Suppose that events E and F are independent. In addition, P(E) = 0.45 and P(F) = 0.2. What is P(E and F)?
> The area between z = -0.34 and z = 1.03.
> The graph shows the ratings on Yelp for Hot Doug’s Restaurant. (a) Which was the most popular rating for Hot Doug’s? (b) How many ratings were posted on Hot Doug’s? (c) How many more 5 Star ratings are there than 4 Star ratings? (d) What percentage of ra
> Explain how to use a normal probability plot to assess normality.
> Explain the difference between a lurking variable and a confounding variable.
> The area to the left of z = -1.04.
> Researchers Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone mineral density. They looked at 1125 men and 1413 women in the Framingham Osteoporosis Study, which is a cohort that began in 1971.
> A pharmaceutical company has developed an experimental drug meant to relieve symptoms associated with the common cold. The company identifies 300 adult males 25 to 29 years old who have a common cold and randomly divides them into two groups. Group 1 is
> List the properties of the normal density curve.
> Nucryst Pharmaceuticals, Inc., announced the results of its first human trial of NPI 32101, a topical form of its skin ointment. A total of 225 patients diagnosed with skin irritations were randomly divided into three groups as part of a double-blind, pl
> A continuous random variable X is uniformly distributed with / (a) Draw a graph of the uniform density function. (b) What is / (c) What is /
> Does the shape of a glass play a role in determining the amount of time it takes to finish the drink? Researchers identified 159 male and female self- professed social drinkers. One week the subjects were given a 12 ounce beer with either a straight g
> According to a USA Today “Snapshot,” 20% of adults surveyed do their most creative thinking while driving. You conduct a survey of 250 adults and find that 30 do their most creative thinking while driving. (a) Compute the probability that, in a random sa
> Each of the following surveys has bias. Identify the type of bias. (a) A television survey that gives 900 phone numbers for viewers to call with their vote. Each call costs $2.00. (b) An employer distributes a survey to her 450 employees asking them how
> In 1798, Henry Cavendish obtained 27 measurements of the density of Earth, using a torsion balance. The following data represent his estimates, given as a multiple of the density of water. Is it reasonable to conclude that the sample data come from a pop
> Describe what is meant by an experiment that has a completely randomized design.
> Hector obtained a random sample of twenty recent college graduates who own cars and asked each to disclose the age of their car (in months). Is it reasonable to conclude that age of car is normally distributed? The normal probability plot is shown below
> Use the results in the table to (a) draw a normal plot, (b) determine the linear correlation between the observed values and expected z-scores, (c) determine the critical value in Table VI to assess the normality of the data.
> A school psychologist wants to test the effectiveness of a new method for teaching reading. She recruits 500 first-grade students in District 203 and randomly divides them into two groups. Group 1 is taught by means of the new method, while group 2 is ta
> A casino manager wants to inspect a sample of 14 slot machines in his casino for quality-control purposes. There are 600 sequentially numbered slot machines operating in the casino. Obtain a systematic sample of 14 slot machines. Be sure to discuss how y
> According to a Gallup poll, 46% of Americans 18 years old or older stated that they had read at least six books (fiction and nonfiction) within the past year. You conduct a random sample of 250 Americans 18 years old or older and ask the individuals to d
> A farmer has a 500-acre orchard in Florida. Each acre is subdivided into blocks of 5. Altogether, there are 2500 blocks of trees on the farm. After a frost, he wants to get an idea of the extent of the damage. Obtain a sample of 10 blocks of trees using
> According to Major League Baseball rules, the ball must weigh between 5 and 5.25 ounces. A factory produces baseballs whose weights are approximately normally distributed, with mean 5.11 ounces and standard deviation 0.062 ounce. Source: www.baseball-alm
> A congresswoman wants to survey her constituency regarding public policy. She asks one of her staff members to obtain a sample of residents of the district. The frame she has available lists 9012 Democrats, 8302 Republicans, and 3012 Independents. Obtain
> The Wechsler Intelligence Scale for Children is approximately normally distributed, with mean 100 and standard deviation 15. (a) What is the probability that a randomly selected test taker will score above 125? (b) What is the probability that a randomly
> A cellular phone company is looking for ways to improve customer satisfaction. They want to select a simple random sample of four stores from their 15 franchises in which to conduct customer satisfaction surveys. Discuss the procedure you would use, and
> Suppose that Dunlop Tire manufactures a tire with a lifetime that approximately follows a normal distribution with mean 70,000 miles and standard deviation 4400 miles. (a) What proportion of the tires will last at least 75,000 miles? (b) Suppose that Dun
> List the steps required to conduct an experiment.
> Use the figure to answer the questions that follow. (a) What is ? (b) What is ? (c) Suppose that the area under the normal curve to the right of x = 75 is 0.0668. Provide two interpretations for this area. (d) Suppose that the area under the normal cur
> To determine if topiramate is a safe and effective treatment for alcohol dependence, researchers conducted a 14-week trial of 371 men and women aged 18 to 65 years diagnosed with alcohol dependence. In this double-blind, randomized, placebo-controlled ex
> Explain why it is important to use a control group and blinding in an experiment.
