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A Pathway To Introductory Statistics 1st Edition Jay Lehmann - Solutions

Table 30 shows the mean changes in weight (in pounds) by people who took part in one of four popular diets. Forty people were randomly assigned to each of the diets. The mean changes were found after 2 months, 6 months, and 12 months.a. Which of the four groups of people had the largest mean
At the website Lending Club®, customers can either borrow money or fund money for others’ loans. Access the data about the loans funded at Lending Club in September, 2014, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website.a. Construct
Access the data about earthquakes, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website.a. Construct a pie chart of the states where earthquakes occurred. Which state had the most earthquakes?b. Construct a relative frequency histogram of
The distribution of the heights of a group of women has mean 66 inches and standard deviation 2 inches. If a 66-inch-tall woman joins the group, will the standard deviation of the heights decrease, increase, or stay the same? Explain.
A distribution of tests scores is unimodal and symmetric with mean = 60 points and standard deviation s = 10 points.a. Estimate the percentage of scores that are between 30 and 90 points.b. How many standard deviations apart are the scores 30 and 90 points?c. Use parts (a) and (b) to explain why
In general, if a distribution is unimodal and symmetric with no outliers, the range is approximately 6s (see Exercise 57). Explain why this suggests that the standard deviation of the distribution is approximately R/6, where R is the range. Exercise 57 A distribution of tests scores is unimodal and
In 2013, 4579 runners completed the Great Cow Harbor 10K Run in Northport, New York. The youngest finisher was 7 years old and the oldest finisher was 82 years old. The age distribution is unimodal and symmetric.a. What is the range of the ages?b. In Exercise 58, you found that if a distribution is
Recall from Example 3 that a household suffers from food in-security if at some point in the year the household eats less, goes hungry, or eats less nutritional meals because there is not enough money for food. The distribution of percentages of households suffering from food insecurity in a U.S.
An investor plans to invest in a stock in such a way that if the stock value increases the investor will earn money and if the stock value decreases the investor will lose money. The more the stock value changes, the more money the investor will earn or lose. The investor is trying to decide
10, 4, 7, 6, 7, 8Find the mean, median, range, standard deviation, and variance for the given data. Use the correct symbols.
The mean prices (in dollars) of regular gasoline in the 50 states on April 27, 2014, are described by the boxplot in Fig. 102.a. Estimate the mean price of regular gasoline in Hawaii, which has the highest mean price of the 50 states. b. What percentage of states have a mean regular gasoline price
At the website Lending Club®, customers can either borrow money or fund money for others€™ loans. When someone applies for a loan, Lending Club grades the potential loan from A to G, where A means the potential loan has very low risk and G means it has very high risk. A loan with grade A will
The amounts (in thousands of dollars) of loans funded at Lending Club in September 2014 are described by the boxplot in Fig. 104.a. Given that the distribution is unimodal, determine whether it is skewed left, symmetric, or skewed right. What does this mean in this situation?b. Estimate the 75th
The scores (in points) on a test are described by the boxplot in Fig. 105.a. Assume the cutoff for the grade D is 50 points and the cutoffs for the grades A, B, and C are at the 75th, 50th, and 25th percentiles, respectively. Find the cutoffs for the grades A, B, and C.b. If 32 students took the
The scores (in points) on a test are described by the boxplot in Fig. 106.a. Assume the cutoff for the grade D is 40 points and the cutoffs for the grades A, B, and C are at the 75th, 50th, and 25th percentiles, respectively. Find the cutoffs for the grades A, B, and C.b. If 40 students took the
The numbers of moons per planet for the 8 planets in our solar system are described by the boxplot in Fig. 107.a. Given that the distribution is unimodal, is it skewed left, skewed right, or symmetric? Which is a better measure of the center, the mean or the median? Explain.b. Estimate the median.
