Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321945525
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 11.1, Problem 10E
Railroad freight. Refer to Problem
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
No chatgpt pls will upvote Already
Find the LaPla se trnsofrom of
a) chi-square Distribution.
b) Normal Distribution.
C) Gamma Distribution.
prove that Binomial (n, 2) Poisson (2)
*********************
2.2, 13.2-13.3)
question: 5 point(s) possible
ubmit test
The accompanying table contains the data for the amounts (in oz) in cans of a certain soda. The cans are labeled to indicate that the contents are 20 oz of soda. Use the sign test and
0.05 significance level to test the claim that cans of this soda are filled so that the median amount is 20 oz. If the median is not 20 oz, are consumers being cheated?
Click the icon to view the data.
What are the null and alternative hypotheses?
OA. Ho: Medi
More Info
H₁: Medi
OC. Ho: Medi
H₁: Medi
Volume (in ounces)
20.3
20.1
20.4
Find the test stat
20.1
20.5
20.1
20.1
19.9
20.1
Test statistic =
20.2
20.3
20.3
20.1
20.4
20.5
Find the P-value
19.7
20.2
20.4
20.1
20.2
20.2
P-value=
(R
19.9
20.1
20.5
20.4
20.1
20.4
Determine the p
20.1
20.3
20.4
20.2
20.3
20.4
Since the P-valu
19.9
20.2
19.9
Print
Done
20 oz
20 oz
20 oz
20 oz
ce that the consumers are being cheated.
Chapter 11 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. 11.1 - Using Figure 3, estimate the median annual income...Ch. 11.1 - Using Figure 6,estimate the revenue and costs in...Ch. 11.1 - Repeat Example 1 for the following intervals: (A)...Ch. 11.1 - The weights (in pounds) were recorded for 20...Ch. 11.1 - (A) Construct a frequency table and histogram for...Ch. 11.1 - (A) Construct a frequency table and histogram for...Ch. 11.1 - The graphing calculator command shown in Figure A...Ch. 11.1 - An experiment consists of rolling a pair of...Ch. 11.1 - Gross domestic product. Graph the data in the...Ch. 11.1 - Corporation revenues. Graph the data in the...
Ch. 11.1 - Gold production. Use the double bar graph on world...Ch. 11.1 - Gasoline prices. Graph the data in the following...Ch. 11.1 - Railroad Freight. Graph the data in the following...Ch. 11.1 - Railroad freight. Refer to Problem 9. If the data...Ch. 11.1 - Federal income. Graph the data in the following...Ch. 11.1 - Gasoline prices. In December 2012, the average...Ch. 11.1 - Starting salaries. The starting salaries (in...Ch. 11.1 - Commute times. Thirty-two people were chosen at...Ch. 11.1 - Common stocks. The following table shows...Ch. 11.1 - Mouse weights. One hundred healthy mice were...Ch. 11.1 - Population growth. Graph the data in the following...Ch. 11.1 - Aims epidemic. One way to gauge the toll of the...Ch. 11.1 - Nutrition. Graph the data in the following table...Ch. 11.1 - Greenhouse gases. The U.S. Department of Energy...Ch. 11.1 - Nutrition. Graph the nutritional information in...Ch. 11.1 - Nutrition. Refer to Problem 21. Suppose that you...Ch. 11.1 - Education. For statistical studies, U.S. states...Ch. 11.1 - Study abroad. Would a pie graph be more effective...Ch. 11.1 - Median age. Use the broken-line graph shown to...Ch. 11.1 - State prisoners. In 1980 in the United States, 6...Ch. 11.1 - Grade point Averages. One hundred seniors were...Ch. 11.2 - For many sets of measurements the median lies...Ch. 11.2 - Find the mean for the sample measurements...Ch. 11.2 - Compute the mean for the grouped sample data...Ch. 11.2 - Add the salary $100,000 to those in Example 3 and...Ch. 11.2 - Find the median for the grouped data in the...Ch. 11.2 - Compute the mode(s), median, and mean for each...Ch. 11.2 - In Problems 1-4, find the mean of the data set....Ch. 11.2 - In Problems 1-4, find the mean of the data set....Ch. 11.2 - In Problems 1-4, find the mean of the data set....Ch. 11.2 - In Problems 1-4, find the mean of the data set....Ch. 11.2 - In Problems 5-8, find the indicated sum. (If...Ch. 11.2 - In Problems 5-8, find the indicated sum. (If...Ch. 11.2 - In Problems 5-8, find the indicated sum. (If...Ch. 11.2 - In Problems 5-8, find the indicated sum. (If...Ch. 11.2 - Find the