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A Pathway To Introductory Statistics 1st Edition Jay Lehmann - Solutions
If five coins are flipped, what is the probability (in fraction form) that all the outcomes are heads?
If a six-sided die is rolled three times, what is the probability (in fraction form) that all the outcomes are fives?
In a survey of 2000 American adults, 57% of women have experienced street verbal harassment (Source: Stop Street Harassment). If four women are randomly selected with re- placement from the sample, what is the probability that they all have experienced street harassment? Round your result to three
A student guesses the answers to four multiple-choice test questions that each have five choices. What is the probability (in fraction form) that the student guesses the correct answers for all four questions?
In a study of 1004 randomly selected adults, 37% of the sample described themselves as middle class. a. If four participants of the study are randomly selected with replacement, what is the probability that all four describe themselves as middle class? Round your result to five decimal places. b.
In an online survey of 1.2 million Americans, 34% of the sample say McDonald’s makes the best French fries of all fast- food chains. a. If three participants of the study are randomly selected with replacement, what is the probability that all three participants say McDonald’s makes the best
In a survey of 34,525 randomly selected adults, 18.1% of the sample smoke cigarettes. a. If five participants of the study are randomly selected with replacement, find the probability that all five participants smoke cigarettes. Round your result to five decimal places. b. If five participants of
On the basis of physical examinations of approximately 40,000 Americans at least 12 years of age, researchers deter- mined that 20.3% of the sample had hearing loss. a. If four individuals of the study are randomly selected with replacement, find the probability that all four individuals have
A total of 34,695 adults were asked whether they agreed with the following statement: €œI often feel that my values are threatened by Hollywood and the entertainment industry.€ Table 24 compares the adults€™ responses and their ages.a. Find the probability that a
A total of 34,695 adults were asked whether they agreed with the following statement: €œEvolution is the best explanation for the origins of human life on earth.€ Table 25 compares the adults€™ responses and their ages.a. Find the probability that a person randomly
A random selection of 1481 adults were asked whether upper- income people pay too much, too little, or their fair share of taxes. Table 26 compares their responses and their political affiliations.One person is randomly selected from the sample. Let F be the event that the person thinks
A random selection of 1481 adults were asked whether upper- income people pay too much, too little, or their fair share of taxes. Table 26 compares their responses and their political affiliations. One person is randomly selected from the sample. Let L be the event that the person thinks
A six-sided die is rolled four times.a. Find the probability (in fraction form) of rolling a 2, then a 6, then a 4, and then a 1.b. Find the probability (in fraction form) of rolling all 6s.c. Compare the results you found in parts (a) and (b).d. A student says the result you found in part (b)
A coin is flipped six times.a. Find the probability (in fraction form) of alternating between getting tails and heads, beginning with tails: THTHTH.b. Find the probability (in fraction form) of getting all tails.c. Compare the results you found in parts (a) and (b).d. A student says the result you
A coin is flipped seven times.a. What is the probability (in fraction form) of getting all tails?b. What is the probability (in fraction form) of getting a tail on the seventh toss, given the first six tosses were all tails?c. Compare the results you found in parts (a) and (b).d. A student says the
A six-sided die is rolled five times.a. What is the probability (in fraction form) of getting all 3s?b. What is the probability (in fraction form) of getting a 3 on the fifth roll, given the first four rolls were all 3s?c. Compare the results you found in parts (a) and (b).d. A student says the
Find P (even number | at least 3) A person rolls a six-sided die once. When finding a probability, write it in fraction form.
