Question: Following is a gender frequency distribution for
Following is a gender frequency distribution for students in Professor Weiss’s introductory statistics class. 
Two students are selected at random. Find the probability that both students are male if the selection is done a. with replacement. b. without replacement. c. Compare the answers obtained in parts (a) and (b). Suppose that Professor Weiss’s class had 10 times the students, but in the same proportions, that is, 170 males and 230 females. d. Repeat parts (a)–(c), using this hypothetical distribution of students. e. In which case is there less difference between sampling without and with replacement? Explain why this is so.
> When one die is rolled, the following six outcomes are possible: List the outcomes constituting A = event the die comes up even, B = event the die comes up 4 or more, C = event the die comes up at most 2, and D = event the die comes up 3.
> Draw a Venn diagram portraying four mutually exclusive events.
> Answer true or false to the following statement and justify your answer: If event A and event B are mutually exclusive, so are events A, B, and C for every event C.
> Answer true or false to the following statement and justify your answer: If event A and event B are not mutually exclusive, neither are events A, B, and C for every event C.
> An experiment has 20 possible outcomes, all equally likely. An event can occur in five ways. The probability that the event occurs is ___.
> What does it mean for three events to be mutually exclusive?
> In a designed experiment, a. what are the experimental units? b. if the experimental units are humans, what term is often used in place of experimental unit?
> What does it mean for two events to be mutually exclusive?
> Consider the set consisting of the first 10 positive whole numbers (i.e., 1–10). Determine explicitly the numbers in the set that satisfy each of the following conditions: a. at least 6 b. at most 3 c. between 2 and 5, inclusive
> Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Dietary Reference Intakes, developed by the Institute of Medicine
> Consider the set consisting of the first 12 positive whole numbers (i.e., 1–12). Determine explicitly the numbers in the set that satisfy each of the following conditions: a. at least 9 b. at most 10 c. between 5 and 8, inclusive
> Construct a Venn diagram representing the event a. (A & (not B)). b. ((A or B) & (not (A & B)))
> Construct a Venn diagram representing the event a. (A or B or C). b. ((not A) & B).
> Construct a Venn diagram representing the event a. (A & B). b. (A & B & C).
> Construct a Venn diagram representing the event a. (not E). b. (A or B).
> What type of graphical displays are useful for portraying events and relationships among events?
> An issue of Travel + Leisure Golf magazine reported several facts about lightning. Here are three of them. - The odds of an individual being struck by lightning in a year in the United States are about 280,000 to 1 (against). - The odds of an individual
> If a member is selected at random from a finite population, probabilities are identical to ___ .
> In simple random sampling, it is also true that each member of the population is equally likely to be selected, the chance for each member being equal to the sample size divided by the population size. Show that this fact is also true for stratified rand
> A study was conducted by the firm Coleman & Associates, Inc. to determine who curses at their computer. The results, which appeared in USA TODAY, indicated that 46% of people age 18–34 years have cursed at their computer. What are the odds against a rand
> Dementia is the loss of intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer’s disease is the most common type of dementia. In the article “Living with Early Onset Dementia: Exploring the
> The Belmont Stakes is the third leg, after the Kentucky Derby and Preakness Stakes, of the Triple Crown of thoroughbred horseracing. The morning-line betting odds of the two favorites, Orb and Revolutionary, for the 2013 Belmont Stakes were 7 to 2 (again
> As found in USA TODAY, results of a survey by International Communications Research revealed that roughly 75% of adult women believe that a romantic relationship over the Internet while in an exclusive relationship in the real world is cheating. What are
> An American roulette wheel contains 38 numbers, of which 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. For a bet on red, the house pays even odds (i.e., 1 to 1). W
> Consider the random experiment of tossing a coin once. There are two possible outcomes for this experiment, namely, a head (H) or a tail (T). a. Repeat the random experiment five times—that is, toss a coin five times—and record the information required i
> At a certain university in the United States, 62% of the students are at least bilingual—speaking English and at least one other language. Of these students, 80% speak Spanish and, of the 80% who speak Spanish, 10% also speak French. Determine the probab
> Explain what is wrong with the following argument: When two balanced dice are rolled, the sum of the dice can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, giving 11 possibilities. Therefore the probability is 1/11 that the sum is 12.
> In 2013, according to the National Governors Association, 30 of the 50 state governors were Republicans. Suppose that on each day of 2013, one U.S. state governor was randomly selected to read the invocation on a popular radio program. On approximately h
> The probability is 0.667 that the favorite in a horse race will finish in the money (first, second, or third place). In 500 horse races, roughly how many times will the favorite finish in the money?
> The probability is 0.314 that the gestation period of a woman will exceed 9 months. In 4000 human gestation periods, roughly how many will exceed 9 months?
