A community college employs 87 full- time faculty members. To gain the faculty’s opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 87. (a) Using Table I from Appendix A, the president closes his eyes and drops his ink pen on the table. It points to the digit in row 5, column 22. Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample. (b) If the president uses technology, determine the numbers for the 9 faculty members who will be included in the sample.
> The weather forecast says there is a 10% chance of rain on Thursday. Jim wakes up on Thursday and sees overcast skies. Since it has rained for the past three days, he believes that the chance of rain is more likely 60% or higher. What method of probabili
> According to the U.S. Census Bureau, 20.2% of American women aged 25 years or older have a Bachelor’s Degree; 16.5% of American women aged 25 years or older have never married; among American women aged 25 years or older who have never married, 22.8% hav
> In the game Text Twist, six letters are given and the player must form words of varying lengths using the letters provided. Suppose that the letters in a particular game are ENHSIC. (a) How many different arrangements are possible using all 6 letters? (b
> In 2002, Valerie Wilson won $1 million in a scratch-off game (Cool Million) from the New York lottery. Four years later, she won $1 million in another scratch-off game ($3,000,000 Jubilee), becoming the first person in New York state lottery history to w
> The president of the student government wants to conduct a survey to determine the student body’s opinion regarding student services. The administration provides you with a list of the names and phone numbers of the 19,935 registered students. (a) Discus
> The distribution of National Honor Society members among the students at a local high school is shown in the table. A student’s name is drawn at random. (a) What is the probability that the student is a junior? (b) What is the probability that the studen
> Shawn is planning for college and takes the SAT test. While registering for the test, he is allowed to select three schools to which his scores will be sent at no cost. If there are 12 colleges he is considering, how many different ways could he fill out
> According to the Statistical Abstract of the United States, about 17% of all 18- to 25-year-olds are current marijuana users. (a) What is the probability that four randomly selected 18- to 25-year-olds are all marijuana users? (b) What is the probability
> The following data represent the survival data for the ill-fated Titanic voyage by gender. The males are adult males and the females are adult females. Suppose a passenger is selected at random. (a) What is the probability that the passenger survived? (b
> Payton’s futsal team consists of 10 girls, but only 5 can be on the field at any given time (four fielders and a goalie). (a) How many starting lineups are possible if all players are selected without regard to position played? (b) How many starting line
> In how many ways can three men and three women be seated around a circular table (that seats six) assuming that women and men must alternate seats?
> A real estate agent conducted a survey of 200 landlords and asked how long their apartments remained vacant before a tenant was found. The results of the survey are shown in the table. The data are based on information obtained from the U.S. Census Burea
> In a survey of 500 randomly selected Americans, it was determined that 22 play soccer. What is the probability that a randomly selected American plays soccer?
> List all combinations of five objects a, b, c, d, and e taken three at a time without replacement.
> Suppose that E and F are two events, P(E) = 0.9, and P(F | E) = 0.3. Find P(E and F).
> The following table lists the 45 presidents of the United States. (a) Obtain a simple random sample of size 8 using Table I in Appendix A, a graphing calculator, or computer software. (b) Obtain a second simple random sample of size 8 using Table I in Ap
> Suppose that E and F are two events, P(E and F) = 0.4, and P(E) = 0.9. Find P(F | E).
> Suppose that events E and F are independent, P(E) = 0.8, and P(F) = 0.5. What is P(E and F)?
> 9C4
> 7P3
>
> P(E or F) if P(E and F) = 0.15
> P(E or F) if E and F are mutually exclusive
> List all permutations of five objects a, b, c, d, and e taken three at a time without replacement.
> F = “a number divisible by three.”
> E = {1, 3, 5, 10}.