The diameter of a planet is the distance through the center of the planet from one point on the equator to the opposite side. The diameters (in thousands of kilometers) of the 8 planets in our solar system are described by the boxplot in Fig. 108.a. Given that the distribution is unimodal, is it
The author surveyed 11 of the students in one of his statistics classes. Here are the one-way distances (in miles) they drove to college:a. Find the smallest observation, the quartiles, and the largest observation.b. Find any outliers.c. Construct a boxplot.d. Given that the distribution is
In one of the author€™s statistics classes, students were asked how many people live in their households, including themselves. Here are the household sizes (in number of people) for 12 of those students:a. Find the smallest observation, the quartiles, and the largest observation.b. Find any
Here are the durations (in seconds) of wood roller coaster rides in Ohio:a. Construct a boxplot.b. What is Q3? What does it mean in this situation?c. What is the IQR? What does it mean in this situation?d. Are there any outliers? If yes, find them.e. If the result you found in part (b) were used to
Here are the 2013 tuitions (dollars) of 10 randomly selected 2-year, public colleges:a. Construct a boxplot.b. Given that the distribution is unimodal, is it skewed left, skewed right, or symmetric? Explain.c. Which would be a better measure of the center, the mean or the median? Explain.d. What is
The following data are the top 50 women€™s times (in minutes) in the 2013 ING New York City Marathon.a. Construct a boxplot.b. What is the median? What does it mean in this situation?c. What is the IQR? What does it mean in this situation?d. Which has greater range, the running times in the top
The following data are the top 50 men€™s times (in minutes) in the 2013 ING New York City Marathon.a. Construct a boxplot.b. What is the median? What does it mean in this situation?c. What is the IQR? What does it mean in this situation?d. Which has greater range, the times of the runners in
Some data with smallest observation 17 and largest observation 78 are described by the density histogram in Fig. 111. Construct a boxplot that describes the data.
Some data with smallest observation 7 and largest observation 34 are described by the density histogram in Fig. 112. Construct a boxplot that describes the data.
Amazon.com€™s prices (in dollars) of new hardcover and paperback elementary statistics textbooks on May 18, 2014, are described by the boxplots in Fig. 113.a. Which has a larger median, the paperback prices or the hardcover prices? What does that mean in this situation?b. Which has the larger
Boxplots describing the highway and city gas mileages (in miles per gallon) of all 2014 cars sold in the United States are shown in Fig. 114.a. Which has the larger median, the highway distribution or the city distribution? What does that mean in this situation?b. Which has the larger Q3, the
In 2011, Forbes surveyed 16,000 alumni (class of 2006) at more than 100 2-year business schools. Of the 30% who responded, Forbes computed the alumni€™s returns on investment from attending the schools. Fig. 115 displays boxplots of the annual tuitions (in thousands of dollars) of the 74
In 2013, Forbes surveyed 17,000 alumni (class of 2008) at more than 100 2-year business schools. Of the 27% who responded, Forbes computed the alumni€™s returns on investment from attending the schools. Fig. 116 displays boxplots of the annual tuitions (in thousands of dollars) of the 70
In Exercises 29 and 30, you analyzed the tuitions, the pre-MBA salaries, and the post-MBA salaries of the classes of 2006 and 2008, respectively, of the business schools with the best returns on investment. Boxplots comparing these observations (in thousands of dollars) for the two classes are
Muhammad Ali is considered by many to be one of the greatest heavyweight boxers in history. Boxplots of the percentages of maximum allowed rounds it took Ali to win his first 28 wins and his last 28 wins are shown in Fig. 118.a. The boxplot for the last 28 wins does not have a right whisker. How is
Access the data about the salaries (in millions of dollars) of the National Baseball League players, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website.a. Construct a boxplot of the average salaries. Given that the distribution is
Access the data about the salaries (in millions of dollars) of the National Baseball League players, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website.a. Construct a pie chart of the positions of the players.b. What proportion of the
On March 1, a group of 10 people signed up for a weight-loss program. During the next two months, the lightest person lost 10 pounds, the heaviest person gained 5 pounds, and everyone else kept their same weight.a. Did the range of the weights decrease, increase, or stay the same over the two-month
At 1 p.m., a meteorologist records the temperatures of seven locations. One hour later, the temperature of the coldest location is 1°F less, the temperature of the hottest location is 2°F more, and the temperatures of the other locations stayed the same.a. Did the range of the temperatures
The IQR of the salaries of employees at company A is larger than the IQR of the salaries of employees at company B. A student concludes that the standard deviation of the salaries at company A is larger than the standard deviation of the salaries at company B. What would you tell the student?
