Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 13.2, Problem 1EE
This exercise makes use of the geometric procedure just explained to calculate the variance and standard deviation of the population 2, 5, 7, 11, 15. The following figure shows the given set of data labeled on a number line, along with its mean, which is 8.
a. Draw the tile associated with each of the five data values 2, 5, 7, 11, and 15.
b. Label each tile with its area.
c Find the sum of the areas of all the tiles.
d. Find the average (mean) of the areas of all 5 tiles.
e. To the right of the above number line, draw a tile whose area is the average found in part d.
f. What is the variance of the data? What geometric figure represents the variance?
g. What is the standard deviation of the data? What geometric figure represents the standard deviation?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Microsoft Excel snapshot for random sampling: Also note the formula used for the last
column
02
x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
A
B
1
No.
States
2
1
ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
B
E
F
G
1
No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
sample
10
3
2 ALASKA
0.4493186 OKLAHOMA
k
5
4
3 ARIZONA
0.707914 KANSAS
5
4 ARKANSAS 0.4831379 NORTH DAKOTA
6
5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
9
8 DELAWARE 0.5783029 MISSOURI
525
10
15
INDIANA
MARYLAND
COLORADO
The spread of an infectious disease is often modeled using the following autonomous differential equation:
dI
-
- BI(N − I) − MI,
dt
where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of
transmission, and μ is the rate at which people recover from infection.
Close
a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria.
b) (5 points) For the equilbria in part a), determine whether each is stable or unstable.
c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
dt
function by hand.) Identify the equilibria as stable or unstable in the graph.
d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.
Find the indefinite integral.
Check
Answer:
7x
4 + 1x
dx
Chapter 13 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 13.1 - Use linear interpolation to find the number that...Ch. 13.1 - Use linear interpolation to find the number that...Ch. 13.1 - A calculator shows that 21.414 and 31.732. Use...Ch. 13.1 - We know that 21=2 and 22=4 . Use linear...Ch. 13.1 - At the present time, a football player weighs 325...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...
Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - Find the mean, median, and mode(s), if any, for...Ch. 13.1 - a. If exactly one number in a set of data is...Ch. 13.1 - If a t of data has a mode, then must the mode be...Ch. 13.1 - Academy Awards The following table displays the...Ch. 13.1 - Academy Awards The following table displays the...Ch. 13.1 - Dental Schools Dental schools provide urban...Ch. 13.1 - Expense Reports A salesperson records the...Ch. 13.1 - Use the above grading system to find each students...Ch. 13.1 - Use the above grading system to find each students...Ch. 13.1 - Use the above grading system to find each students...Ch. 13.1 - Use the above grading system to find each students...Ch. 13.1 - Calculate a Course Grade A professor grades...Ch. 13.1 - Calculate a Course Grade A professor grades...Ch. 13.1 - Baseball In baseball, a batters slugging average,...Ch. 13.1 - Baseball In baseball, a batters slugging average,...Ch. 13.1 - Baseball In baseball, a batters slugging average,...Ch. 13.1 - Baseball In baseball, a batters slugging average,...Ch. 13.1 - Find the mean, the median, and all modes for the...Ch. 13.1 - Find the mean, the median, and all modes for the...Ch. 13.1 - Find the mean, the median, and all modes for the...Ch. 13.1 - Find the mean, the median, and all modes for the...Ch. 13.1 - Use the following information about another...Ch. 13.1 - Use the following information about another...Ch. 13.1 - Use the following information about another...Ch. 13.1 - Use the following information about another...Ch. 13.1 - Test Scores After 6 biology tests. Ruben has a...Ch. 13.1 - Test Scores After 4 algebra tests. Alisa has a...Ch. 13.1 - Baseball For the first half of a baseball season,...Ch. 13.1 - Commuting Times Mark averaged 60 mph during the...Ch. 13.1 - Consider the data in the following table. Summary...Ch. 13.1 - Consider the data in the following table. Summary...Ch. 13.2 - This exercise makes use of the geometric procedure...Ch. 13.2 - a. to g. Repeat all of the steps described in...Ch. 13.2 - Meteorology During a 12-hour period on December...Ch. 13.2 - Meteorology During a 2-hour period on January 12....Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Find the range, the standard deviation, and the...Ch. 13.2 - Mountain Climbing A mountain climber plans to buy...Ch. 13.2 - Lotteries Which would you expect to be larger: the...Ch. 13.2 - Weights of Students Which would you expect to be...Ch. 13.2 - Evaluate the accuracy of the following statement:...Ch. 13.2 - Fuel Efficiency The fuel efficiency, in miles per...Ch. 13.2 - Waiting Times A customer at a specialty coffee...Ch. 13.2 - Fast-food Calories A survey of 10 fast-food...Ch. 13.2 - Energy Drinks A survey of 16 energy drinks noted...Ch. 13.2 - Weekly Commute Times A survey of 15 large cities...Ch. 13.2 - Biology Some studies show that the mean normal...Ch. 13.2 - Recording Industry The table below shows a random...Ch. 13.2 - Pick 5 numbers and compute the population standard...Ch. 13.2 - Pick 6 numbers and compute the population standard...Ch. 13.2 - a. All of the numbers in a sample are the same...Ch. 13.2 - 27. Under what condition would the variance of a...Ch. 13.3 - The following table lists the ages of customers...Ch. 13.3 - Two groups of people were pan of a test to...Ch. 13.3 - The exercise heart rate, in beats per minute...Ch. 13.3 - Round each z-score to the nearest hundredth. A...Ch. 13.3 - Round each z-score to the nearest hundredth. A...Ch. 13.3 - Round each z-score to the nearest hundredth. A...Ch. 13.3 - Round each z-score to the nearest hundredth. A...Ch. 13.3 - Blood Pressure A blood pressure test was given to...Ch. 13.3 - Fruit Juice A random sample of 1000 oranges showed...Ch. 13.3 - Cholesterol A test involving 380 men ages 20 to 24...Ch. 13.3 - Tire Wear A random sample of 80 tires showed that...Ch. 13.3 - Test Scores Which of the following three test...Ch. 13.3 - Physical Fitness Which of the following Illness...Ch. 13.3 - Reading Test On a reading (est. Shaylens score of...Ch. 13.3 - Placement Exams On a placement examination. Rick...Ch. 13.3 - Test Scores Kevin scored at the 65th percentile on...Ch. 13.3 - 14. Test Scores Rene scored at the 84th percentile...Ch. 13.3 - Median Income In 2015, the median family income in...Ch. 13.3 - Monthly Rents A recent survey by the U.S. Census...Ch. 13.3 - Commute to School A survey was given to 18...Ch. 13.3 - Prescriptions The following table shows the number...Ch. 13.3 - Home Sales The accompanying table shows the median...Ch. 13.3 - The table below shows the heights, in inches. of...Ch. 13.3 - The table below shows the numbers of bushels of...Ch. 13.3 - 22. The blood lead concentrations, in micrograms...Ch. 13.3 - 23. a. The population 3, 4, 9, 14, and 20 has a...Ch. 13.3 - For each of the following, determine whether the...Ch. 13.4 - A professor finds that the grades in a large class...Ch. 13.4 - The results of a statew1e examination of the...Ch. 13.4 - A secondary school system finds that the...Ch. 13.4 - Boys Heights Humans are, on average, taller today...Ch. 13.4 - Biology A biologist measured the lengths of...Ch. 13.4 - Use the Empirical Rule to answer each question. In...Ch. 13.4 - Use the Empirical Rule to answer each question. In...Ch. 13.4 - Use the Empirical Rule to answer each question....Ch. 13.4 - Use the Empirical Rule to answer each question....Ch. 13.4 - Use the Empirical Rule to answer each question....Ch. 13.4 - Use the Empirical Rule to answer each question....Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the area, to the nearest thousandth, of the...Ch. 13.4 - Find the z-score, to the nearest hundredth, that...Ch. 13.4 - Find the z-score, to the nearest hundredth, that...Ch. 13.4 - Find the z-score, to the nearest hundredth, that...Ch. 13.4 - Find the z-score, to the nearest hundredth, that...Ch. 13.4 - Find the z-score, to the nearest hundredth, that...Ch. 13.4 - Find the z-score, to the nearest hundredth, that...