> In simple random sampling, it is also true that each member of the population is equally likely to be selected, the chance for each member being equal to the sample size divided by the population size. a. Under what circumstances is that fact also true f
> Objects such as asteroids and comets that come into proximity with the Earth are called near-Earth objects (NEOs). The National Aeronautics and Space Administration (NASA) tracks and catalogues all NEOs that are at least 1 kilometer wide. Data on NEOs ca
> What is the difference between selecting a member at random from a finite population and taking a simple random sample of size 1?
> Refer to Exercise 5.24. a. Which, if any, of the events in parts (a)–(e) are certain? impossible? b. Determine the probability of each event identified in part (a). Data from Exercise 5.24: A family is defined to be a group of two or more persons relate
> Refer to Exercise 5.19. a. Which, if any, of the events in parts (a)–(e) are certain? impossible? b. Determine the probability of each event identified in part (a). Data from Exercise 5.19: The U.S. Census Bureau publishes data on housing units in Ameri
> A balanced dime is tossed three times. The possible outcomes can be represented as follows. Here, for example, HHT means that the first two tosses come up heads and the third tails. Find the probability that a. exactly two of the three tosses come up hea
> Two balanced dice are rolled. Refer to Fig. and determine the probability that the sum of the dice is a. 6. b. even. c. 7 or 11. d. 2, 3, or 12.
> A family is defined to be a group of two or more persons related by birth, marriage, or adoption and residing together in a household. According to Current Population Survey, published by the U.S. Census Bureau, the size distribution of U.S. families is
> According to Survey of Graduate Science Engineering Students and Postdoctorates, published by the U.S. National Science Foundation, the distribution of graduate science students in doctorate-granting institutions is as follows. Frequencies are in thousan
> From Wikipedia and the article “Which Country Has the Best Brains?” from BBC News Magazine, we obtained a frequency distribution of the number of Nobel Prize winners, by country. Suppose that a recipient of a Nobel Prize is selected at random. Find the p
> The population of Seoul was studied in an article by B. Lee and J. McDonald, “Determinants of Commuting Time and Distance for Seoul Residents: The Impact of Family Status on the Commuting of Women” (Urban Studies, Vol. 40, No. 7, pp. 1283–1302). The auth
> As reported by the Federal Bureau of Investigation in Crime in the United States, the age distribution of murder victims between 20 and 59 years old is as shown in the following table. A murder case in which the person murdered was between 20 and 59 year
> Consider the following sample of exam scores, arranged in increasing order. The sample mean and sample standard deviation of these exam scores are 85 and 16.1, respectively. Modeling your solutions after those in Example 3.15 on pages 117–118, solve the
> In simple random sampling, all samples of a given size are equally likely. Is that true in systematic random sampling? Explain your answer.
> Concerning the equal-likelihood model of probability, a. what is it? b. how is the probability of an event found?
> Another important discrete probability distribution is the Poisson distribution, named in honor of the French mathematician and physicist Simeon Poisson (1781–1840). This probability distribution is often used to model the frequency with which a specifie
> The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing units. The frequencies are in thousands. A U.S. housing
> In this exercise, we discuss the geometric distribution, the probability distribution for the number of trials until the first success in Bernoulli trials. The geometric probability formula is where X denotes the number of trials until the first success
> In this exercise, we discuss the hypergeometric distribution in more detail. When sampling is done without replacement from a finite population, the hyper geometric distribution is the exact probability distribution for the number of members sampled that
> Refer to the discussion on the binomial approximation to the hypergeometric distribution. a. If sampling is with replacement, explain why the trials are independent and the success probability remains the same from trial to trial—always the proportion of
> A success, s, in Bernoulli trials is often derived from a collection of outcomes. For example, an American roulette wheel consists of 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally lik
> In the Scientific American article “Reducing Crime: Rehabilitation is Making a Comeback,” R. Doyle examined rehabilitation of felons. One aspect of the article discussed recidivism of juvenile prisoners between 14 and 17 years old, indicating that 82% of
> Apply the empirical rule to solve each exercise. The data set has 150 observations and has mean 35 and standard deviation 4. Approximately how many observations lie between 31 and 39?
> A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by
> In the early part of 2005, the Terri Schiavo case received national attention as her husband sought to have life support removed, and her parents sought to maintain that life support. The courts allowed the life support to be removed, and her death ensue
> A poll commissioned by Friends of the Earth and conducted by the Mellman Group found that 72% of American voters are in favor of a carbon tax. Suppose that six voters in the United States are randomly sampled and asked whether they favor a carbon tax. De
> J. Fetto, in the article “Love Stinks” (American Demographics, Vol. 25, No. 1, pp. 10–11), reports that Americans split with their significant other for many reasons—including indiscretion, infidelity, and simply “growing apart.” According to the article
> A student takes a multiple-choice exam with 10 questions, each with four possible selections for the answer. A passing grade is 60% or better. Suppose that the student was unable to find time to study for the exam and just guesses at each question. Find
> From the Florida State Center for Health Statistics report Women and Cardiovascular Disease Hospitalization, we obtained the following table showing the number of female hospitalizations for cardiovascular disease, by age group, during one year. One of t
> The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the probability is 0.40 that a traffic fatality will involve an intoxicated or alcohol-impaired driver or nonoccupant. In eight tr
> The probability is 0.314 that the gestation period of a woman will exceed 9 months. In six human births, what is the probability that the number in which the gestation period exceeds 9 months is a. exactly three? b. exactly five? c. at least five? d. bet
> According to the Daily Racing Form, the probability is about 0.67 that the favorite in a horse race will finish in the money (first, second, or third place). In the next five races, what is the probability that the favorite finishes in the money a. exact
> If we repeatedly roll a balanced die, then, in the long run, it will come up “4” about one-sixth of the time. But what is the probability that such a die will come up “4” exactly once in six rolls?
