MATH IN OUR WORLD (LL) W/18 WEEKS ALEKS
4th Edition
ISBN: 9781266240829
Author: sobecki
Publisher: MCG CUSTOM
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Textbook Question
Chapter 11, Problem 17RE
For a data set with 90 values that is
(a) The range from 190 to 210.
(b) The range of values greater than 240.
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Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
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Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
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Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.
Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars)
are as follows.
From
To
Hamilton Butler
Clermont
Southern Gas
10
20
15
Northwest Gas
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15
18
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
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Chapter 11 Solutions
MATH IN OUR WORLD (LL) W/18 WEEKS ALEKS
Ch. 11.1 - A marketing firm is hired to study the occupants...Ch. 11.1 - A health-food store recorded the type of vitamin...Ch. 11.1 - In one math class, the data below represent the...Ch. 11.1 - Prob. 4TTOCh. 11.1 - Prob. 5TTOCh. 11.1 - What are data?Ch. 11.1 - Define statistics.Ch. 11.1 - Explain the difference between a population and a...Ch. 11.1 - How is a random sample selected?Ch. 11.1 - How is a systematic sample selected?
Ch. 11.1 - How is a stratified sample selected?Ch. 11.1 - How is a cluster sample selected?Ch. 11.1 - Prob. 8ECh. 11.1 - Describe the difference between descriptive and...Ch. 11.1 - How do inductive and deductive reasoning play a...Ch. 11.1 - For Exercises 1116, classify each sample as...Ch. 11.1 - For Exercises 1116, classify each sample as...Ch. 11.1 - For Exercises 1116, classify each sample as...Ch. 11.1 - For Exercises 1116, classify each sample as...Ch. 11.1 - For Exercises 1116, classify each sample as...Ch. 11.1 - For Exercises 1116, classify each sample as...Ch. 11.1 - In Exercises 1722, decide if you think the method...Ch. 11.1 - In Exercises 172, decide if you think the method...Ch. 11.1 - In Exercises 1722, decide if you think the method...Ch. 11.1 - In Exercises 1722, decide if you think the method...Ch. 11.1 - In Exercises 1722, decide if you think the method...Ch. 11.1 - In Exercises 1722, decide if you think the method...Ch. 11.1 - At a college financial aid office students who...Ch. 11.1 - A questionnaire about how students primarily get...Ch. 11.1 - Twenty-five fans of reality TV were asked to rate...Ch. 11.1 - A small independent developer of apps for...Ch. 11.1 - The ages of the signers of the Declaration of...Ch. 11.1 - The percentage of traffic fatalities in which at...Ch. 11.1 - Prob. 29ECh. 11.1 - The acreage (in thousands of acres) of the 39 U.S....Ch. 11.1 - Prob. 31ECh. 11.1 - 32. During the 1998 baseball season, Mark McGwire...Ch. 11.1 - Prob. 33ECh. 11.1 - Twenty-nine executives reported the number of...Ch. 11.1 - The National Insurance Crime Bureau reported that...Ch. 11.1 - Prob. 36ECh. 11.1 - The data shown represent the percentage of...Ch. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - For Exercises 3944, decide whether descriptive or...Ch. 11.1 - For Exercises 3944, decide whether descriptive or...Ch. 11.1 - For Exercises 3944, decide whether descriptive or...Ch. 11.1 - For Exercises 3944, decide whether descriptive or...Ch. 11.1 - For Exercises 3944, decide whether descriptive or...Ch. 11.1 - Prob. 46ECh. 11.1 - In addition to the four basic sampling methods,...Ch. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.2 - Prob. 1TTOCh. 