Unusual Eventsa. 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
Range Rule of Thumb for Unusual Events 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.
Mean and Standard Deviation Find the mean and standard deviation for the numbers of girls in 10 births.
a. Eye colors of humans on commercial aircraft flightsb. Weights of humans on commercial aircraft flightsc. Numbers of passengers on commercial aircraft flightsd. Numbers of randomly generated digits before getting the digit 3e. Political party affiliations of adults in the United Statesf. Exact
a. Exact weights of quarters now in circulation in the United Statesb. Numbers of tosses of quarters required to get headsc. 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 7e. Exact foot
Unusual 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?
Probability Distribution Does Table 7 describe a probability distribution? Show how the requirements are satisfied or are not satisfied.
Discrete or Continuous? Is the random variable given in Table 7 discrete or continuous? Explain.
Random Variable Table 7 lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?
Identifying Probability Valuesa. “You have a 50-50 chance of choosing the correct road.”b. “There is a 20% chance of rain tomorrow.”c. “You have a snowball’s chance in hell of marrying my daughter.”
Writing Write an essay about the importance of statistics for one of the following. • A study on the effectiveness of a new drug • An analysis of a manufacturing process • Making conclusions about voter opinions using surveys

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Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions

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