increased by 10 points and s stayed the sameSuppose that students in an algebra class take a first test and their scores (in points) are described well by the normal curve shown in Fig. 85. The given information describes how the mean and standard deviation changed on the second test. Assuming the
decreased by 10 points and s stayed the same.Suppose that students in an algebra class take a first test and their scores (in points) are described well by the normal curve shown in Fig. 85. The given information describes how the mean and standard deviation changed on the second test. Assuming the
stayed the same and s decreased.Suppose that students in an algebra class take a first test and their scores (in points) are described well by the normal curve shown in Fig. 85. The given information describes how the mean and standard deviation changed on the second test. Assuming the scores on
stayed the same and s increased.Suppose that students in an algebra class take a first test and their scores (in points) are described well by the normal curve shown in Fig. 85. The given information describes how the mean and standard deviation changed on the second test. Assuming the scores on
increased by 10 points and s decreased.Suppose that students in an algebra class take a first test and their scores (in points) are described well by the normal curve shown in Fig. 85. The given information describes how the mean and standard deviation changed on the second test. Assuming the
The heights (in inches) of NBA basketball player draft picks are described by the density histogram in Fig. 86. The heights of the bars were drawn using densities rounded to the second place to make it easier to estimate the heights of the barsa. Estimate the area of each of the six bars of the
The hourly temperatures (in degrees Fahrenheit) at Eppley Airfield Airport in Omaha, Nebraska, in May 2014 are de- scribed by the density histogram in Fig. 87. The heights of the bars were drawn using densities rounded to one of the values shown on the vertical axis to make it easier to estimate
Smoke alarms with a UL label have been certified to last 10 years (Source: Underwriters Laboratories). Assume the lifetimes of smoke alarms with a UL label are normally distributed with mean 10.8 years and standard deviation 0.3 year. Find the probability that a randomly selected smoke alarm with a
A researcher measured the lifetimes of some zinc-air batteries when used for hearing aids. For the Activair® 13 HPX batteries, the mean lifetime was 252.4 hours and the standard deviation was 18.4 hours. For the Rayovac® 13 AE battery, the mean lifetime was 272.1 hours and the standard deviation
Recall that scores on the Wechsler IQ test are normally distributed with mean 100 points and standard deviation 15 points. If a prisoner has a low enough IQ, it is against the law to sentence the prisoner to death. Florida used to have an inflexible cutoff of 70 points to decide whether prisoners
For students who graduated from high school in 2013, their SAT math scores were approximately normally distributed with a mean of 514 points and a standard deviation of 118 points (Source: College Board).a. If a student is randomly selected from those who graduated from high school in 2013 and took
For students who graduated from high school in 2013, the ACT math scores are approximately normally distributed with mean 20.9 points and standard deviation 5.3 points.a. If a freshman at Thomas More College (TMC) scored 17 points on the math sections of the ACT, the student was required to take a
For students who graduated from high school in 2013, their SAT math scores had a mean of 514 points and a standard deviation of 118 points.a. Assuming the SAT math scores are normally distributed, find the percentiles for the following scores (in points): 400, 600, and 800.b. Table 30 displays some
For students who graduated from high school in 2013, their ACT English scores had a mean of 20.2 points and a standard deviation of 6.5 points.a. Assuming the ACT English scores are normally distributed, find the percentiles for the following scores (in points): 15, 25, and 35.b. Table 31 displays
HDL is the “good” cholesterol. The higher a person’s HDL level, the lower the person’s risk of heart attack and stroke will be. In a study of 1751 women in their twenties, the women’s HDL cholesterol levels are approximately normally distributed with mean 55 mg/dl and standard deviation
HDL is the “good” cholesterol. The higher a person’s HDL level, the lower the person’s risk of heart attack and stroke will be. In a study of 1541 men in their twenties, the men’s HDL cholesterol levels are approximately normally distributed with mean 47 mg/dl and standard deviation 12.5
The risk of coronary disease for diabetes patients is related not only to the mean glucose level in the bloodstream but also to the standard deviation.a. A diabetes patient we will call Frank posted online that his blood glucose has mean 93.1 mg/dL and standard deviation 41.5 mg/dL. Dr. Irl B.
The lower a person’s bone mineral density (BMD), the greater the person’s risk of a bone fracture will be. BMD levels of 75-year-old Caucasian women’s hips are approximately normally distributed with mean 740 mg/cm2 and standard deviation 129 mg/cm2. a. Find the probability of randomly
A total of 940 healthy, pregnant women between 20 and 34 years of age participated in a study. Their lengths (in days) of pregnancy are approximately normally distributed (see the normal curve in Fig. 88).a. Interpret the area of the orange region in Fig. 88 as a probability. b. Interpret the area
In a study of U.S. veteran patients undergoing a first liver transplant, the ages (in years) of patients are approximately normally distributed (see the normal curve in Fig. 89).Interpret the area of the orange region in Fig. 89 as a a. Probability. b. Proportion. c. Percentile.
