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) How many different arrangements are possible using only 4 letters? (c) The solution to this game has three 6-letter words. To advance to the next round, the player needs at least one of the six-letter words. If the player simply guesses, what is the probability that he or she will get one of the six-letter words on their first guess of six letters?
> Use the probability distribution from Problem 20 and a DISCRETE command for some statistical software to simulate 100 repetitions of the experiment. Approximate the mean and standard deviation of the random variable X based on the simulation. Repeat the
> After scoring a touchdown in football, the scoring team is entitled to either earn 1 extra point (by kicking the ball through goal posts) or 2 extra points (by advancing the ball past the goal line). Up until the 2016–2017 football season, teams who atte
> Some standardized tests, such as the SAT test, incorporate a penalty for wrong answers. For example, a multiple-choice question with five possible answers will have 1 point awarded for a correct answer and 1/4 point deducted for an incorrect answer. Ques
> Powerball is a multistate lottery. The following probability distribution represents the cash prizes of Powerball with their corresponding probabilities. (a)If the grand prize is $15,000,000, find and interpret the expected cash prize. If a ticket costs
> The following table shows the net winnings from a $1 bet in a video poker game. (a) Compute and interpret the expected net winnings from the player’s point of view. Round your answer to three decimal places (nearest tenth of a penny). (b) Suppose over th
> In the game of roulette, a player can place a $5 bet on the number 17 and have a 1/38 probability of winning. If the metal ball lands on 17, the player wins $175. Otherwise, the casino takes the player’s $5. What is the expected value of the game to the
> An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $50,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if
> Open the data set 1_3_17 from www.pearsonhighered.com/sullivanstats. The data set represents a list of every high school in the city of Chicago. Suppose you wish to conduct a survey of all the students enrolled for a simple random sample of 8 high school
> Blackjack is a popular casino game in which a player is dealt two cards where the value of the card corresponds to the number on the card, face cards are worth ten, and aces are worth either one or eleven. The object is to get as close to 21 as possible
> To the nearest dollar, what is the standard deviation of the value of the life insurance policy from Problem 26? Why is the value so high?
> To the nearest dollar, what is the standard deviation of the value of the life insurance policy from Problem 25? Why is the value so high?
> A life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old male for $350. According to the National Vital Statistics Report, 58(21), the probability that the male survives the year is 0.998734. Compute and interpret the
> A life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old female for $200. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. Compute and interpret
> The graph of the discrete probability distribution represents the number of rooms in rented housing units in 2017. Source: U.S. Department of Commerce. (a) What is the probability that a randomly selected rental unit has five rooms? (b) What is the proba
> The graph of the discrete probability distribution below represents the number of live births by a mother 50–54 years old who had a live birth in 2017. Source: National Vital Statistics Report. (a) What is the probability that a randomly selected 50- to
> What is the ideal number of children to have in a family? The following data represent the ideal number of children for a random sample of 900 adult Americans.
> The following data represent the number of games played in each World Series from 1923 to 2018.
> A Wendy’s manager performed a study to determine a probability distribution for the number of people, X, waiting in line during lunch. The results were as follows: (a) Verify that this is a discrete probability distribution. (b) Draw a graph of the proba
> The owner of a private food store is concerned about employee morale. She decides to survey the employees to learn about work environment and job satisfaction. Obtain a simple random sample of size 5 from the names in the given table. Write a short descr
> In the 2004 baseball season, Ichiro Suzuki of the Seattle Mariners set the record for the most hits in a season with a total of 262 hits. In the following probability distribution, the random variable X represents the number of (a) Verify that this is a
> In the following probability distribution, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. (a) Verify that this is a discrete probability distribution. (b) Draw a graph of the probabilit
> In the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households. (a) Verify this is
>
>
>
>
>
>
>
> The Future Government Club wants to sponsor a panel discussion on the upcoming national election. The club wants four of its members to lead the panel discussion. Obtain a simple random sample of size 4 from the below table. Write a short description of
>
> What is the difference between a discrete random variable and a continuous random variable? Provide your own examples of each.
> (a) The number of defects in a roll of carpet. (b) The distance a baseball travels in the air after being hit. (c) The number of points scored during a basketball game. (d) The square footage of a house.
> (a) The amount of rain in Seattle during April. (b) The number of fish caught during a fishing tournament. (c) The number of customers arriving at a bank between noon and 1:00 P.M. (d) The time required to download a file from the Internet.
> (a) The time it takes for a light bulb to burn out. (b) The weight of a T-bone steak. (c) The number of free-throw attempts before the first shot is made. (d) In a random sample of 20 people, the number with type A blood.
> (a) The number of light bulbs that burn out in the next week in a room with 20 bulbs. (b) The time it takes to fly from New York City to Los Angeles. (c) The number of hits to a website in a day. (d) The amount of snow in Toronto during the winter.
> In your own words, provide an interpretation of the mean (or expected value) of a discrete random variable.
> What are the two requirements for a discrete probability distribution?
> What is the difference between a permutation and a combination?
> Suppose that you roll a pair of dice 1000 times and get seven 350 times. Based on these results, what is the probability that the next roll results in seven?
> Which type of compound event is generally associated with multiplication? Which is generally associated with addition?
> The mayor of Justice, Illinois, asks you to poll the residents of the village and provides you with a list of the names and phone numbers of the 5832 residents of the village. (a) Discuss the procedure you would follow to obtain a simple random sample of
> What method of assigning probabilities to a simple event uses relative frequencies?
> In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers corresponding to the numbers remaining on their Lingo board. There are also three prize ball
> If the 2019 Hyundai Genesis has 2 engine types, 2 vehicle styles, 3 option packages, 8 exterior color choices, and 2 interior color choices, how many different Genesis’s are possible?
> Todd is putting together an exercise routine and feels that the sequence of exercises can affect his overall performance. He has 12 exercises to select from, but only has enough time to do 9. How many different exercise routines could he put together?
> An essay test in European History has 12 questions. Students are required to answer 8 of the 12 questions. How many different sets of questions could be answered?
> 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 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
> 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 fro
> 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?