Some data have Q1 =6 and Q3 = 10.a. A student says the mean must be between 6 and 10. Is the student correct? If yes, explain. If no, give an example of some data that show the student is incorrect.b. A student says the range must be at least 4. Is the student correct? If yes, explain. If no, give
The author surveyed the Facebook users in one of his statistics classes, asking how many Facebook friends they had. The observations ranged from 0 to 2400 friends, with Q1 = 200, Q2 = 500, and Q3 = 900. A student constructed the boxplot shown in Fig. 119. Why is the boxplot incorrect? Construct a
The following data are the savings (in thousands of dollars) of six adults: 3, 7, 8, 10, 13, and 15.a. Find the standard deviation of the savings.b. Find the IQR of the savings.c. Suppose that the adult who had $15 thousand in savings wins $700 thousand (after taxes) from the lottery. So, the
The 2013 mean personal incomes (in thousands of dollars) of the 50 states are described by the boxplot in Fig. 101.a. Estimate the mean personal income of Connecticut, which has the largest mean personal income of all 50 states. b. Estimate the percentage of states that have mean personal incomes
The ages (in years) of tenured and tenure-eligible (TTE) male professors at 4-year colleges and universities are described by the relative frequency histogram in Fig. 122. The mean age is 51.3 years, and the standard deviation is 12.0 years.a. Why can the Empirical Rule be applied?b. Use the
The average math scores (in points) of eighth-grade students from various countries are described by the boxplot in Fig. 123.a. Given that the distribution is unimodal, determine whether it is skewed left, symmetric, or skewed right.b. Estimate Bahrain€™s average score, which is at the 25th
Here are the number (in millions) of viewers of the 10 most-watched TV series finales:a. Construct a boxplot.b. Given that the distribution is unimodal, determine whether it is skewed left, symmetric, or skewed right. What does this mean in this situation?c. Which is a better measure of the center,
Air pollution can be measured using the units average particulate pollution (PM2.5). Air pollution levels over 10 PM2.5 are considered hazardous to health by the World Health Organization (WHO). The names and the levels of pollution (in PM2.5) for the five worst U.S. cities are shown in Table
Here are the numbers of times the alternative songs and hip-hop songs in the top 100 were listened to at Last.fm during the week ending on February 15, 2015:a. Construct boxplots of the alternative distribution and the hip-hop distribution that share the same horizontal axis.b. Was the genre of the
The following data are the 2013 monthly fuel consumptions (in millions of gallons) by United Airlines.a. Find the mean. b. Find the median. c. Find the mode. d. Is the mode a reasonable measure of the center? Explain. e. United Airlines€™ fuel consumption in December 2013 was 125 million
The values (in billions of dollars) of the 73 worldwide startup companies worth at least $1 billion are described by the relative frequency histogram in Fig. 120. The values are rounded to the first decimal place.a. Describe the shape of the distribution.b. Which is larger, the mean or the median?
The values (in billions of dollars) of the worldwide startup companies worth at least $1 billion are described by the relative frequency histogram in Fig. 120. The values are rounded to the first decimal place.a. Estimate the percentile of the value of Dropbox, which is worth $10 billion.b.
On September 20, 2014, the Chicago Cubs baseball team played the Los Angeles Dodgers. The heights of pitches in which the batters did not make contact with the ball were determined by a system of cameras.a. Six of the observations were negative. Discuss various options of what could be done with
The ages (in years) of tenured and tenure-eligible (TTE) female professors at 4-year colleges and universities are described by the relative frequency histogram in Fig. 125. The ages are rounded to the ones place.a. Describe the shape of the distribution.b. Which is larger, the mean or the median?
Find the mean, median, mode, range, standard deviation, and variance of the data 92, 27, 55, 48, 80, 41, 62, 80, and 16.
Here are the sales (in thousands) of the best-selling vinyl albums in 2014:a. Find the mean sales. b. Find the standard deviation of the sales. c. Find the variance of the sales.