In a study of African American and Caucasian girls of ages 9 and 10 years, the girls recorded their diets in a diary for three days. The researcher then computed the daily salt intake. The distribution of daily salt intakes for the African American girls has a mean of 3073 mg and a standard
In a study of African American and Caucasian girls of ages 9 and 10 years, the girls recorded their diets in a diary for three days. The researcher then computed the daily salt intake. The distribution of daily salt intakes for the African American girls has a mean of 3073 mg and a standard
The age distribution of prisoners on death row in Florida has mean 48.4 years and standard deviation 11.0 years.a. Assuming the distribution is normally distributed, find the probability that a randomly selected death-row prisoner in Florida isi. Between 40 and 60 years of age.ii. Between 30 and 70
In 2013, 4579 runners completed the Great Cow Harbor 10K Run in Northport, New York. Their age distribution has mean 40.2 years and standard deviation 12.4 years.a. Assuming the distribution is normally distributed, find the probability that a randomly selected runner’s age wasi. Between 40 and
Access the data about sea levels, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website. Did you know that the sea level varies around the Earth and is increasing at different rates? For example, the sea level along the West Coast of the
Access the data about lengths of alternative rock songs, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website. At the start of this section, we analyzed the lengths of songs played on the alternative rock radio station Live 105. You will
Explain why the area under a normal curve is equal to 1. Include a comparison to a density histogram in your explanation.
Explain why a normal curve for a distribution with larger standard deviation is wider and flatter than a normal curve for a distribution with smaller standard deviation.
Describe how to compute a z-score. What does it mean?
The wait times of 2444 patients at 18 health care clinics in the Wake Forest University Baptist Medical Center located in Winston-Salem, North Carolina, were studied. The mean wait time was 21.0 minutes with standard deviation 14.7 minutes.a. Explain why the wait-time distribution cannot be normal
The wait times of 4534 patients at an emergency department in a hospital in Akron, Ohio, were studied. The mean wait time was 63.7 minutes with standard deviation 62.4 minutes.a. Explain why the wait-time distribution cannot be normal or even approximately normal.b. On the basis of the mean,
American women’s heights are approximately normally distributed with mean 63.8 inches and standard deviation 4.2 inches. American men’s heights are approximately normally distributed with mean 69.4 inches and standard deviation 4.7 inches (Source: National Health Statistics Report). a. At what
American women’s heights are approximately normally distributed with mean 63.8 inches and standard deviation 4.2 inches. American men’s heights are approximately normally distributed with mean 69.4 inches and standard deviation 4.7 inches (Source: National Health Statistics Report).a. What
The age distribution of inmates on death row in Alabama is approximately normal with mean 43.0 years and standard deviation 9.7 years (Source: Alabama Department of Corrections).a. What age is at the 10th percentile?b. What age is at the 90th percentile?c. According to the normal-curve model, what
The age distribution of prisoners on death row in Florida has mean 48.4 years and standard deviation 11.0 years (Source: Florida Department of Corrections).a. What age is at the 10th percentile?b. What age is at the 90th percentile?c. According to the normal-curve model, what percentage of
One way to measure a person’s reading fluency is to have him or her read an unpracticed passage for one minute. The researcher then counts the number of words read correctly, which is called words correct per minute (WCPM). In a study at a private college in the Northeast, the WCPMs of
One way to measure a person’s reading fluency is to have them read an unpracticed passage for one minute. The researcher then counts the number of words read correctly, which is called words correct per minute (WCPM). The WCPMs for eighth-graders are approximately normally distributed with mean
Students A and B took tests on probability in two different sections of prestatistics. Student A scored 81 points on a test with mean 73 points and standard deviation 3 points. Student B scored 92 points on a test with mean 74 points and standard deviation 8 points.a. Find the z-score for Student
Students A and B took tests on probability in two different sections of prestatistics. Student A scored 89 points on a test with mean 74 points and standard deviation 7 points. Student B scored 78 points on a test with mean 66 points and standard deviation 4 points.a. Find the z-score for Student
For students who graduated from high school in 2013, the means and standard deviations of SAT and ACT math test scores are shown in Table 33. Assume the distributions are normally distributed. Many students who apply to top colleges take both tests and submit their better performance in their
For students who graduated from high school in 2013, the means and standard deviations of SAT and ACT math test scores are shown in Table 33. Assume the distributions are normally distributed. Many students who apply to top colleges take both tests and submit their better performance in their