> State the condition required to use the Empirical Rule to check for unusual observations in a binomial experiment.
> Compare and contrast observational studies and designed experiments. Which study allows a researcher to claim causality?
> Consider a binomial probability distribution with parameters n = 8 and p = 0.75. (a) Construct a binomial probability distribution with these parameters. (b) Compute the mean and standard deviation of the distribution. (c) Graph the discrete probability
> Contrast the three major types of observational studies in terms of the time frame when the data are collected.
> According to a Gallup poll, 60% of U.S. women 18 years old or older stated that the minimum driving age should be 18. In a random sample of 15 U.S. women 18 years old or older, find the probability that: (a) Exactly 10 believe that the minimum driving ag
> A pollster asks 800 adult Americans whether the gap between the rich and poor will grow or shrink over the next 30 years.
> The probability that a randomly selected patient who visits the emergency room (ER) will die within 1 year of the visit is 0.05. Source: SuperFreakonomics. (a) What is the probability that exactly 1 of 10 randomly selected visitors to the ER will die wit
> A random sample of 30 digital cameras is selected and divided into two groups. One group uses a brand-name battery, while the other uses a generic plain-label battery. All variables besides battery type are controlled. Pictures are taken under identical
> Determine whether the probability experiment represents a binomial experiment. If not, explain why. (a) According to the Chronicle of Higher Education, the probability that a randomly selected incoming freshman will graduate from college within 6 years i
> Researchers wanted to determine the association between number of times one chews food and food consumption. They identified 45 individuals who were 18 to 45 years of age. First, the researchers determined a baseline for number of chews before swallowing
> The number of surface imperfections on a camera lens.
> A popular casino table game is three-card poker. One aspect of the game is the “pair plus” bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of the hand the dealer has. The table shows the profit and probability o
> Video game rating system by the Entertainment Software Rating Board (EC, E, E10 +, T, M, AO, RP)
> The Stanley Cup is a best-of-seven series to determine the champion of the National Hockey League. The following data represent the number of games played, X, in the Stanley Cup before a champion was determined from 1939 to 2019. Note: There was no champ
> Determine whether the distribution is a discrete probability distribution. If not, state why.
> According to the article “Self-injurious Behaviors in a College Population,” 17% of undergraduate or graduate students have had at least one incidence of self- injurious behavior. The researchers conducted a survey of 40 college students who reported a h
> In sampling from finite populations without replacement, the assumption of independence required for a binomial experiment is violated. Under what circumstances can we sample without replacement and still use the binomial probability formula to approxima
> Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of students in a randomly selected elementary school classroom (b) The amount of snow that falls in Minneapoli
> Suppose that P(E) = 0.8, P(F) = 0.5, and P(E and F) = 0.24. Are events E and F independent? Why?
> Generally, the goal of an experiment is to determine the effect that treatments will have on the response variable.
> Suppose that P(E) = 0.36, P(F) = 0.12, and E and F are mutually exclusive. What is P(E or F)?
> Suppose that P(E) = 0.76, P(F) = 0.45, and P(E and F) = 0.32. What is P(E or F)?
> Suppose that E = {yellow}. Compute the probability of Ec.
> E = {red or blue or yellow}
> (a) Patti and John each played 100 games of Solitaire on their smart phone. Patti won 7 of her games and estimated the probability of winning Solitaire as 0.07. John won 6 of his games and estimated the probability of winning Solitaire as 0.06. Why are t
> The following data represent the number of cases of coffee or filters sold by four sales reps in a recent sales competition. (a) What is the probability that a randomly selected case was sold by Bryce? Is this unusual? (b) What is the probability that a
> In 1996, a New York couple won $2.5 million in the state lottery. Eleven years later, the couple won $5 million in the state lottery using the same set of numbers. The odds of winning the New York lottery twice are roughly 1 in 16 trillion, described by
> During the 1998 Major League Baseball season, Mark McGwire of the St. Louis Cardinals hit 70 home runs. Of the 70 home runs, 34 went to left field, 20 went to left center field, 13 went to center field, 3 went to right center field, and 0 went to right f
> F = {green or orange}
> In the game of five-card stud, one card is dealt face down to each player and the remaining four cards are dealt face up. After two cards are dealt (one down and one up), the players bet. Players continue to bet after each additional card is dealt. Suppo
> Distinguish between nonsampling error and sampling error.
> Explain what is meant by a subjective probability. List some examples of subjective probabilities.
> Use a graphing calculator or statistical software to simulate the playing of the game of roulette, using an integer distribution with numbers 1 through 38. Repeat the simulation 100 times. Let the number 37 represent 0 and the number 38 represent 00. Use
> Because of a mistake in packaging, a case of 12 bottles of red wine contained five Merlot and seven Cabernet, each without labels. All the bottles look alike and have an equal probability of being chosen. Three bottles are randomly selected. (a) What is
> In one of Arizona’s lotteries, balls are numbered 1–35. Five balls are selected randomly, without replacement. The order in which the balls are selected does not matter. To win, your numbers must match the five selected. Determine your probability of win
> How many different simple random samples of size 8 can be obtained from a population whose size is 55?
