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mathematics
statistics

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

There are many Native American tribes that are not recognized by the U.S. government, which means they cannot seek the same health and educational opportunities as federal tribes. Because of difficult requirements to achieve recognition, many tribes have never completed the process. The number of
General Motors (GM) struggled from 2005 to 2012. In fact, GMs share of new-vehicle sales was 25.59% in 2005, and it decreased by about 1.15 percentage points per year until 2012 (Source: GM). Let f(t) be GM’s share of new-vehicle sales at t years since 2005.a. Find an equation of f.b. Find f (7).
In 2010, the percentage of private-sector workers who were in a union was 6.95%, and it decreased by about 0.25 percentage point per year until 2014.a. Find an equation of a model to describe the situation. Explain what your variables represent.b. Estimate when the percentage was 6.20%.c. Estimate
In 2010, the total number of overnight visits to national parks was 13.91 million visits, and it decreased by about 0.21 million visits per year until 2014.a. Find an equation of a model to describe the situation. Explain what your variables represent.b. Estimate in which year there were 13.0
Chicago taxis charge $2.25 plus $1.80 for each mile traveled.a. Find an equation of a linear model to describe the situation. Explain what your variables represent.b. What would be the cab fare for the 8.8-mile trip from South Side, Chicago, to Lincoln Park Zoo?c. If a person paid $25.65 for a cab
Houston taxis charge $2.55 plus $2.20 for each mile traveled.a. Find an equation of a linear model to describe the situation. Explain what your variables represent.b. What would be the cab fare for the 3.5-mile trip from Minute Maid Park to the Museum of Fine Arts, Houston?c. If a person paid
In 2013, the mean annual per-person consumption of butter was 5.5 pounds, up 12.2% from 2010. What was the mean annual per- person consumption of butter in 2010?
In 2013, the mean annual per-person consumption of cheese was 33.7 pounds, up 13.1% from 2000. What was the mean annual per- person consumption of cheese in 2000?
In 2013, total Visa® debit card purchases were $1.187 trillion, up 7.3% from 2012. What were the total Visa debit card purchases in 2012?
3 (4x – 5) – (2x + 3) = 2 (x –4)
In 2013, total MasterCard® debit card purchases were $491.1 billion, up 9.5% from 2012. What were the total MasterCard debit card purchases in 20 12?
In 2012, the mean office space per worker was 176 square feet, down 21.8% from 2010. What was the mean office space per worker in 2010?
In 2013, worldwide revenue for Ivory® bar soap was $94 mil- lion, down 10.5% from 2010. What was the worldwide revenue in 2010?
In 2014, the number of U.S. bank failures was 18 failures, down 88.5% from 2010. What was the number of U.S. bank failures in 2010?
The mean ratio of students per teacher in U.S. public schools was 15.1 students per teacher in 2013, down 5.6% from 2000. What was the mean ratio of students per teacher in 2000?
The mean numeric grades given by full-time and part- time faculty at Siena College are shown in Table 9 for various years.Let F and P be the mean numeric grades (in points) given by full-time faculty and part-time faculty, respectively, both at t years since 2000.a. Construct a scatterplot that
The percentages of college freshmen whose average grade in high school was an A are shown in Table 10 for various years.Let p be the percentage of college freshmen whose average grade in high school was an A at t years since 1970.a. Construct a scatterplot.b. Describe the four characteristics of
American child death rates (per 100,000 children ages 5€“14 years) are shown in Table 11 for various years.Let C = f (t) be the U.S. child death rate (per100,000 children) at t years since 1980.a. Graph the model f (t) = -0.55t + 30.09 on a scatterplot. Does it come close to the data points?b.
Banks charge an overdraft fee for writing a check for an amount that is more than the balance in the account. The mean overdraft fees are shown in Table 12 for various years.Let F = g(t) be the mean overdraft fee (in dollars) at t years since 2000.a. Graph the model g (t) = 0.68 t + 23.30 on a
The mean selling prices of a home sold in San Bruno, California, are shown in Table 13 for various square footages.Let p be the mean selling price (in thousands of dollars) of a home measuring s square feet.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute
P (E OR F) = P(E) +P(F) -P(E AND F) ; P(E OR F) = 0.63,P(E) = 0.39,P(E AND F) = 0.21 (general addition rule)
In what cases would you first solve a formula for a variable and then make substitutions for any other variables, and in what cases would you first make substitutions for all but one variable and then solve for the remaining variable?
E = t ∙ s / √n: E = 2.94, s = 4.83, n = 9 (margin of error)
X = + zs; x = 58.98, = 8.7, s = 2.6 (value of an observation)
Y – y = m (x – x1); y = 4, y1 = 7, x = 1, x1 = 5 (equation of a line)
x/a + y/b = 1; a = 3, y = 4, b = 7 (equation of a line)
Let be the mean (in points) of five test scores, x1, x2, x3, x4, and x5, all in points. a. Find a formula for the mean of the test scores.b. If a student has test scores of 74, 81, 79, and 84, find the score he needs on the fifth test so that his five-test mean score is 80 points, which is
Let be the mean (in points) of four test scores, x1, x2, x3, and x4, all in points. a. Find a formula for the mean of the test scores. b. If a student has test scores of 87, 92, and 86, find the score she needs on the fourth test so that her four-test mean score is 90 points, which is the cutoff
Today, Americans’ scores on the Wechsler IQ test are normally distributed with mean 100 points and standard deviation 15 points. However, the typical IQ of Americans has been increasing about 3 points per decade. a. Estimate the typical IQ (by today’s standards) of Americans two decades ago. b.