In a study of 1541 men in their twenties, the men’s HDL cholesterol levels are approximately normally distributed with mean 47 mg/dl and standard deviation 12.5 mg/dl. In a study of 823 men in their fifties, the men’s HDL cholesterol levels are approximately normally distributed with mean 44
In a study of 1744 women in their thirties, the women’s HDL cholesterol levels are approximately normally distributed with mean 54 mg/dl and standard deviation 15.0 mg/dl. In a study of 955 women in their fifties, the women’s HDL cholesterol levels are approximately normally distributed with
The lower a person’s bone mineral density (BMD), the greater the person’s risk of a bone fracture will be. BMD levels of 45-year-old African American women’s hips are approximately normally distributed with mean 1034 mg/cm2 and standard deviation 160 mg/cm2a. A 45-year-old African American
The lower a person’s bone mineral density (BMD), the greater the person’s risk of a bone fracture will be. BMD levels of 45-year-old Caucasian women’s hips are approximately normally distributed with mean 920 mg/cm2 and standard deviation 136 mg/cm2.a. A 45-year-old Caucasian woman’s hip
Recall that scores on the Wechsler IQ test are normally distributed with mean 100 points and standard deviation 15 points.a. A student’s IQ is at the 95th percentile. Find the student’s IQ. Is it an unusual IQ?b. Mensa is a high-IQ society with members in more than 100 countries. Membership is
Recall that score son the Wechsler IQ test are normally distributed with mean 100 points and standard deviation 15 points.a. A student’s IQ is at the 87th percentile. Find the student’s IQ. Is it an unusual IQ? Explain.b. Alexis Martin, who just turned 3 years old, has an IQ of 160 points. She
American women’s heights are approximately normally distributed with mean 63.8 inches and standard deviation 4.2 inches. American men’s heights are approximately normally distributed with mean 69.4 inches and standard deviation 4.7 inches. a. Tulsa Cambage and Phoenix Griner are the two tallest
American women’s heights are approximately normally distributed with mean 63.8 inches and standard deviation 4.2 inches. American men’s heights are approximately normally distributed with mean 69.4 inches and standard deviation 4.7 inches.a. Tamara De Treaux played the role of the alien in the
For students who graduated from high school in 2013, their SAT math scores are approximately normally distributed with a mean of 514 points and a standard deviation of 118 points. a. A student who graduated from high school in 2013 scored 704 points on the math sections of the SAT. Is that an un-
For students who graduated from high school in 2013, their ACT math scores are approximately normally distributed with mean 20.9 points and standard deviation 5.3 points.a. Is 25 points an unusual score on the math sections of the ACT? Explain.b. Is 35 points an unusual score on the math sections
A company claims that its low-salt tortillas contain only 130 mg of sodium per serving on average. An independent company randomly selects a package of the tortillas, which turns out to contain 141 mg of sodium per serving. a. Assuming the sodium levels per serving of the low-salt tortillas are
A company claims that its low-fat yogurt contains only 3 g of fat per cup on average. An independent company randomly selects a cup of the yogurt, which turns out to contain 3.5 g of fat. a. Assuming the fat levels per cup of the yogurt are approximately normally distributed with mean 3 g and
A pizza restaurant claims that its mean delivery time is 30 minutes. An independent company times a randomly selected delivery, which takes 40 minutes. a. Assuming the delivery times are approximately normally distributed with mean 30 minutes and standard deviation 4 minutes, find the probability
A car company claims that its only hybrid car has a highway gas mileage of 40 mpg on average. An independent company randomly selects one of the cars, which turns out to have a gas mileage of 38 mpg.1. Assuming the gas mileages of the cars are approximately normally distributed with mean 40 mpg and
A car company claims that its only hybrid car has a highway gas mileage of 40 mpg on average. An independent company randomly selects one of the cars, which turns out to have a gas mileage of 38 mpg. a. Assuming the gas mileages of the cars are approximately normally distributed with mean 40 mpg
A company claims that its high-protein shake contains 30 g of protein per serving on average. An independent company randomly selects a package of the shake, which turns out to contain 28.6 g of protein per serving. a. Assuming the protein levels per serving of the shake are approximately normally
A husband is taller than his wife. A student says the husband’s relative height (compared with other men) is there- fore greater than the women’s relative height (compared with other women). What would you tell the student?
Recall that a boxplot consists of four parts: the left whisker, the left part of the box, the right part of the box, and the right whisker. Assume a boxplot is constructed for a normal distribution.a. Is the left whisker longer, shorter, or the same length as the right whisker? Explain.b. Is the
Describe two methods to determine whether an observation is unusual. In your opinion, which method is easier? Explain.
