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statistics for experimentert
Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions
state and apply the permutations and combinations rules.
apply counting rules to solve probability problems where appropriate.
A and B are independent events such that P(A) = 0.3 and P(B) = 0.6. Find P(A & B).
For the first four letters in the English alphabet,a. list the possible permutations of three letters from the four.b. list the possible combinations of three letters from the four.c. Use parts (a) and (b) to obtain 4P3 and 4C3.d. Use the permutations and combinations rules to obtain 4P3 and 4C3.
Adjusted Gross Incomes. The Internal Revenue Service compiles data on income tax returns and summarizes its findings in Statistics of Income. The first two columns of Table 4.16 show a frequency distribution (number of returns) for adjusted gross income (AGI) from federal individual income tax
Adjusted Gross Incomes. Refer to Problem 30. A federal individual income tax return is selected at random. Let H = event the return shows an AGI between $20K and $100K, I = event the return shows an AGI of less than $50K, J = event the return shows an AGI of less than $100K, and K = event the
Adjusted Gross Incomes. For the following groups of events from Problem 31, determine which are mutually exclusive.a. H and Ib. I and Kc. H and (not J )d. H, (not J ), and K
Adjusted Gross Incomes. Refer to Problems 30 and 31.a. Use the second column of Table 4.16 and the f/N rule to compute the probability of each of the events H, I, J, and K.b. Express each of the events H, I, J , and K in terms of the mutually exclusive events displayed in the third column of Table
Adjusted Gross Incomes. Consider the events (not J ),(H & I), (H or K), and (H & K) discussed in Problem 31.a. Find the probability of each of those four events, using the f/N rule and your answers from Problem 31.b. Compute P(J ), using the complementation rule and your answer for P(not J ) from
The National Center for Education Statistics publishes information about school enrollment in the Digest of Education Statistics. Table 4.17 provides a contingency table for enrollment in public and private schools by level. Frequencies are in thousands of students.a. How many cells are in this
Refer to the information given in Problem 35. A student is selected at random.a. Describe the events L3, T1, and (T1 & L3) in words.b. Find the probability of each event in part (a), and interpret your answers in terms of percentages.c. Construct a joint probability distribution corresponding to
Refer to the information given in Problem 35. A student is selected at random.a. Find P(L3 | T1) directly, using Table 4.17 and the f/N rule.Interpret the probability you obtain in terms of percentages.b. Use the conditional probability rule and your answers from Problem 36(b) to find P(L3 | T1).c.
Refer to the information given in Problem 35. A student is selected at random.a. Use Table 4.17 to find P(T2) and P(T2 | L2).b. Are events L2 and T2 independent? Explain your answer in terms of percentages.c. Are events L2 and T2 mutually exclusive?* Public Programs.
During one year, the College of Public Programs at a major university awarded the following number of master’s degrees.Type of degree Frequency Master of arts 3 Master of public administration 28 Master of science 19 Two students who received such master’s degrees are selected at random without
Research by B. Hatchwell et al. on divorce rates among the long-tailed tit (Aegithalos caudatus) appeared in Science News (Vol. 157, No. 20, p. 317). Tracking birds in Yorkshire from one breeding season to the next, the researchers noted that 63% of pairs divorced and that “. . . compared with
According to M. Neitz and J. Neitz of the Medical College of Wisconsin Eye Institute, 9% of men are color blind. For four randomly selected men, determine the probability thata. none are color blind.b. the first three are not color blind and the fourth is color blind.c. exactly one of the four is
The Pew Internet & American Life Project compiles data on smartphone ownership and publishes the results in the document Smartphone Ownership. The first two columns of the following table provide a percentage distribution for age of U.S. adults. The third column of the table shows the percentage of
In Example 4.31 on page 233, we considered exacta wagering in horse racing. Two similar wagers are the quinella and the trifecta. In a quinella wager, the bettor picks the two horses that he or she believes will finish first and second, but not in a specified order. In a trifecta wager, the bettor
A bridge hand consists of an unordered arrangement of 13 cards dealt at random from an ordinary deck of 52 playing cards.a. How many possible bridge hands are there?b. Find the probability of being dealt a bridge hand that contains exactly two of the four aces.c. Find the probability of being dealt
In the NCAA basketball tournament, 64 teams compete in 63 games during six rounds of single-elimination bracket competition. During the “Sweet Sixteen” competition (the third round of the tournament), 16 teams compete in eight games. If you were to choose in advance of the tournament the 8
Let X denote the number of siblings of a randomly selected student. Explain the difference between {X = 3} and P(X = 3).