The scores on the Wechsler IQ test are normally distributed with mean 100 and standard deviation 15 points. Actor James Woods is reported to have an IQ of 180 points. a. Substitute appropriate values for all but one of the variables in the formula z = x – /s and then solve the equation to find
In a survey about work, employees were asked for what personal expenses they most wanted their company to reimburse them. Let L be the event lunch expenses and G be the event gym membership. a. Write a formula for P (L OR G) b. Of 1000 randomly selected employees, 11% said they most wanted to be
In a survey about work, employees were asked for what personal expenses they most wanted their company to reimburse them. Let C be the event cell phone charges and T be the event transportation expenses.a. Write a formula for P(C OR T).b. Of 1000 randomly selected employees, 10% said they most
M = Σxi P(x1); x1 = 0, x2 = 1, x3 = 2, x4 = 3, P(x1) = 0.027, P (x2) = 0.189, P(x3) = 0.441, P (x4) = 0.343 (mean of binomial distribution)
M = Σxi P (xi); x1 = 0, x2 = 1, x3 = 2, x4 = 3, x5 = 4, P (x1) = 0.240, P (x2) = 0.412, P (x3) = 0.265, P (x4) = 0.076, P (x5) = 0.008 (mean of binomial distribution)
X2 = ∑ (Oi – Ei)2 /Ei; Oi = 15, O2 = 28, O3 = 19, E1 = 11.3, E2 = 32.5, E3 = 18.2 (test statistic for goodness-of-fit test)
MST = ∑ni (x̅ – x̅)2 / k – 1; n1 = 19, n2 = 24, n3 = 15, x̅1 = 35, x̅2 = 39, x̅3 = 30, x̅ = 33, k = 3 (mean square due to treatment)
σ = √∑ [x21P(Xi)] – μ2; x1 = 0, x2 = 1, x3 = 2, x4 = 3, P(x1) = 0.4, P(x2) = 0.1, P (x3) = 0.2, P (x4) = 0.3, μ = 1.4 (standard deviation of a discrete random variable)
Se = √ ∑(Yi –x̅i)2 / n –2; y1 = 2 y2 = 7, y3 = 9, x̅1 = 3, x̅2 = 4, x̅3 = 11, n = 14 (standard error of the estimate)
P (E OR F) =P (E) +P (F) -P (E AND F), for P(E and F)
y – y1 = m (x – x1), for x1
Ur = 2n1 n2 / n + 1, for n2
Rs = z0 / √n – 1, For n
a. Solve the formula P (E OR F) = P (E) + P (F) - P (E AND F) for P (E). b. Substitute 0.8 for P (F), 0.9 for P (E OR F), and 0.2 for P (R AND F) in the formula that you found in part (a) and solve for P(E).
a. Solve the formula P (E OR F) = P (E) + P (F) - P(E OR F) for P (E AND F). b. Substitute 0.3 for P (E), 0.4 for P (F), and 0.6 for P (E OR F) in the formula that you found in part (a) and solve for P (E AND F).
Let be the mean (in points) of four test scores, x1, x2, x3, and x4, all in points. a. Write a formula for the mean of the test scores. b. Solve the formula you found in part (a) for x4. c. If a student has test scores of 85, 93, and 89, all in points, use the formula you found in part (b) to
Let be the mean (in points) of five test scores, x1, x2, x3, x4, and x5, all in points. a. Write a formula for the mean of the test scores. b. Solve the formula you found in part (a) for x. c. If a student has test scores of 71, 75, 88, and 81, all in points, use the formula you found in part (b)
The price of an adult one-day ticket to Walt Disney World was $46 in 2000, and it increased by about $3.75 per year until 2012. Let p be the price (in dollars) of a ticket at t years since 2000. a. Find an equation of a linear model to describe the situation. b. Solve the equation you found in part
The number of cases of unruly passenger behavior on board aircraft was 339 in 2007, and it increased by about 1346 cases per year until 2013 (Source: International Air Transport Association). Let n be the number of cases of unruly passenger behavior in the year that is t years since 2007. a. Find
Due to the airline industry charging more fees, the percentage of revenue from fares was only 71% in 2010, and it decreased by 0.8 percentage point per year until 2014 (Source: Bureau of Transportation Statistics). Let p be the percentage of revenue from fares at t years since 2010.a. Find an
Some 213.9 million pounds of fireworks were used in the United States in 2009, and that amount decreased by about 20.1 million pounds per year until 2013 (Source: American Pyrotechnics Association). Let F be the amount (in millions of pounds) of fireworks used in the year that is t years since
The scatterplot in Fig. 28 compares the sizes of people€™s heads with the weights of their brains.Let h be the size (in cubic centimeters) of a person€™s head, and let w be the weight (in grams) of the person€™s brain.a. Describe the four characteristics of the association.b. A
In an experiment of 40 college soccer players (20 women and 20 men), the total distance each participant could cover in three single-leg hops was recorded. The players also jumped vertically, and their jump heights were recorded. The scatter- plot in Fig. 29 compares the triple-hop distances of the
The numbers of cremations in the United States are shown in Table 18 for various years.Let p be the percentage of bodies that are cremated in the year that is t years since 1990.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r as part of
The percentages of new-vehicle buyers who use the Internet during the shopping process are shown in Table 19 for various years.Let p be the percentage of new-vehicle buyers who use the Internet during the shopping process at t years since 2000.a. Construct a scatterplot.b. Describe the four