Are the events odd and black independent? Red: 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 Black: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 Green: 0, 00
A total of 801 adults were asked whether they prefer to drink coffee, tea, or neither. Table 34 compares the adults€™ responses with their ages.Suppose that one person in the sample is randomly selected.a. Find P (coffee | 18-29 years).b. Find P (coffee | 30-44 years).c. Find P (coffee | 45-64
A total of 801 adults were asked whether they prefer to drink coffee, tea, or neither. Table 34 compares the adults’ responses with their ages. a. Find the probability that a person randomly selected from the study prefers tea. b. Find the probability that a person randomly selected from the
In a survey of 1000 randomly selected adults, 68% of the respondents think that the government should require parents to have their children vaccinated. a. If five individuals of the study are randomly selected, find the probability that all five individuals think that the government should require
The ages of Americans who died from alcohol poisoning are normally distributed with mean 46.6 years and standard deviation 12.5 years (Source: Centers for Disease Control and Prevention). a. Find the proportion of alcohol-poisoning fatalities in which the victims were under the minimum drinking age
For students who graduated from high school in 2013, their SAT math scores are approximately normally distributed with a mean of 514 points and a standard deviation of 118 points. Their ACT math scores are approximately normally distributed with mean 20.9 points and standard deviation 5.3 points.a.
A company claims that its cheddar cheese contains 3.5 g of fat per serving on average. An independent company randomly selects a package of the cheese, which turns out to contain 3.8 g of fat per serving. a. Assuming the fat levels per serving of the cheese are approximately normally distributed
P (red OR at least 26) Red: 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 Black: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 Green: 0, 00 Consider the random experiment of dropping the ball onto the wheel once. When finding a probability, write it in
The Trends in International Mathematics and Science Study (TIMSS) measures the mathematical achievement of eighth- graders of various countries.a. The scores of countries in 2007 are approximately normally distributed with mean 454.1 points and standard deviation 74.2 points. Is the United
A company claims that its low-salt potato chips contain only 85 mg of sodium per serving on average. An independent company randomly selects a package of the potato chips, which turns out to contain 93 mg of sodium per serving. a. Assuming the sodium levels per serving of the low-salt potato chips
In a study of patients with coronary heart disease, 605 patients were randomly assigned to follow a Mediterranean- type diet or the step 1 American Heart Association (AHA) prudent diet for four years. Table 35 describes whether the individuals were healthy (other than having coronary heart
For students who graduated from high school in 2013, their SAT math scores were approximately normally distributed with a mean of 514 points and a standard deviation of 118 points (Source: College Board). a. If a student is randomly selected from those who graduated from high school in 2013 and
Let h be the height (in inches) of a professional basketball player, and let P be the player’s mean points scored per game. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
Let c be a person’s cholesterol level (in mg/dl) after ingesting d milligrams of an experimental cholesterol drug each day for one month. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical
Let p be the percentage of men at age a year’s who have gray hair. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
Let T be the increase in height (in feet) of a tree one year after n experimental fertilizer stakes were driven into the ground 10 feet from the tree’s trunk. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How
Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis? Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system?
Let t be the number of seconds after a baseball is hit upward, and let h be the baseball’s height (in feet). Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
Let p be the percentage of people at age a years who own a computer. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
Let T be the total number of T-shirts (in thousands) a hip-hop group sells at C concerts per year. A group sells a total of 29.4 thousand T-shirts at 98 concerts in a year.Describe the situation with an ordered pair. Which variable should be described by the horizontal axis of a coordinate system?
Let B be the bonus (in thousands of dollars) a car dealership pays a salesperson if the salesperson makes a quota of selling at least 15 cars in a month, and let n be the number of sales- people who make the quota. A dealership offers a bonus of $3 thousand for making the quota, and 4 salespeople
Let n be the number (in millions) of Americans impacted by bans or fees on single-use plastic bags, and let t be the number of years since 2010. In 2014, 18.3 million Americans were impacted by bans or fees on single-use plastic bags (Source: Earth Policy Institute).Describe the situation with an
The numbers of nominees for best picture at the Academy Awards and the numbers of winners are compared in the scatterplot in Fig. 16 for 17 genres. The genres were determined by the description of the movies at IMDb. If a nominated or winning movie is described as being a combination of genres,
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