A variable y of a finite population has the following frequency distribution:y 12 3 4 f 2 2 10 6 Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained.a. Determine the probability distribution of the random variable Y .b. Use
A variable y of a finite population has the following frequency distribution:y 0 146 f 18 14 8 10 Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained.a. Determine the probability distribution of the random variable Y .b.
A variable x of a finite population has the following frequency distribution:x 578 f 25 40 60 Suppose a member is selected at random from the population and let X denote the value of the variable x for the member obtained.a. Determine the probability distribution of the random variable X.b. Use
Space Shuttles. The National Aeronautics and Space Administration (NASA) compiles data on space-shuttle launches and publishes them on its website. The following table displays a frequency distribution for the number of crew members on each shuttle mission from April 12, 1981 to July 8, 2011.Crew
Persons per Housing Unit. From the document American Housing Survey for the United States, published by the U.S. Census Bureau, we obtained the following frequency distribution for the number of persons per occupied housing unit, where we have used “7” in place of “7 or more.” Frequencies
Major Hurricanes. The Atlantic Hurricane Database extends back to 1851, recording among other things the number of major hurricanes striking the U.S. Atlantic and Gulf Coast per year. A major hurricane is a hurricane measuring at least a Category 3 on the SaffirSimpson hurricane wind scale (i.e.,
Accident. On an average nearly 3 accidents happen per second in a certain city. Let us denote the number of deaths that occur in an accidents per second as X.a. Identify the possible values of the random variable X.b. Determine the probability distribution of X. (Hint: There are 9 possible equally
Dice. When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 4.1 on page 181. Let Y denote the sum of the dice.a. What are the possible values of the random variable Y ?b. Use random-variable notation to represent the event that the sum of the dice is 7.c.
World Series. The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. From the document World Series History on the
10 Air Meter Pistol Event. In a 10-Metre-Air-Pistol event, a 4.5 mm caliber air gun is shot from a distance of 10 meters into a circular target with a 6 feet radius whose center we call the origin. The program consists of 60 shots within 105 minutes for men. The outcome of this random experiment is
Batting Average. The official website for International Cricket Council provides information on the best batsman’s batting average in the world cups from 1975 to 2015. As of 2015 cricket was played by only 20 countries in the world.a. Let X denote the batting average of the best batsman. Is X a
Black Bear Litters. In the article “Reproductive Ecology and Cub Survival of Florida Black Bears” (Journal of Wildlife Management, Vol. 71, Issue 3, pp. 720–727), E. Garrison et al. investigated cub survival rates of the Florida black bear. Through the observation of female Florida black
All-Numeric Passwords. The technology consultancy DataGenetics published the online document PIN analysis. In addition to analyzing PIN numbers, password trends were examined. Seven million all-numeric passwords were collected and yielded the following estimate of the probability distribution of
Suppose that P(Z > 1.96) = 0.025. Find P(Z ≤ 1.96). (Hint:Use the complementation rule.)
Suppose that T and Z are random variables.a. If P(T > 0.3) = 0.1 and P(T < −3.0) = 0.05, determine P(−3.0 ≤ T ≤ 0.3).b. Suppose that P(−0.8 ≤ Z ≤ 0.8) = 0.90 and also suppose that P(Z > 0.8) = P(Z < −0.8). Find P(Z > 0.8).
Let c > 0 and 0 ≤ α ≤ 1. Also let X, Y, and T be random variables.a. If P(X >c) = α, determine P(X ≤c) in terms of α.b. Suppose that P(Y >c) = α/2 and P(Y < −c) = P(Y > c).Determine P(−c ≤ Y ≤c) in terms of α.c. Suppose that P(−c ≤ T ≤c) = 1 − α and also suppose that P(T
Simulation. Refer to the probability distribution displayed in Table 5.6 on page 250.a. Use the technology of your choice to repeat the simulation done in Example 5.5 on page 250.b. Obtain the proportions for the number of heads in three tosses and compare them to the probability distribution in
Comparing Investments. Suppose that the random variables X and Y represent the amount of return on two different investments. Further suppose that the mean of X equals the mean of Y but that the standard deviation of X is greater than the standard deviation of Y .a. On average, is there a
Space Shuttles. The random variable X is the crew size of a randomly selected shuttle mission between April 12, 1981 and July 8, 2011. Its probability distribution is as follows.x 245678 P(X = x) 0.030 0.022 0.267 0.207 0.467 0.007
Persons per Housing Unit. The random variable Y is the number of persons living in a randomly selected occupied housing unit.Its probability distribution is as follows.y 1234567 P(Y = y) 0.265 0.327 0.161 0.147 0.065 0.022 0.013
Major Hurricanes. The random variable Y is the number of major hurricanes for a randomly selected year between 1851 and 2012. Its probability distribution is as follows.y P(Y = y) y P(Y = y)0 0.185 5 0.056 1 0.296 6 0.037 2 0.266 7 0.012 3 0.093 8 0.006 4 0.049
Accident. Let X be the random variable representing number of motorcycle accidents that has happened in a region per second. Its probability distribution is as follows.x 0123 P(X = x) 0.125 0.375 0.375 0.125
Dice. The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is as follows.y 2 3 4 5 6 7 8 9 10 11 12 P(Y = y) 1
World Series. The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). From the document World Series History on the Baseball Almanac website, as of November 2013, the lengths of the World Series are as
10 Air Meter Pistol Event. In a 10-Metre-Air-Pistol event, a 4.5 mm caliber air gun is shot from a distance of 10 meters into a circular target with a 6 feet radius whose center we call the origin. The program consists of 60 shots within 105 minutes for men. The outcome of this random experiment is
All-Numeric Passwords. The technology consultancy DataGenetics published the online document PIN analysis. In addition to analyzing PIN numbers, passwords trends were examined. Seven million all-numeric passwords were collected and yielded the following estimate of the probability distribution of
Roulette. An American roulette wheel contains 38 numbers:18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers.Suppose that you bet $1 on red. If the ball lands on a red number, you win $1; otherwise you lose your $1.
Evaluating Investments. An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year’s economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments.Investment Next year’s economy
Life of AA Battery. A company wants to design an AA battery that lasts longer than the existing batteries. The data compiled by the company gives the life of the batteries, X, in minutes. We are assuming X as a random variable with the following probability distribution.x 360 380 400 420 440 P(X =
Bulbs. A distributor orders 100 boxes of bulbs. A box of 10 flashbulbs contains 3 defective bulbs. A random sample of 2 bulbs is selected and tested. The probability distribution is shown in the following table, where X denotes the number of defective bulbs.x 012 P(X = x) 0.181 0.459 0.36a.
Simulation. Let X be the value of a randomly selected decimal digit, that is, a whole number between 0 and 9, inclusive.a. Use simulation to estimate the mean of X. Explain your reasoning.b. Obtain the exact mean of X by applying Definition 5.4 on page 254. Compare your result with that in part (a).
