[SOLVED] What does the “bi” in “binomial” signify?

> 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

> 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 r

> 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.

> Determine the value of each binomial coefficient.

> 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!.

> 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?

> 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.

> 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. a. Compute and interpret the mean of the random variable Y. b. In a large number o

> Students in the dormitories of a university in the state of New York live in clusters of four double rooms, called suites. There are 48 suites, with eight students per suite. a. Describe a cluster sampling procedure for obtaining a sample of 24 dormitory

> 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.

> A factory manager collected data on the number of equipment breakdowns per day. From those data, she derived the probability distribution shown in the following table, where W denotes the number of breakdowns on a given day. a. Determine μW and σW . Roun

> One method for deciding among various investments involves the concept of expected utility. Economists describe the importance of various levels of wealth by using utility functions. For instance, in most cases, a single dollar is more important (has gre

> An insurance company wants to design a homeowner’s policy for mid-priced homes. From data compiled by the company, it is known that the annual claim amount, X, in thousands of dollars, per homeowner is a random variable with the following probability dis

> Apply the empirical rule to solve each exercise. The data set has size 50. Approximately how many observations lie within one standard deviation to either side of the mean?

> Use the specified grouping method to a. determine a frequency distribution. b. obtain a relative-frequency distribution. c. construct a frequency histogram based on your result from part (a). d. construct a relative-frequency histogram based on your resu

> 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. Let V, W, X, a

> 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, yo

> The technology consultancy Data Genetics 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 probab

> An ordinary deck of playing cards has 52 cards. There are four suits—spades, hearts, diamonds, and clubs— with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probab

> An archer shoots an arrow into a square target 6 feet on a side whose center we call the origin. The outcome of this random experiment is the point in the target hit by the arrow. The archer scores 10 points if she hits the bull’s eye—a disk of radius 1

> 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 o

> In the game of keno, 20 balls are selected at random from 80 balls numbered 1–80. In Exercise 1.48 on page 16, you used simple random sampling to simulate one game of keno. a. Use systematic random sampling to obtain a sample of 20 of the 80 balls. b. Wh

> At the beginning of this chapter, we discussed research by J. Sholl et al. on the relationship between gender and sense of direction. Recall that, in their study, the spatial orientation skills of 30 male and 30 female students were challenged in a woode

> The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is as follows. a. Find and interpret the mean of the random variable. b. Obtain the standard deviation of the random variable by using one of the

> The random variable X is the number of girls of four children born to a couple that is equally likely to have either a boy or a girl. Its probability distribution is as follows. a. Find and interpret the mean of the random variable. b. Obtain the standar

> Regarding simple random sampling: a. What is simple random sampling? b. What is a simple random sample? c. Identify two forms of simple random sampling and explain the difference between the two.

> 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. a. Find and interpret the mean of the random variable. b. Obtain the standard deviation of the random

> The random variable Y is the number of persons living in a randomly selected occupied housing unit. Its probability distribution is as follows. a. Find and interpret the mean of the random variable. b. Obtain the standard deviation of the random variable

> 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. a. Find and interpret the mean of the random variable. b. Obtain the standard deviation of

> a. Find the mean of the random variable. b. Obtain the standard deviation of the random variable by using one of the formulas given in Definition 5.10.

> Refer to Table 5.1. a. List the possible samples without replacement of size 4 that can be obtained from the population of five officials. If a simple random sample without replacement of four officials is taken from the five officials, determine the pro

> a. Find the mean of the random variable. b. Obtain the standard deviation of the random variable by using one of the formulas given in Definition 5.10.

> You used simple random sampling to obtain a sample of 10 firms from Fortune Magazine’s list of “The International 500.” a. Use systematic random sampling to accomplish that same task. b. Which method is easier: simple random sampling or systematic random

> 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

> We discussed Texas hold’em and described the basic rules of the game. Here we examine some of the simplest probabilities associated with the game. Recall that, to begin, each player is dealt 2 cards face down, called “hole cards,” from an ordinary deck o

> What concept does the mean of a discrete random variable Generalize?

> Refer to the probability distribution displayed in Table 5.11 on page 222. a. Use the technology of your choice to repeat. b. Obtain the proportions for the number of heads in three tosses and compare them to the probability distribution in Table 5.11. c

> 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

> Suppose that T and Z are random variables. a. If P(T > 2.02) = 0.05 and P(T < −2.02) = 0.05, determine P(−2.02 ≤ T ≤ 2.02). b. Suppose that P(−1.64 ≤ Z ≤ 1.64) = 0.90 and also suppose that P(Z > 1.64) = P(Z < −1.64). Find P(Z > 1.64).

> Suppose that P(Z > 1.96) = 0.025. Find P(Z ≤ 1.96).

> The technology consultancy Data Genetics 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 probabi

> 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

> The World Almanac provides information on past and projected total solar eclipses from 1955 to 2015. Unlike total lunar eclipses, observing a total solar eclipse from Earth is rare because it can be seen along only a very narrow path and for only a short

> Refer to Table 5.1. a. List the possible samples without replacement of size 3 that can be obtained from the population of five officials. If a simple random sample without replacement of three officials is taken from the five officials, determine the pr

> During one year, a university wanted to gauge the sentiment of the people using the university’s parking facilities. Each of the 8493 people that used the parking facilities had a sticker with a unique number between 1 and 8493. The university committee

Question: What does the “bi” in “binomial” signify?