> How many different vertical arrangements are there of 10 flags if 4 are white, 3 are blue, 2 are green, and 1 is red?
> If four students enter a classroom that has 10 vacant seats, in how many ways can they be seated?
> A license plate is designed so that the first two characters are letters and the last four characters are digits (0 through 9). How many different license plates can be formed assuming that letters and numbers can be used more than once?
> Suppose that you draw 3 cards without replacement from a standard 52-card deck. What is the probability that all 3 cards are aces?
> E = {yellow}
> Match each word or phrase to the definition.
> The Illinois Lottery’s PICK 4 game is similar to PICK 3, except a player must match a sequence of four repeatable numbers, ranging from 0 to 9, in exact order (for example, 5–8–5–1). With a single ticket, what is the probability of matching the four winn
> For the Illinois Lottery’s PICK 3 game, a player must match a sequence of three repeatable numbers, ranging from 0 to 9, in exact order (for example, 3–7–2). With a single ticket, what is the probability of matching the three winning numbers?
> According to the National Constitution Center, 18% of Americans trust organized religion. (a) If an American is randomly selected, what is the probability he or she trusts organized religion? (b) If an American is randomly selected, what is the probabili
> The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation. (a) What is the probability that a randomly selected baby born in 2017 was postterm? (b) What is the probability that a randomly selecte
> In a poll conducted by Genworth Financial, a random sample of adults was asked, “What age would you like to live to?” The results of the survey are given in the table. (a)Construct a probability model of the data. (b) Is it unusual for an individual to w
> In 2016, there were 34,439 traffic fatalities in the United States. Of these, 9477 were alcohol related. (a) What is the probability that a randomly selected traffic fatality in 2016 was alcohol related? (b) What is the probability that a randomly select
> In the game of roulette, a wheel consists of 38 slots, numbered 0, 00, 1, 2,…., 36. (See the photo in Problem 27 from Section 5.1.) To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numb
> Determine the value of each of the following: (a) 7! (b) 0! (c) 9C4 (d) 10C3 (e) 9P2 (f) 12P4
> Suppose that P(E and F) = 0.35 and P(F) = 0.7. What is P(E | F)?
> Suppose that P(E) = 0.59 and P(F | E) = 0.45. What is P(E and F)?
> What does it mean when a part of the population is under- represented?
> (a) Which among the following numbers could be the probability of an event? 0, -0.01, 0.75, 0.41, 1.34 (b) Which among the following numbers could be the probability of an event?
> The correlation between the number of visitors to the state of Florida and the number of shark attacks since 1990 is 0.946. Should the number of visitors to Florida be reduced in an attempt to reduce shark attacks? Explain your reasoning. Source: Florida
> Use Queens data and the results from Problems 3 and 5 to compute and interpret R2.
> Use the results from Problems 2 and 4 to compute and interpret R2.
> (a) Draw a scatter diagram treating x as the explanatory variable and y as the response variable. (b) Select two points from the scatter diagram, and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on th
> Using the Queens data and results from Problem 3, do the following: (a) Find the least-squares regression line, treating square footage as the explanatory variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Is the rent on the 825-squar
> Using the data and results from Problem 2, do the following: (a) Find the least-squares regression line treating fat content as the explanatory variable. (b) Draw the least-squares regression line on the scatter diagram. (c) Interpret the slope and y-int
> The following data represent the square footage and rent for apartments in the borough of Queens and Nassau County, New York. (a) On the same graph, draw a scatter diagram for both Queens and Nassau County apartments treating square footage as the explan
> A nutritionist was interested in developing a model that describes the relation between the amount of fat (in grams) in cheeseburgers at fast-food restaurants and the number of calories. She obtains the following data from the websites of the companies.
> In studies of monozygotic (identical) twins, the correlation of intelligence (IQ) scores is 0.85. (a) What or who are the individuals in this scenario? (b) What are the variables? (c) What proportion of the variability in one twin’s IQ is explained by th
> What is a closed question? What is an open question? Discuss the advantages and disadvantages of each type of question.
> In a newspaper article written in the Chicago Tribune, it was claimed that poorer school districts have shorter school days. (a) The following scatter diagram was drawn using the data supplied in the article. In this scatter diagram, the response variabl
> List the eight properties of the linear correlation coefficient.
> (a) The correlation between number of married residents and number of unemployed residents for the 50 states and Washington, DC, is 0.922. A scatter diagram of the data is shown. What type of relation appears to exist between number of marriages and numb
> Recessions are defined as two consecutive quarters of reduced national output. One measure to assess the severity of a recession is the rate of unemployment. The table shows the number of employed and unemployed residents of the United States at the peak
> Are you more likely to be satisfied with your automobile purchase when it is new or used? The following data represent the level of satisfaction of the buyer for both new and used cars. (a) How many were extremely satisfied with their automobile purchase
> In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is fa