Queuing Simulation. Benny’s Barber Shop in Cleveland has five chairs for waiting customers. The number of customers waiting is a random variable Y with the following probability distribution.y 012345 P( Y = y) 0.424 0.161 0.134 0.111 0.093 0.077a. Compute and interpret the mean of the random
Mean as Center of Gravity. Let X be a discrete random variable with a finite number of possible values, say, x1, x2,..., xm . For convenience, set pk = P(X = xk ), for k = 1, 2, ..., m. Think of a horizontal axis as a seesaw and each pk as a mass placed at point xk on the seesaw. The center of
Bulbs. Refer to Exercise 5.43. Assume that the number of defective bulbs on different boxes are independent of one another. Let X and Y denote the number of defective bulbs on each of two boxes.x y0 1 2 P(X = x)0 12 P( Y = y)a. Complete the preceding joint probability distribution table. Hint:To
Bulbs. The distributor in Exercise 5.43 estimates that each defective bulb costs him $5 for replacement. If X is the number of defective bulbs in a box, then $5 X is the cost of defective bulbs in a box.a. Refer to the probability distribution shown in Exercise 5.43 and determine the probability
Consider the data set 1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 11, 12.a. Obtain the mean and median of the data.b. Replace the 10 in the data set by 100 and again compute the mean and median. Decide which measure of center works better here, and explain your answer.c. For the data set in part (b), the
Floor Space. The U.S. Department of Housing and Urban Development compiles information on new, privately owned singlefamily houses. According to the document Characteristics of New Housing, in 2012 the mean floor space of such homes was 2505 sq ft and the median was 2306 sq ft. Which measure of
It was reported that in 2004, the mean net worth of families in a certain region was $469.6 thousand and the median net worth was$92.1 thousand. Which measure of center do you think is more appropriate? Explain your answer.In Exercises 3.9–3.14, we have provided simple data sets for you to
Consider these sample data: x1 = 1, x2 = 7, x3 = 4, x4 = 5, x5 = 10, x6 = 15, x7 = 8, x8 = 12.a. Find n.b. Compute xi .c. Determine x¯
Consider these sample data: x1 = 12, x2 = 8, x3 = 9, x4 = 17.a. Find n.b. Compute xi .c. Determine x¯.Applying the Concepts and Skills In Exercises 3.19–3.26, find thea. mean.b. median.c. mode(s).For the mean and the median, round each answer to one more decimal place than that used for the
Amphibian Embryos. In a study of the effects of radiation on amphibian embryos titled “Shedding Light on Ultraviolet Radiation and Amphibian Embryos” (BioScience, Vol. 53, No. 6, pp. 551–561), L. Licht recorded the time it took for a sample of seven different species of frogs’ and toads’
Hurricanes. An article by D. Schaefer et al. (Journal of Tropical Ecology, Vol. 16, pp. 189–207) reported on a long-term study of the effects of hurricanes on tropical streams of the Luquillo Experimental Forest in Puerto Rico. The study shows that Hurricane Hugo had a significant impact on
Tornado Touchdowns. Each year, tornadoes that touch down are recorded by the Storm Prediction Center and published in Monthly Tornado Statistics. The following table gives the number of tornadoes that touched down in the United States during each month of one year.[SOURCE: National Oceanic and
Artistic Gymnastics. In the 2012 Summer Olympics, held in London, 8 participants had participated in the final round of the men’s floor exercises event of the artistic gymnastics category. The participants’ timings (in seconds), taken from olympic.org, are shown in the following table. 15.933
Billionaires’ Club. Each year, Forbes magazine compiles a list of the 400 richest Americans. As of September 19, 2012, the top 10 on the list are as shown in the following table.Person Wealth ($ billions)Bill Gates 66.0 Warren Buffett 46.0 Larry Ellison 41.0 Charles Koch 31.0 David Koch 31.0
Tablet Computers. Tablet personal computers such as iPad and Kindle Fire are one-piece portable computers that typically offer a touchscreen. Tablets are available in different sizes but generally offer a screen that is greater than 7 inches diagonally. Consumer Reports reviews tablets of different