> Apply the empirical rule to solve each exercise. The data set has 200 observations and has mean 20 and standard deviation 4. Approximately how many observations lie between 16 and 24?
> If we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time. But what is the probability that such a coin will come up heads exactly half the time in 10 tosses?
> Use Procedure 5.1 to solve part (g) of Exercise 5.166. Data from Exercise 5.166: The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Four randomly selected adult American
> The Peace Corps is an independent U.S. government agency that provides trained volunteers for countries requesting assistance. According to Peacecorps.org, as of September 2012, volunteers currently serve in about 76 different host countries. The average
> Use Procedure 5.1 to solve part (g) of Exercise 5.165. Data from Exercise 5.165: Pinworm infestation, which is commonly found in children, can be treated with the drug pyrantel pamoate. According to the Merck Manual, the treatment is effective in 90% of
> n = 4, p = 1/4, P(X = 2) a. the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a).
> n = 5, p = 3/4, P(X = 4) a. the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a).
> n = 3, p = 0.4, P(X = 1) a. the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a).
> According to the Central Election Commission of the Russian Federation, a frequency distribution for the March 4, 2012 Russian presidential election is as follows. Find the probability that a randomly selected voter voted for a. Putin. b. either Zhirinov
> n = 6, p = 0.5, P(X = 4) a. the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a).
> n = 5, p = 0.6, P(X = 3) a. the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a).
> We have provided simple data sets for you to practice the basics of finding measures of center. 1, 9, 8, 4, 3 a. mean. b. median. c. mode(s).
> n = 4, p = 0.3, P(X = 2) a. the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a).
> The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Four randomly selected adult Americans are examined for psychiatric disorders. a. If you let a success correspond to an
> Pinworm infestation, which is commonly found in children, can be treated with the drug pyrantel pamoate. According to the Merck Manual, the treatment is effective in 90% of cases. Suppose that three children with pinworm infestation are given pyrantel pa
> There are 435 representatives in the 113th session of the U.S. House of Representatives. On the website www.house.gov, you can find an alphabetized list of the 435 congresspersons. In 2013, the first representative listed is Robert Aderholt, a Republican
> For each of the following probability histograms of binomial distributions, specify whether the success probability is less than, equal to, or greater than 0.5. Explain your answers.
> For each of the following probability histograms of binomial distributions, specify whether the success probability is less than, equal to, or greater than 0.5. Explain your answers.
> Determine the value of each binomial coefficient.
> Evaluate the following binomial coefficients.
> Evaluate the following binomial coefficients.
> Preeclampsia is a medical condition characterized by high blood pressure and protein in the urine of a pregnant woman. It is a serious condition that can be life threatening to the mother and child. In the article “Women’s Experiences of Preeclampsia: Au
> Apply the empirical rule to solve each exercise. The data set has 250 observations and has mean 100 and standard deviation 16. Approximately how many observations lie between 52 and 148?
> Evaluate the following binomial coefficients.
> Find 1!, 2!, 4!, and 6!.
> Compute 3!, 7!, 8!, and 9!.
> What does the “bi” in “binomial” signify?
> In an issue of Newsweek (Vol. CXLV, No. 20, pp. 48–57), B. Kantrowitz listed “The 100 best high schools in America” according to a ranking devised by J. Mathews. Another characteristic measured from the high school is the percent free lunch, which is the
> Give two examples of Bernoulli trials other than those presented in the text.
> Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks. a. If sampling is with replacement, the probability distribution
> What is the binomial distribution?
> Discuss the pros and cons of binomial probability tables.
> Explain the significance of binomial coefficients with respect to Bernoulli trials.
> Apply the empirical rule to solve each exercise. The data set has 80 observations and has mean 30 and standard deviation 5. Approximately how many observations lie between 20 and 40?
> Under what three conditions are repeated trials of an experiment called Bernoulli trials?
> A bowl contains 12 poker chips—3 red, 4 white, and 5 blue. If one of these poker chips is selected at random from the bowl, what is the probability that its color is a. red? b. red or white? c. not white?
> In probability and statistics, what is each repetition of an experiment called?