> Suppose the president of the United States wants to hold a forum with the governors of ten states. Use the frame shown to answer parts (a) and (b). (a) Obtain a simple random sample of size 10 using Table I in Appendix A, a graphing calculator, or comput
> Nation of origin
> Craps is a popular casino game. In its most basic form, two dice are initially thrown. If the outcome of the roll is 2, 3, or 12 (that is, the sum of the two die is 2, 3, or 12), the player loses his or her “pass line” bet. If the outcome of the roll is
> An interesting problem from probability is the birthday problem. The problem deals with determining the likelihood that at least two people share the same birthday in a room of n individuals. The data file 5_6_1 located at www.pearsonhighered.com/sulliva
> Recently, the Gallup Organization reported that the proportion of adult Americans aged 18 years or older who believe the state of moral values in the country is getting worse is 0.77. There are approximately 241,000,000 Americans aged 18 years or older i
> Recently, Pew Research reported that the proportion of adult Americans aged 18 or older who believe online dating is a good way to meet people is 0.59. There are approximately 241,000,000 Americans aged 18 years or older in the United States. (a) Use the
> Suppose you would like to estimate the number of rolls it typically takes before observing a seven when rolling a pair of fair dice. (a) Explain how you might use simulation to determine the typical number of rolls before observing a seven. (b) Use stati
> Suppose that polls suggest a candidate in a local school board election has 52% of the voters in favor of her as the candidate. (a) Explain how you could use the integers from 1 to 100 to simulate votes. (b) Use statistical software or a random table to
> In the gameshow The Price Is Right, two players get to spin a wheel with the values 05, 10, 15,……….. ,95, 100 on it. In the game, Player 1 spins the wheel one time and gets to decide whether he/she would like to spin a second time in the hope that the su
> A_____ is an ordered arrangement of r objects chosen from n distinct objects without repetition.
> According to the Sefton Council Password Policy (August 2007), the United Kingdom government recommends the use of “Environ passwords with the following format: consonant, vowel, consonant, consonant, vowel, consonant, number, number (for example, pinray
> The Federal Bureau of Investigation (FBI) maintains a records system that houses civil background checks and criminal histories in a database. Each file has its own identification number (ID). With its initial algorithm for generating IDs, the system wil
> The same community college from Problem 9 has 7656 students currently enrolled in classes. To gain the students’ opinions about an upcoming building project, the college president wishes to obtain a simple random sample of 20 students. He numbers the stu
> Suppose that you have just received a shipment of 100 televisions. Although you don’t know this, 6 are defective. To determine whether you will accept the shipment, you randomly select 5 televisions and test them. If all 5 televisions work, you accept th
> Suppose that you have just received a shipment of 20 modems. Although you don’t know this, 3 of the modems are defective. To determine whether you will accept the shipment, you randomly select 4 modems and test them. If all 4 modems work, you accept the
> Follow the outline presented in Problem 67 to determine the probability of being dealt exactly one pair.
> You are dealt 5 cards from a standard 52-card deck. Determine the probability of being dealt three of a kind (such as three aces or three kings) by answering the following questions: (a) How many ways can 5 cards be selected from a 52-card deck? (b) Each
> Through a manufacturing error, three cans marked “regular soda” were accidentally filled with diet soda and placed into a 12-pack. Suppose that three cans are randomly selected from the 12-pack. (a) Determine the probability that exactly two contain d
> Suppose a Spotify playlist you just created has 13 tracks. After listening to the playlist, you decide that you like 5 of the songs. The random feature on Spotify is set up to play each of the 13 songs once in a random order. Find the probability that am
> A box containing twelve 40-watt light bulbs and eighteen 60-watt light bulbs is stored in your basement. Unfortunately, the box is stored in the dark and you need two 60-watt bulbs. What is the probability of randomly selecting two 60-watt bulbs from the
> Suppose that a shipment of 120 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality- control engineer randomly selects 4 of the components and tests them. If 1 or more of the components is
> Suppose that there are 55 Democrats and 45 Republicans in the U.S. Senate. A committee of seven senators is to be formed by selecting members of the Senate randomly. (a) What is the probability that the committee is composed of all Democrats? (b) What is
> The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability
> In Mega Millions, an urn contains balls numbered 1–56, and a second urn contains balls numbered 1–46. From the first urn, 5 balls are chosen randomly, without replacement and without regard to order. From the second urn, 1 ball is chosen randomly. For a
> In the Illinois Lottery game Little Lotto, an urn contains balls numbered 1–39. From this urn, 5 balls are chosen randomly, without replacement. For a $1 bet, a player chooses one set of five numbers. To win, all five numbers must match those chosen from
> A baseball team consists of three outfielders, four infielders, a pitcher, and a catcher. Assuming that the outfielders and infielders are indistinguishable, how many batting orders are possible?