The Beatles. The English rock band, The Beatles, was formed in Liverpool in 1960. There are 12 studio albums that are considered part of their core catalogue. In the article, “Length of The Beatles’Songs” (Chance, Vol. 25, No. 1, pp. 30–33), T. Koyama lists the album title, date of release,
Router Horsepower. In the article “Router Roundup” (Popular Mechanics, Vol. 180, No. 12, pp. 104–109), T. Klenck reported on tests of seven fixed-base routers for performance, features, and handling. The following table gives the horsepower (hp) for each of the seven routers tested. 1.75 2.25
Medieval Cremation Burials. In the article “Material Culture as Memory: Combs and Cremations in Early Medieval Britain”(Early Medieval Europe, Vol. 12, Issue 2, pp. 89–128), H. Williams discussed the frequency of cremation burials found in 17 archaeological sites in eastern England. Here are
Global Warming. The following data (taken from the article“Effects of climate change on global food production under SRES emissions and socio-economic scenarios”, published in Global Environmental Change, Vol. 14, 2004, pp. 53–67), shows the potential changes (%) in national cereal yields for
A transportation company compiles data on motorcycle accidents. During one year, the numbers of motorcycle accidents in a particular country were tabulated by day of the week for builtup roads and nonbuiltup roads and resulted in the accompanying data table.Complete parts (a)-(d) below.Motorcycle
Honeymoons. Popular destinations for the newlyweds of today are the Caribbean and Hawaii. According to a recent American Wedding Study by the Conde Nast Bridal Group, a honeymoon, on average, lasts 9.4 days and costs $5111. A sample of 12 newlyweds reported the following lengths of stay of their
The data set below shows the additional sleep in hours obtained by a sample of 10 patients given a certain medication. Complete parts(a) through (c). 1.7 1.4 0.9 −0.1 0.4 3.5 3.7 1.8 4.4 3.3a. Find n.b. Compute xi .c. Determine the sample mean.
Pesticides in Pakistan. Pesticides are chemicals often used in agriculture to control pests. In Pakistan, 70% of the population depends on agriculture, and pesticide use there has increased rapidly.In the article, “Monitoring Pesticide Residues in Fresh Fruits Marketed in Peshawar, Pakistan”
Annual Hydro-electricity Production. From Wikipedia, we found the annual hydro-electricity production of a few countries (in TWh). 652.05 369.5 363.8 250.6 167.0 140.5-.-115.6 85.96 69.2 65.5 In each of Exercises 3.34–3.41,a. determine the mode of the data.b. decide whether it would be
Primetime Broadcast Shows. From the TVbytheNumbers website, we obtained the networks for the top 20 primetime broadcast TV shows by total viewership for the week ending August 18, 2013.CBS NBC NBC ABC CBS CBS CBS CBS CBS FOX CBS CBS CBS CBS NBC NBC FOX CBS NBC ABC
Olympics. From olympics.org—the official Web site for the Olympics—we obtained the names of the countries who won the 100-meter race between 1900 and 2012. They are listed in the following table.Year Champion Year Champion 1900 USA 1964 USA 1904 USA 1968 USA 1908 South Africa 1972 Soviet Union
Road Rage. The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and J. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggressive driving and road rage. As
U.S. Supreme Court Justices. From Wikipedia, we found that the law schools of the justices of the U.S. Supreme Court, as of September 9, 2013, are as follows.Harvard Harvard Harvard Yale Columbia Harvard Yale Yale Harvard
Robbery Locations. The Department of Justice and the Federal Bureau of Investigation publish a compilation on crime statistics for the United States in Crime in the United States. The following table provides a frequency distribution for robbery type during a one-year period.Robbery type Frequency
Freshmen Politics. The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views as liberal, 51.9% as
Medical School Faculty. The Association of American Medical Colleges (AAMC) compiles data on medical school faculty and publishes the results in AAMC Faculty Roster. The following table presents a frequency distribution of rank for medical school faculty during one year.Rank Frequency Professor