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - In Exercises 31 to 40, answer each question. Round...Ch. 13.4 - Heights Consider the data set of the heights of...Ch. 13.4 - Weights Consider the data set of the weights - of...Ch. 13.4 - In Exercises 43 to 49, determine whether the given...Ch. 13.4 - In Exercises 43 to 49, determine whether the given...Ch. 13.4 - In Exercises 43 to 49, determine whether the given...Ch. 13.4 - In Exercises 43 to 49, determine whether the given...Ch. 13.4 - In Exercises 43 to 49, determine whether the given...Ch. 13.4 - In Exercises 43 to 49, determine whether the given...Ch. 13.4 - In Exercises 43 to 49, determine whether the given...Ch. 13.4 - a. Make a sketch of two normal distributions that...Ch. 13.4 - Determine the approximate z-scores for the first...Ch. 13.5 - The following table shows Earths atmospheric...Ch. 13.5 - Which of the scatter diagrams below suggests the...Ch. 13.5 - Which of the scatter diagrams below suggests a. a...Ch. 13.5 - Prob. 3ESCh. 13.5 - Given the bivariate data: a. Draw a scatter...Ch. 13.5 - Find the equation of the least squares line and...Ch. 13.5 - Find the equation of the least squares line and...Ch. 13.5 - Find the equation of the least squares line and...Ch. 13.5 - Find the equation of the least squares line and...Ch. 13.5 - Find the equation of the least squares line and...Ch. 13.5 - Find the equation of the least squares line and...Ch. 13.5 - Use the statistics features of a graphing...Ch. 13.5 - Use the statistics features of a graphing...Ch. 13.5 - Use the statistics features of a graphing...Ch. 13.5 - Use the statistics features of a graphing...Ch. 13.5 - Use the statistics features of a graphing...Ch. 13.5 - Life Expectancy The average remaining life times...Ch. 13.5 - Use the statistics features of a graphing...Ch. 13.5 - Use the statistics features of a graphing...Ch. 13.5 - Tuition The following table shows the average...Ch. 13.5 - ____ Search for bivariate data (in a magazine. in...Ch. 13 - Find the mean, median, mode, range, population...Ch. 13 - A set of data has a mean of 16, a median of 15,...Ch. 13 - Write a set of data with five data values for...Ch. 13 - State whether the mean, Median, or mode is being...Ch. 13 - Bridges The lengths of cantilever bridges in the...Ch. 13 - Average Speed Cleone traveled 45 ml to her sisters...Ch. 13 - Grade Point Average In a 4.0 grading system, each...Ch. 13 - Test Scores A teacher finds that the test scores...Ch. 13 - Airline Industry An airline recorded the times it...Ch. 13 - Ticket Prices The following table gives the...Ch. 13 - Test Scores One student received test ores of 85,...Ch. 13 - A population data set has a mean of 81 and a...Ch. 13 - Cholesterol Levels The cholesterol levels for 10...Ch. 13 - Test Scores The following histogram shows the...Ch. 13 - Teacher Salaries Use the following relative...Ch. 13 - Greenhouse Gas Emissions The table below shows...Ch. 13 - Alternative Fuels Alternative fuel vehicles that...Ch. 13 - Test Scores A professor gave a final examination...Ch. 13 - Waiting Time The amount of time customers spend...Ch. 13 - Pet Food The weights of all the sacks of dog food...Ch. 13 - Telecommunication A telephone manufacturer finds...Ch. 13 - Astronomy The following table gives the distances,...Ch. 13 - Given the bivariate data a. Draw a scatter diagram...Ch. 13 - Physics A student has recorded the data in the...Ch. 13 - 25. ____ Internet A test of an Internet service...Ch. 13 - Blood alcohol content (BAC) is measured in grams...Ch. 13 - Find the mean, median, and mode for the following...Ch. 13 - Grade Point Average Use the 4.0 grading system:...Ch. 13 - Find the range, standard deviation, and variance...Ch. 13 - A sample data set has a mean of x=65 and a...Ch. 13 - Basketball Draw a box-and-whisker plot for the...Ch. 13 - Movie Attendance Use the following relative...Ch. 13 - During I month, an overnight delivery company...Ch. 13 - Box Weights The weights of all the boxes of cake...Ch. 13 - A psychologist wants to determine whether there is...Ch. 13 - Nutrition The following table shows the percent of...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?arrow_forwardFind the indefinite integral. Check Answer: In(5x) dx xarrow_forwardHow to solve 2542000/64132 without a calculator?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License