mean, median, and mode for the sets of...Ch. 11.2 - Find the mean, median, and mode for the sets of...Ch. 11.2 - Find the mean, median, and/or mode, whichever are...Ch. 11.2 - Find the mean, median, and/or mode, whichever are...Ch. 11.2 - Find the mean for the sets of grouped data in...Ch. 11.2 - Find the mean for the sets of grouped data in...Ch. 11.2 - Which single measure of central tendency-mean,...Ch. 11.2 - Which single measure of central tendency mean,...Ch. 11.2 - A data set is formed by recording the results of...Ch. 11.2 - A data set is formed by recording the sums on 200...Ch. 11.2 - (A) Construct a set of four numbers that has mean...Ch. 11.2 - (A) Construct a set of five numbers that has mean...Ch. 11.2 - Price earnings ratios. Find the mean, median, and...Ch. 11.2 - Gasoline tax. Find the mean, median, and mode for...Ch. 11.2 - Light bulb lifetime. Find the mean and median for...Ch. 11.2 - Price earnings ratios. Find the mean and median...Ch. 11.2 - Financial aid. Find the mean, median, and mode for...Ch. 11.2 - Tourism. Find the mean, median, and mode for the...Ch. 11.2 - Mouse weights. Find the mean and median for the...Ch. 11.2 - Blood cholesterol levels. Find the mean and median...Ch. 11.2 - Immigration. Find the mean, median, and mode for...Ch. 11.2 - Grade point averages. Find the mean and median for...Ch. 11.2 - Entrance examination scores. Compute the median...Ch. 11.2 - Presidents. Find the mean and median for the...Ch. 11.3 - (A) When is the sample standard deviation of a set...Ch. 11.3 - Find the standard deviation for the sample...Ch. 11.3 - Find the standard deviation for the grouped sample...Ch. 11.3 - Prob. 1ECh. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - (A) Find set of the ungrouped mean and sample...Ch. 11.3 - (A) Find the mean and standard deviation of the...Ch. 11.3 - In Problems 11 and 12, find the standard deviation...Ch. 11.3 - In Problems 11 and 12, find the standard deviation...Ch. 11.3 - In Problems 13-18, discuss the validity of each...Ch. 11.3 - In Problems 13-18, discuss the validity of each...Ch. 11.3 - In Problems 13-18, discuss the validity of each...Ch. 11.3 - In Problem 1318, discuss the validity of each...Ch. 11.3 - In Problem 1318, discuss the validity of each...Ch. 11.3 - In Problems 13-18, discuss the validity of each...Ch. 11.3 - A data set is formed by recording the sums in 100...Ch. 11.3 - A data set is formed by recording the results of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.4 - Find p and q for a single roll of a fair die,...Ch. 11.4 - In Example 2, find the probability of the outcome...Ch. 11.4 - Using the same die experiment as in Example 3,...Ch. 11.4 - Use the binomial formula to expand q+p4.Ch. 11.4 - Repeat Example 5, where the binomial experiment...Ch. 11.4 - Compute the mean and standard deviation for the...Ch. 11.4 - Repeat Example 7 for four patients. The...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, a fair die is rolled three...Ch. 11.4 - If a baseball player has a batting average of 350...Ch. 11.4 - If a true-false test with 10 questions is given,...Ch. 11.4 - A multiple-choice test consists of 10 questions,...Ch. 11.4 - If 60 of the electorate supports the mayor, what...Ch. 11.4 - Construct a histogram for each of the binomial...Ch. 11.4 - Construct a histogram for each of the binomial...Ch. 11.4 - Construct a histogram for each of the binomial...Ch. 11.4 - Construct a histogram for each of the binomial...Ch. 11.4 - A random variable represents the number of...Ch. 11.4 - A random variable represents the number of...Ch. 11.4 - In Problems 35 and 36 a coin is loaded so that the...Ch. 11.4 - In Problems 35 and 36 a coin is loaded so that the...Ch. 11.4 - Find conditions on p that guarantee the histogram...Ch. 11.4 - Consider two binomial distributions for 1,000...Ch. 11.4 - A random variable represents the number of heads...Ch. 11.4 - A random variable represents the number of times a...Ch. 11.4 - Management training each year a company selects a...Ch. 11.4 - Employee turnover. If the probability of a new...Ch. 11.4 - Quality control A manufacturing process produces,...Ch. 