Motor Production. According to knowindia.net, India produced 19.75 million motor vehicles in 2014-2015. The following table shows the frequency of domestic motor vehicle sales for 2014-15 (in million units).Vehicle 2-Wheeler 3-Wheeler -Passenger Vehicles Number 16.0 0.53 2.60
Japanese Vehicle Exports. The Japan Automobile Manufacturer’s Association provides data on exported vehicles in Motor Vehicle Statistics of Japan. In 2010, cars, trucks, and buses constituted 88.3%, 9.3%, and 2.4% of vehicle exports, respectively. A random sample of last year’s exports yielded
U.S. Hospitals. The American Hospital Association conducts annual surveys of hospitals in the United States and publishes its findings in AHA Hospital Statistics. Data on hospital type for U.S. registered hospitals can be found on the WeissStats site. For convenience, we use the following
Marital Status and Drinking. Research by W. Clark and L. Midanik (Alcohol Consumption and Related Problems: Alcohol and Health Monograph 1. DHHS Pub. No. (ADM) 82–1190) examined, among other issues, alcohol consumption patterns of U.S. adults by marital status. Data for marital status and number
Ballot Preferences. In Issue 338 of the Amstat News, thenpresident of the American Statistical Association Fritz Scheuren reported the results of a survey on how members would prefer to receive ballots in annual elections. On the WeissStats site, you will find data for preference and highest degree
The Great White Shark. In an article titled “Great White, Deep Trouble” (National Geographic, Vol. 197(4), pp. 2–29), Peter Benchley—the author of JAWS—discussed various aspects of the Great White Shark (Carcharodon carcharias). Data on the number of pups borne in a lifetime by each of 80
The Beatles. In the article, “Length of The Beatles’ Songs”(Chance, Vol. 25, No. 1, pp. 30–33), T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of 229 Beatles’ songs are presented on the WeissStats site.
High School Completion. As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed high school is provided on the WeissStats site.
Bachelor’s Completion. As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed a bachelor’s degree is provided on the WeissStats site.
Body Temperature. A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit of the Normal Body
Treating Psychotic Illness. L. Petersen et al. evaluated the effects of integrated treatment for patients with a first episode of psychotic illness in the paper “A Randomised Multicentre Trial of Integrated Versus Standard Treatment for Patients with a First Episode of Psychotic Illness”
The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest,
Food Choice. As you discovered earlier, ordinal data are data about order or rank given on a scale such as 1, 2, 3,... or A, B, C,.... Most statisticians recommend using the median to indicate the center of an ordinal data set, but some researchers also use the mean.In the paper “Measurement of
Outliers and Trimmed Means. Some data sets contain outliers, observations that fall well outside the overall pattern of the data.(We discuss outliers in more detail in Section 3.4.) Suppose, for instance, that you are interested in the ability of high school algebra students to compute square
Darts. The following dartboards represent darts thrown by two players, Tracey and Joan.20 1 18 413 610 15 219 3 17 716 811 14 912 5Tracey Joan 20 1 18 413 610 15 219 3 17 716 811 14 912 5For the variable “distance from the center,” which player’s board represents data with a smaller sample
Consider the following four data sets.Data Set I Data Set II Data Set III Data Set IV 1 5 1 9 5 5 2 4 1 8 1 9 5 5 4 4 2 8 1 9 5 5 4 4 2 9 1 9 5 5 4 10 5 9 1 9 5 5 4 10a. Compute the mean of each data set.b. Although the four data sets have the same means, in what respect are they quite different?c.
Age of Australian Residents. The Australian Bureau of Statistics publishes information about ages of people in Australia in Australian Social Trends. A sample of five Australian residents has the following ages, in years.29 35 70 14 55a. Determine the range of these ages.b. Find the sample standard
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