The scores on a first test are unimodal and symmetric with mean 75 points and standard deviation 8 points.a. Find the approximate percentage of scores within three standard deviations of the mean.b. Find the approximate percentage of scores between 67 points and 83 points.c. If 40 students took the
The 2012 infant mortality rates (deaths per 1000 births) of 195 countries are described by the boxplot in Fig. 126.a. Given that the distribution is unimodal, determine whether it is skewed left, symmetric, or skewed right. What does this mean in this situation? b. Jordan€™s infant
Here are the average numbers of tornados per month in July from 1989 to 2013 for states in which the average is at least 2 tornados per month:a. Is the variable numerical or categorical?b. Construct a boxplot.c. Given that the distribution is unimodal, determine whether it is skewed left,
A person plays a gambling game in which a six-sided die is rolled once. The person bets $5 on the numbers 1 and 2. the number 1 or 2 is rolled, the person will get the $5 he bet plus another $5. If the number 3, 4, or 5 is rolled, the person will lose the $5 he bet. If the number 6 is rolled, the
A total of 1487 randomly selected adults who are at least 22 years in age were asked, €œHow frequently do you visit quick service restaurants?€ Their responses are described by the pie chart in Fig. 16.a. Find the probability that a person randomly selected from the survey visits quick
Some randomly selected adults who are at least 22 years in age were asked, €œHow frequently do you visit quick service restaurants?€ Their responses are described by the pie chart in Fig. 16.a. Find the probability that a person randomly selected from the survey visits quick service
The simulations of flipping a coin 5 times and an additional 10,000 times are shown in Figs. 9 and 10, respectively.a. Determine the first five outcomes of the simulated experiment.b. What was the relative frequency of heads after 5 flips of the coin? Is this a good estimate of the probability of
The author surveyed students in one of his statistics classes about the number of hours they worked per week. The density histogram in Fig. 17 describes their responses.For a randomly selected student in the class, let X be the number of hours the student works per week.a. Find P(X ≥ 25).b. Find
The author surveyed students in one of his statistics classes about the number of hours they worked per week. The density histogram in Fig. 17 describes their responses. For a randomly selected student in the class, let X be the number of hours the student works per week.a. Find P(X ≥ 20).b. Find
The mean numbers of days it took Chicago€™s Department of Streets & Sanitation to respond to requests to fix potholes are described by the density histogram in Fig. 18 for each of the weeks in 2012 and 2013.a. Interpret the area of the orange region in the density histogram as a
The average prices (in dollars) of 2014 Major League Baseball (MLB) tickets at the stadiums are described by the density histogram in Fig. 19.a. Interpret the area of the orange region in the density histogram as a proportion.b. Interpret the area of the orange region in the density histogram as a
A total of 940 healthy, pregnant women between 20 and 34 years of age, inclusive, participated in a study. The distribution of their lengths of pregnancy is unimodal and symmetric with mean 281 days and standard deviation 8 days (Source: The Length of Human Pregnancy as Calculated by
In a study of U.S. veteran patients undergoing a first liver transplant, the distribution of their ages is unimodal and symmetric with mean 54 years and standard deviation 6 years (Source: Impact of the MELD Score on Waiting Time and Disease Severity in Liver Transplantation in United States
The simulations of rolling a six-sided die 5 times and an additional 10,000 times are shown in Figs.11 and 12, respectively.a. In which of the first five rolls did a 4 occur?b. What was the relative frequency of the outcome 4 after 5 rolls of the die? Is this a good estimate of the probability of
A student uses technology to simulate flipping a coin. After 1000 flips, the proportion of heads is 0.51. After 2000 flips, the proportion of heads is 0.52. The student thinks that the simulation must be broken, because the proportion did not get closer to the probability of getting heads (0.5).
A student plays a gambling card game called blackjack, winning 6 of 10 rounds. She concludes that the probability of winning blackjack is 0.6. What would you tell the student?
A car insurance company wants to estimate the probability that a 20-year-old American driver will get in a car accident in the next year. Describe how relative frequency could be used to make such an estimate.
A life insurance company wants to estimate the probability that a 60-year-old American who smokes will die in the next year. Describe the research and the calculations that would need to be performed to use relative frequency to make such an estimate.
P(black OR at least 30)Red: 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36Black: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35Green: 0, 00
P (red OR at least 28)Red: 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36Black: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35Green: 0, 00
P (even OR at least 3) A person rolls a six-sided die once. Find the given probability in fraction form.
P (odd OR at most 3) A person rolls a six-sided die once. Find the given probability in fraction form.
P(odd OR at most 2)Suppose someone spins the spinner shown in Fig. 24 once. Find the given probability in fraction form.