11.4 - Guarantees. A manufacturing process produces, on...Ch. 11.4 - Quality control. A manufacturing process produces,...Ch. 11.4 - Management training. Each year a company selects 5...Ch. 11.4 - Medical diagnosis A tuberculosis patient is given...Ch. 11.4 - Harmful drug side effect. A pharmaceutical...Ch. 11.4 - Genetics. The probability that brown-eyed parents,...Ch. 11.4 - Gene mutation the probability of gene mutation...Ch. 11.4 - Epidemics. If the probability of a person...Ch. 11.4 - Drug side effect the probability that a given drug...Ch. 11.4 - Testing A multiple-choice test is given with 5...Ch. 11.4 - Opinion polls. An opinion poll based on a small...Ch. 11.4 - Testing. A multiple-choice test is given with 5...Ch. 11.4 - Sociology. The probability that a marriage will...Ch. 11.4 - Sociology. If the probability is .55 that a...Ch. 11.5 - What percentage of the light bulbs in Example 1...Ch. 11.5 - Refer to Example 1. What is the probability that a...Ch. 11.5 - In Example 3, Use the normal curve to approximate...Ch. 11.5 - Suppose in Example 4 that the manufacturing...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - Consider the normal distribution with mean 60 and...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - The probability of success in a Bernoulli trial is...Ch. 11.5 - For a binomial distribution with n=100, explain...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - To graph Problems 59-62, use a graphing calculator...Ch. 11.5 - To graph Problems 59-62, use a graphing calculator...Ch. 11.5 - To graph Problems 59-62, use a graphing calculator...Ch. 11.5 - To graph Problems 59-62, use a graphing calculator...Ch. 11.5 - (A) If 120 scores are chosen from a normal...Ch. 11.5 - (A) If 250 scores are chosen from a normal...Ch. 11.5 - Sales Salespeople for a solar technology company...Ch. 11.5 - Guarantees. The average lifetime for a car battery...Ch. 11.5 - Quality control. A manufacturing process produces...Ch. 11.5 - Quality control. An automated manufacturing...Ch. 11.5 - Marketing claims. A company claims that 60 of the...Ch. 11.5 - Labor relation A union representative 60 claims of...Ch. 11.5 - Medicine. The average healing time of a certain...Ch. 11.5 - Agriculture. The average height of a hay crop is...Ch. 11.5 - Genetics. In a family with 2 children, the...Ch. 11.5 - Genetics. In Problem 73, what is the approximate...Ch. 11.5 - Testing. Scholastic Aptitude Tests (SATs) are...Ch. 11.5 - Politics. Candidate Harkins claims that she will...Ch. 11.5 - Grading on a curve. An instructor grades on a...Ch. 11.5 - Psychology. A test devised to measure...Ch. 11 - Graph the following data using a bar graph and a...Ch. 11 - Graph the data in the following table using two...Ch. 11 - (A) Draw a histogram for the binomial distribution...Ch. 11 - For the set of sample measurements...Ch. 11 - If a normal distribution has a mean of 100 and a...Ch. 11 - Given the sample of 25 quiz scores listed in the...Ch. 11 - For the set of grouped sample data given in the...Ch. 11 - (A) Construct a histogram for the binomial...Ch. 11 - What are the mean and standard deviation for a...Ch. 11 - In Problems 10 and 11, discuss the validity of...Ch. 11 - In Problems 10 and 11, discuss the validity of...Ch. 11 - If the probability of success in a single trial of...Ch. 11 - Given a normal distribution with mean 50 and...Ch. 11 - A data set is formed by recording the sums of 100...Ch. 11 - For the sample quiz scores in Problem 6, find the...Ch. 11 - A fair die is rolled five times. What is the...Ch. 11 - Two dice are rolled three times. What is the...Ch. 11 - Ten students take an exam worth 100 points. (A)...Ch. 11 - In the last presidential election, 39 of a city’s...Ch. 11 - A random variable represents the number of wins in...Ch. 11 - Retail sales. The daily number of bad checks...Ch. 11 - Preference survey. Find the mean, median, and/or...Ch. 11 - Plant safety. The weekly record of reported...Ch. 11 - Personnel screening.The scores on a screening test...Ch. 11 - Market research A newspaper publisher claims that...Ch. 11 - Health care. A small town has three doctors on...