> A golf-course architect has four linden trees, five white birch trees, and two bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?
> How many distinguishable DNA sequences can be formed using one A, four Cs, three Gs, and four Ts?
> How many distinguishable DNA sequences can be formed using three As, two Cs, two Gs, and three Ts?
> A family has eight children. If this family has exactly three boys, how many different birth and gender orders are possible?
> A family has six children. If this family has exactly two boys, how many different birth and gender orders are possible?
> How many different simple random samples of size 7 can be obtained from a population whose size is 100?
> How many different simple random samples of size 5 can be obtained from a population whose size is 50?
> To complete the Citizenship in the World merit badge, one must select two of the following seven organizations and describe their role in the world. Source: Boy Scouts of America 1. The United Nations 2. The World Court 3. World Organization of the Scout
> In the U.S. Senate, there are 21 members on the Committee on Banking, Housing, and Urban Affairs. Nine of these 21 members are selected to be on the Subcommittee on Economic Policy. How many different committee structures are possible for this subcomm
> A lottery exists where balls numbered 1–25 are placed in an urn. To win, you must match the four balls chosen in the correct order. How many possible outcomes are there for this game?
> Four members from a 50-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fou
> Four members from a 20-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fou
> In how many ways can the top 2 horses finish in a 10-horse race?
> Suppose 40 cars start at the Indianapolis 500. In how many ways can the top 3 cars finish the race?
> How many different license plate numbers can be made by using one letter followed by five digits selected from the digits 0 through 9?
> A combination lock has 50 numbers on it. To open it, you turn counterclockwise to a number, then rotate clockwise to a second number, and then counterclockwise to the third number. Repetitions are allowed. (a) How many different lock combinations are the
> How many user names are possible in Problem 41 if the last character must be a digit?
> Suppose that a local area network requires eight letters for user names. Lower- and uppercase letters are considered the same. How many user names are possible for the local area network?
> A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program. EPR 616, Research in Child Development EPR 630, Educational Research Planning and Interpret
> A Social Security number is used to identify each resident of the United States uniquely. The number is of the form xxx–xx–xxxx, where each x is a digit from 0 to 9. (a) How many Social Security numbers can be formed? (b) What is the probability of corre
> Outside a home there is a keypad that will open the garage if the correct four-digit code is entered. (a) How many codes are possible? (b) What is the probability of entering the correct code on the first try, assuming that the owner doesn’t remember the
> Companies whose stocks are listed on the NASDAQ stock exchange have their company name represented by either four or five letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the NASDAQ?
> Companies whose stocks are listed on the New York Stock Exchange (NYSE) have their company name represented by either one, two, or three letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the New Yor
> The music player on an iPhone plays each of 10 songs. Once a song is played, it is not repeated until all the songs have been played. In how many different ways can the player play the 10 songs?
> A salesperson must travel to eight cities to promote a new marketing campaign. How many different trips are possible if any route between cities is possible?
> In how many ways can 15 students be lined up?
> Suppose Dan is going to create a Spotify playlist with 12 songs. In how many ways can the 12 songs be played without repetition?
> A woman has five blouses and three skirts. Assuming that they all match, how many different outfits can she wear?
> A man has six shirts and four ties. Assuming that they all match, how many different shirt-and-tie combinations can he wear?
> A coach must select two players to serve as captains. He wants to randomly select two players to be the captains. Obtain a simple random sample of size 2 from the following list: Mady, Breanne, Evin, Tori, Emily, Clair, Caty, Jory, Payton, Jordyn. Write
> List all the combinations of four objects a, b, c, and d taken two at a time. What is 4C2?
> List all the combinations of five objects a, b, c, d, and e taken two at a time. What is 5C2?
> List all the permutations of four objects a, b, c, and d taken two at a time without repetition. What is 4P2?
> List all the permutations of five objects a, b, c, d, and e taken two at a time without repetition. What is 5P2?
> 30C4
> 48C3
> 40C40
> 52C1
> 12C3
> 10C2
> As part of a college literature course, students must read three classic works of literature from the provided list. Obtain a simple random sample of size 3 from this list. Write a short description of the process you used to generate your sample.
> 9C2
> 8C3
> 9P4
> 8P3
> 4P0
> 5P0
> 7P7