A person travels d miles at a constant speed s (in miles per hour) for t hours.a. Complete Table 20 to help find a formula that describes the association among s, t, and d. Show the arithmetic to help you see a pattern.b. Solve the formula you found in part (a) for t.c. Use the formula you found in
An employee is paid a total of E dollars for working T hours at P dollars per hour.a. Complete Table 21 to help find a formula that describes the association among T, P, and E. Show the arithmetic to help you see a pattern.b. Solve the formula you found in part (a) for T.c. Use the formula you
Y + 2x = 4Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
Y – 3x = 2Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
3y = 2xDetermine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
2y = –5xDetermine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
5y = 4x – 15Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
4y = 7x – 20Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
3x – 4y = 8Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
4x + 3y = 9Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
6x – 15y = 30Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
6x – 8y = 16Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
4x + y + 2 = 0Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
2x – y – 3 = 0Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
6x – 4y + 8 = 0Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
15x + 12y – 36 = 0Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
Y – 3 = 0Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
Y + 5 = 0Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
3(x – 2y) = 9Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
2(y –3x) = 8Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
4x – 5y + 3 = 2x – 2y – 3Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
3y – 6x + 2 = 7y – x – 6Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
1 – 3 (y – 2x) = 7 + 3 (x – 3y)Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
8 – 2 (y – 3x) = 2 + 4 (x – 2y)Determine the slope and the y-intercept. Use the slope and the y-intercept to graph the equation by hand.
Let x be the mean (in points) and s be the standard deviation (in points) of three test scores, x1, x2, and x3, all in points.a. Write a formula for the mean of the three test scores.b. Use the formula you found in part (a) to show that if all three test scores are equal, then the mean score is
Let M be the median (in points) and R be the range (in points) of four test scores (all in points), x1, x2, x3, and x4, where the scores are listed from smallest to largest.a. Write a formula for the median of the test scores.b. Use the formula you found in part (a) to help you show that if the two
a. Solve the equation mx + b = 0, where m ≠ 0, for x.b. Explain why a linear equation in one variable has exactly one solution.
a. Find the slope of the line 3x + 5y = 7.b. Find the slope of the line 2x + 7y = 3.c. Find the slope of the line ax + by = c, where a, b, and c are constants and b is nonzero.
A student says the graph of 3y + 2x = 6 has slope 2 because the coefficient of the 2x term is 2. Is the student correct? If yes, explain why. If no, find the slope
A student says the y-intercept of the line 2y = 3x + 4 is (0, 4) because the constant term is 4. Is the student correct? If yes, explain why. If no, find the y-intercept.
Recall that we can describe some or all of the solutions of an equation in two variables with an equation, a table, a graph, or words.a. Describe the solutions of the equation 3x - 5y = 10 by using a graph.b. Describe the solutions of the equation 3x - 5y = 10 by using words.
Recall that we can describe some or all of the solutions of an equation in two variables with an equation, a table, a graph, or words.a. Describe the solutions of the equation 5x + 2y = 4 by using a graph.b. Describe three solutions of the equation 5x + 2y = 4 by using a table.c. Describe the
a. Solve the equation 2y - 6 = 4x for y.b. Explain why it makes sense that the graphs of 2y- and y = 2x + 3arethesame.
X + 5 ≤ 9Describe the solution set as an inequality, in interval notation, and on a graph.
X – 1 < – 4Describe the solution set as an inequality, in interval notation, and on a graph.
X – 3 ≥ – 1Describe the solution set as an inequality, in interval notation, and on a graph.
2x ≤ 6Describe the solution set as an inequality, in interval notation, and on a graph.
3x > 9Describe the solution set as an inequality, in interval notation, and on a graph.
4x ≥ – 8Describe the solution set as an inequality, in interval notation, and on a graph.
2x < – 10Describe the solution set as an inequality, in interval notation, and on a graph.
–3t ≥ 6Describe the solution set as an inequality, in interval notation, and on a graph.
–2w ≤ 2Describe the solution set as an inequality, in interval notation, and on a graph.
–2x > 1Describe the solution set as an inequality, in interval notation, and on a graph.
–4x < –2Describe the solution set as an inequality, in interval notation, and on a graph.
5x ≤ 0Describe the solution set as an inequality, in interval notation, and on a graph.
– 3x > 0Describe the solution set as an inequality, in interval notation, and on a graph.

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