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
- T Teenage obesity (O), and weekly fast-food meals (F), among some selected Mississippi teenagers are: Name Obesity (lbs) # of Fast-foods per week Josh 185 10 Karl 172 8 Terry 168 9 Kamie Andy 204 154 12 6 (a) Compute the variance of Obesity, s²o, and the variance of fast-food meals, s², of this data. [Must show full work]. (b) Compute the Correlation Coefficient between O and F. [Must show full work]. (c) Find the Coefficient of Determination between O and F. [Must show full work]. (d) Obtain the Regression equation of this data. [Must show full work]. (e) Interpret your answers in (b), (c), and (d). (Full explanations required). Edit View Insert Format Tools Tablearrow_forwardH.w WI M Wz dy A Sindax Sind ①dlmax У тах at 0.75m from A W=6KN/M L=2 W2 = 9 KN/m P= 10 KN Barrow_forwardNo chatgpt pls will upvotearrow_forward
- Q4*) Find the extremals y, z of the the functional 1 = √² (2yz — 2z² + y² — z¹²) dx, - - with y(0) = 0, y(1) = 1, z(0) = 0, z(1) = 0.arrow_forwardlet h0, h1, h2,..., hn,....be the sequence defined by hn = (n C 2), (n choose 2). (n>=0). Determine the generating function for the sequence.arrow_forwardDraw the triangle and show all the workarrow_forward
- The average miles per gallon for a sample of 40 cars of model SX last year was 32.1, with a population standard deviation of 3.8. A sample of 40 cars from this year’s model SX has an average of 35.2 mpg, with a population standard deviation of 5.4. Find a 99 percent confidence interval for the difference in average mpg for this car brand (this year’s model minus last year’s).Find a 99 percent confidence interval for the difference in average mpg for last year’s model minus this year’s. What does the negative difference mean?arrow_forwardA special interest group reports a tiny margin of error (plus or minus 0.04 percent) for its online survey based on 50,000 responses. Is the margin of error legitimate? (Assume that the group’s math is correct.)arrow_forwardSuppose that 73 percent of a sample of 1,000 U.S. college students drive a used car as opposed to a new car or no car at all. Find an 80 percent confidence interval for the percentage of all U.S. college students who drive a used car.What sample size would cut this margin of error in half?arrow_forward
- You want to compare the average number of tines on the antlers of male deer in two nearby metro parks. A sample of 30 deer from the first park shows an average of 5 tines with a population standard deviation of 3. A sample of 35 deer from the second park shows an average of 6 tines with a population standard deviation of 3.2. Find a 95 percent confidence interval for the difference in average number of tines for all male deer in the two metro parks (second park minus first park).Do the parks’ deer populations differ in average size of deer antlers?arrow_forwardSuppose that you want to increase the confidence level of a particular confidence interval from 80 percent to 95 percent without changing the width of the confidence interval. Can you do it?arrow_forwardA random sample of 1,117 U.S. college students finds that 729 go home at least once each term. Find a 98 percent confidence interval for the proportion of all U.S. college students who go home at least once each term.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
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY