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 attempted to earn 1 extra point had a success rate of 0.993; teams who attempted to earn 2 extra points had a success rate of 0.480. (a) Use the concept of expected value to explain why teams would typically go for 1 extra point. (b) Use the concept of expected value to explain the justification in moving the snap for an extra point back to the 15-yard line after scoring a touchdown in professional football. Hint: The success rate of kicks where the snap is at the 15-yard line is 0.959.
> We have given population data for a variable. For each exercise, do the following tasks. a. Find the mean, μ, of the variable. b. For each of the possible sample sizes, construct a table and draw a dotplot for the sampling distribution of the sample mean
> Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.
> Does the sample size have an effect on the mean of all possible sample means? Explain your answer.
> Why is obtaining the mean and standard deviation of x¯ a first step in approximating the sampling distribution of the sample mean by a normal distribution?
> Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it?
> Suppose that a random sample of size 1 is to be taken from a finite population of size N. a. How many possible samples are there? b. Identify the relationship between the possible sample means and the possible observations of the variable under considera
> Suppose that a sample is to be taken without replacement from a finite population of size N. If the sample size is the same as the population size, a. how many possible samples are there? b. what are the possible sample means? c. what is the relationship
> Explain what the dotplots in part (c) of Exercises 7.17–7.22 illustrate about the impact of increasing sample size on sampling error. Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United States. As of
> Repeat parts (b)–(e) of Exercise 7.17 for samples of size 6. What is the relationship between the only possible sample here and the population? Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United Stat
> The Internal Revenue Service (IRS) publishes data on adjusted gross incomes in Statistics of Income, Individual Income Tax Returns. The following relative frequency histogram shows one year’s individual income tax returns for adjusted gross incomes of le
> At the beginning of this chapter, we presented a cross classification of data on eye color and hair color collected as part of a class project by students in an elementary statistics course at the University of Delaware. a. Explain what it would mean for
> We presented some information on the 12 studio albums by The Beatles, specifically, names, release dates, and number of songs per album. The following table gives the lengths, in seconds, of the songs, by album: Please Please Me (PPM), With The Beatles (
> n = 10, p = 0.2
> n = 9, p = 0.75
> n = 8, p = 0.5
> n = 6, p = 0.3
> n = 11, p = 0.75, x ≥ 8
> n = 12, p = 0.35, x ≤ 4
> n = 20, p = 0.7, x ≥ 12
> n = 7, p = 0.5, x > 3
> n = 10, p = 0.65, x < 5
> n = 9, p = 0.2, x ≤ 3
> What does it mean when sampling is done without replacement?
> n = 20, p = 0.6, x = 17
> n = 8, p = 0.35, x = 3
> n = 50, p = 0.02, x = 3
> n = 40, p = 0.99, x = 38
> n = 15, p = 0.85, x = 12
> n = 10, p = 0.4, x = 3
> In a town with 400 citizens, 100 randomly selected citizens are asked to identify their religion. The number who identify with a Christian religion is recorded.
> One hundred randomly selected U.S. parents with at least one child under the age of 18 are surveyed and asked if they have ever spanked their child. The number of parents who have spanked their child is recorded.
> A baseball player who reaches base safely 30% of the time is allowed to bat until he reaches base safely for the third time. The number of at-bats required is recorded.
> A basketball player who makes 80% of her free throws is asked to shoot free throws until she misses. The number of free- throw attempts is recorded.
> Define simple random sampling.
> Three cards are selected from a standard 52-card deck with replacement. The number of kings selected is recorded.
> Three cards are selected from a standard 52-card deck without replacement. The number of aces selected is recorded.
> A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should reform Social Security.
> An experimental drug is administered to 100 randomly selected individuals, with the number of individuals responding favorably recorded.
> A random sample of 30 cars in a used car lot is obtained, and their mileages recorded.
> A random sample of 15 college seniors is obtained, and the individuals selected are asked to state their ages.
> As a rule of thumb, if______ , the probability distribution of a binomial random variable X is approximately bell shaped.
> The expected number of successes in a binomial experiment with n trials and probability of success p is______ .
> The phrase “no more than” is represented by the math symbol ______.
> True or False: In the binomial probability distribution function, nCx represents the number of ways of obtaining x successes in n trials.
> What is a frame?
> What is a random variable?
> A major theme during the 2018 election in both the House and Senate was the popularity of President Trump (a Republican). The scatter diagram below shows the presidential approval rating (percent of registered voters who approve of the job the president
> One question from the Sullivan Statistics Survey I was “How many credit cards do you currently have?” This question was asked only of those individuals who have at least one credit card. Go to www.pearsonhighered.com/sullivanstats to obtain the survey re
> 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
> 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
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> 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
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> 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 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