P(even OR at least 3)Suppose someone spins the spinner shown in Fig. 24 once. Find the given probability in fraction form.
The percentages of weapons used in murders in 2010 are described by the pie chart in Fig. 25a. Find the probability that a weapon randomly selected from those used in murders in 2010 was a firearm.b. Find the probability that a weapon randomly selected from those used in murders in 2010 was NOT a
The percentages of weapons used in murders in 2010 are described by the pie chart in Fig. 25.a. Find the probability that a weapon randomly selected from those used in murders in 2010 was a personal weapon.b. Find the probability that a weapon randomly selected from those used in murders in 2010
A total of 18,525 randomly selected adults were contacted by phone and asked to what degree social media influenced their purchasing decisions. Their responses are summarized by the pie chart in Fig. 26.Suppose an adult from the study is randomly selected. Consider the following events, which
A total of 18,525 adults were asked to what degree social media influenced their purchasing decisions. Their responses are summarized by the pie chart in Fig. 26. Suppose an adult from the study is randomly selected. Consider the following events, which describe to what degree social media
In 2013, 4579 runners completed the Great Cow Harbor 10K Run in Northport, New York. Their ages (in years) are de- scribed by the density histogram in Fig. 27.a. Find the probability that a randomly selected runner€™s age was between 10 and 69 years, inclusive.b. Find the probability that a
In 1994, California passed a three-strikes sentencing law man- dating that defendants convicted of a third felony should serve a state prison term of 25 years to life. The density histogram in Fig. 28 describes the ages (in years) of third-strike felons in California€™s state prison population
The numbers of minutes that United Airlines flights were delayed are described by the density histogram in Fig. 29 for the 1219 United flights that departed from O€™Hare Airport in Chicago during the period October 2€“7, 2013. Some flights were delayed at least 150 minutes, but the bars
The numbers of minutes that United Airlines flights were delayed are described by the density histogram in Fig. 30 for the 922 United flights that departed from O€™Hare Airport in Chicago during the period December 22€“28, 2013. Some flights were delayed at least 175 minutes, but the bars
P (in the second week OR a Sunday)
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 12 compares the adults€™ responses and their ages.a. Find the probability that a person randomly selected
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 13 compares the adults€™ responses and their ages.a. Find the probability that a person randomly selected from the
A total of 803 adults were asked whether they prefer to drink coffee, tea, or neither. Table 14 compares the adults€™ responses and the regions of the country where they live.Let S stand for a person who lives in the South, C stand for a person who prefers coffee, and T stand for a person who
A total of 803 adults were asked whether they prefer to drink coffee, tea, or neither. Table 14 compares the adults’ responses and the regions of the country where they live. Let N stand for a person who lives in the Northeast, W stand for a person who lives in the West, and C stand for a person
Find a general addition rule for three events.
Find P (odd number | atmost5) A person rolls a six-sided die once. When finding a probability, write it in fraction form.
A 3, given the number is at least 3Suppose someone spins the spinner shown in Fig. 34 once. Find the probability (in fraction form) that the outcome is
A 1, given the number is oddSuppose someone spins the spinner shown in Fig. 34 once. Find the probability (in fraction form) that the outcome is
Are the events Wednesday and in the fifth week independent? Explain.
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 18 compares the adults€™ responses and their ages.a. Find the probability that a person randomly selected
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 19 compares the adults€™ responses and their ages.a. Find the probability that a person randomly selected from the
Table 20 compares the numbers (in thousands) of students who started college at a 4-year private, a 4-year public, or a 2-year public institution in fall 2007 and their educational status as of spring 2013 (six years later). The category €œCompleted a degree or certificate€ includes students
A random selection of 969 married adults were asked about their level of happiness. Table 21 compares their responses and their genders.a. Find the probability that a person randomly selected from the 969 married adults is fairly happy, given the person is a woman.b. Find the probability that a
Researchers observed 15,824 individuals in malls, schools, stadiums, and other public places, recording whether each person smiled within 10 seconds. Table 22 compares their observations and the researchers€™ estimates of the individuals€™ ages.Suppose one participant from the study is
Between August 1973 and September 1974, 957 randomly selected adults in Washington County, Maryland, were interviewed about whether they wore seat belts and whether they had undergone a dental checkup in the past two years. Their responses are summarized in Table 23. During that period, no state

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