11.2 - Prob. 2TTOCh. 11.2 - Prob. 3TTOCh. 11.2 - Prob. 4TTOCh. 11.2 - Prob. 5TTOCh. 11.2 - Prob. 6TTOCh. 11.2 - Describe how to draw a bar graph and a pie chart...Ch. 11.2 - Explain why bar graphs and pie charts are...Ch. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - How are histograms and frequency polygons similar?...Ch. 11.2 - Prob. 7ECh. 11.2 - Describe the purpose of a time series graph.Ch. 11.2 - Prob. 9ECh. 11.2 - The data below show the number of students...Ch. 11.2 - 11. Draw a bar graph for the number of registered...Ch. 11.2 - Prob. 12ECh. 11.2 - The number of students at one campus who had a 4.0...Ch. 11.2 - In an insurance company study of the causes of...Ch. 11.2 - In a survey of 100 college students, the numbers...Ch. 11.2 - Prob. 16ECh. 11.2 - For 108 randomly selected college applicants, the...Ch. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - The number of employed registered nurses tin...Ch. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - 42. If you’re going to compare data sets by...Ch. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Make up your own frequency polygon problem: using...Ch. 11.3 - Try This One 1
The total areas, in thousands of...Ch. 11.3 - Prob. 2TTOCh. 11.3 - Prob. 3TTOCh. 11.3 - Prob. 4TTOCh. 11.3 - Prob. 5TTOCh. 11.3 - Prob. 6TTOCh. 11.3 - Prob. 7TTOCh. 11.3 - Try This One 8
For the land area of the top 15...Ch. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Which of the measures of average can be used to...Ch. 11.3 - In Questions 710, describe some strengths and...Ch. 11.3 - In Questions 710, describe some strengths and...Ch. 11.3 - In Questions 710, describe some strengths and...Ch. 11.3 - In Questions 710, describe some strengths and...Ch. 11.3 - Prob. 11ECh. 11.3 - For Exercises 1122, find the mean, median, mode,...Ch. 11.3 - For Exercises 1122, find the mean, median, mode,...Ch. 11.3 - For Exercises 11–22, find the mean, median, mode,...Ch. 11.3 - For Exercises 1122, find the mean, median, mode,...Ch. 11.3 - Prob. 16ECh. 11.3 - For Exercises 1122, find the mean, median, mode,...Ch. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - For Exercises 2330, find the mean of the data set....Ch. 11.3 - For Exercises 2330, find the mean of the data set....Ch. 11.3 - For Exercises 2330, find the mean of the data set....Ch. 11.3 - Prob. 26ECh. 11.3 - For Exercises 2330, find the mean of the data set....Ch. 11.3 - Prob. 28ECh. 11.3 - For Exercises 2330, find the mean of the data set....Ch. 11.3 - For Exercises 2330, find the mean of the data set....Ch. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - For Exercises 3338, describe which measure of...Ch. 11.3 - For Exercises 3338, describe which measure of...Ch. 11.3 - For Exercises 3338, describe which measure of...Ch. 11.3 - For Exercises 3338, describe which measure of...Ch. 11.3 - For Exercises 3338, describe which measure of...Ch. 11.3 - For Exercises 3338, describe which measure of...Ch. 11.3 - Prob. 39ECh. 11.3 - Exercises 39 and 40 refer back to Exercise 24. The...Ch. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - 43. In Exercise 26, we calculated the mean life...Ch. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - Prob. 46ECh. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.4 - Prob. 1TTOCh. 11.4 - Prob. 2TTOCh. 11.4 - Prob. 3TTOCh. 11.4 - Prob. 4TTOCh. 11.4 - Name three measures of variation.Ch. 11.4 - What is the range?Ch. 11.4 - Why is the range not usually the best measure...Ch. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - For Exercises 710, discuss the relative sizes of...Ch. 11.4 - Prob. 8ECh. 11.4 - For Exercises 710, discuss the relative sizes of...Ch. 11.4 - Prob. 10ECh. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - Prob. 19ECh. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - Prob. 21ECh. 11.4 - For Exercises 1126, find the range, variance, and...Ch. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - The three data sets have the same mean and range,...Ch. 11.4 - Prob. 28ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.5 - The weights in pounds for the 12 members of a...Ch. 11.5 - Prob. 2TTOCh. 11.5 - Prob. 3TTOCh. 11.5 - Prob. 4TTOCh. 11.5 - Prob. 5TTOCh. 11.5 - If your score in your math class puts you in the...Ch. 11.5 - Does a score in the 90th percentile mean that you...Ch. 11.5 - Explain what quartiles are.Ch. 11.5 - Prob. 4ECh. 11.5 - What does the portion inside the box in a box plot...Ch. 11.5 - What is meant by the term outlier? How can you...Ch. 11.5 - The scores for 20 students on a 50-point math test...Ch. 11.5 - The heights (in inches) of the 12 students in a...Ch. 11.5 - In a class of 500 students, Carvetas rank was 125....Ch. 11.5 - In a class of 400 students, Johns rank was 80....Ch. 11.5 - In a charity marathon to raise money for AIDS...Ch. 11.5 - Prob. 12ECh. 11.5 - On an exam, Angela scored in the 20th percentile....Ch. 11.5 - Out of 600 applicants to a graduate program at an...Ch. 11.5 - Eldrick finished at the 77th percentile of a mens...Ch. 11.5 - Tinas application for a nursing position is ranked...Ch. 11.5 - Leas percentile rank on an exam in a class of 600...Ch. 11.5 - In an English class of 30 students, Audrelias...Ch. 11.5 - The Bowling Green State University mens basketball...Ch. 11.5 - Prob. 20ECh. 11.5 - In an evening statistics class, the ages of 20...Ch. 11.5 - Twenty subjects in a psychology class experiment...Ch. 11.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 11.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 11.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 11.5 - Prob. 26ECh. 11.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 11.5 - Prob. 28ECh. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - In Problems 2932, draw a box plot for the data,...Ch. 11.5 - Prob. 32ECh. 11.5 - Is it possible to score 90% on a test and have a...Ch. 11.5 - Prob. 34ECh. 11.5 - Prob. 35ECh. 11.5 - Prob. 36ECh. 11.5 - Prob. 37ECh. 11.5 - Prob. 38ECh. 11.5 - Prob. 39ECh. 11.5 - 40. What is unusual about the score at the 80th...Ch. 11.5 - 41. How many scores are lower than the score you...Ch. 11.5 - Prob. 43ECh. 11.6 - Prob. 1TTOCh. 11.6 - A standard test of intelligence is scaled so that...Ch. 11.6 - Prob. 3TTOCh. 11.6 - Prob. 4TTOCh. 11.6 - Find the area under the standard normal...Ch. 11.6 - Find the area under the standard normal...Ch. 11.6 - Prob. 7TTOCh. 11.6 - What is the distinguishing characteristic of a...Ch. 11.6 - Prob. 2ECh. 11.6 - What does the area under a portion of a normal...Ch. 11.6 - Explain what the empirical rule says.Ch. 11.6 - What percentage of the area under a normal curve...Ch. 11.6 - Why does it make sense that the total area under a...Ch. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Prob. 9ECh. 11.6 - Prob. 10ECh. 11.6 - Prob. 11ECh. 11.6 - Prob. 12ECh. 11.6 - For Exercises 1116, the data set described is...Ch. 11.6 - Prob. 14ECh. 11.6 - For Exercises 1116, the data set described is...Ch. 11.6 - Prob. 16ECh. 11.6 - For Exercises 1116, the data set described is...Ch. 11.6 - Prob. 18ECh. 11.6 - Prob. 19ECh. 11.6 - For Exercises 19–24, find the z score for the...Ch. 11.6 - Prob. 21ECh. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 26ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 28ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 30ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 32ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 34ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 36ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 38ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 40ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 42ECh. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - For Exercises 1738, find the area under the...Ch. 11.6 - Prob. 46ECh. 11.6 - As we know from Chapter 11, the probability of an...Ch. 11.6 - As we know from Chapter 11, the probability of an...Ch. 11.6 - As we know from Chapter 11, the probability of an...Ch. 11.6 - As we know from Chapter 11, the probability of an...Ch. 11.6 - Prob. 51ECh. 11.6 - Prob. 52ECh. 11.6 - Prob. 53ECh. 11.6 - Prob. 54ECh. 11.6 - Prob. 55ECh. 11.6 - Prob. 56ECh. 11.6 - Find two z values, one positive and one negative...Ch. 11.7 - Based on data compiled by the World Health...Ch. 11.7 - Prob. 2TTOCh. 11.7 - The mean for a reading test given nationwide is...Ch. 11.7 - The ages of 33 randomly selected inmates at a...Ch. 11.7 - Explain why the normal distribution can be used to...Ch. 11.7 - Given a data set, how could you decide if the...Ch. 11.7 - Describe the connection between area under a...Ch. 11.7 - Prob. 4ECh. 11.7 - Prob. 5ECh. 11.7 - Prob. 6ECh. 11.7 - Prob. 7ECh. 11.7 - Average sales for an online textbook distributor...Ch. 11.7 - A survey found that people keep their televisions...Ch. 11.7 - The average age of CEOs is 56 years. Assume the...Ch. 11.7 - Prob. 11ECh. 11.7 - Prob. 12ECh. 11.7 - The average amount of snow per season in Trafford...Ch. 11.7 - The average waiting time for a drive-in window at...Ch. 11.7 - The average time it takes college freshmen to...Ch. 11.7 - A brisk walk at 4 miles per hour burns an average...Ch. 11.7 - During September, the average temperature of...Ch. 11.7 - If the systolic blood pressure for a certain group...Ch. 11.7 - An IQ test has a mean of 100 and a standard...Ch. 11.7 - Prob. 20ECh. 11.7 - Prob. 21ECh. 11.7 - The average price of Stephen King paperbacks sold...Ch. 11.7 - Refer to Exercise 5. If your buddy Earl gets a job...Ch. 11.7 - Refer to Exercise 9. If you buy a TV for your dorm...Ch. 11.7 - Prob. 25ECh. 11.7 - Prob. 26ECh. 11.7 - In Problems 2730, (a) construct a histogram for...Ch. 11.7 - In Problems 2730, (a) construct a histogram for...Ch. 11.7 - In Problems 2730, (a) construct a histogram for...Ch. 11.7 - In Problems 2730, (a) construct a histogram for...Ch. 11.7 - Discuss whether or not you think each of the given...Ch. 11.7 - The number of incoming students at two campuses of...Ch. 11.7 - If a distribution of raw scores were plotted and...Ch. 11.7 - A researcher who is in charge of an educational...Ch. 11.7 - Prob. 37ECh. 11.7 - Prob. 38ECh. 11.7 - Prob. 39ECh. 11.7 - Prob. 40ECh. 11.8 - Try This One 1
Do you think there should be a...Ch. 11.8 - Prob. 2TTOCh. 11.8 - Prob. 3TTOCh. 11.8 - Prob. 4TTOCh. 11.8 - Prob. 5TTOCh. 11.8 - Prob. 6TTOCh. 11.8 - Describe what a scatter plot is and how one is...Ch. 11.8 - Explain what is meant when two variables are...Ch. 11.8 - Explain what is meant when two variables are...Ch. 11.8 - Prob. 4ECh. 11.8 - Prob. 5ECh. 11.8 - Prob. 6ECh. 11.8 - Describe the key difference between correlation...Ch. 11.8 - Prob. 8ECh. 11.8 - Prob. 9ECh. 11.8 - Prob. 10ECh. 11.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 11.8 - Prob. 12ECh. 11.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 11.8 - Prob. 14ECh. 11.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 11.8 - Prob. 16ECh. 11.8 - Prob. 17ECh. 11.8 - Prob. 18ECh. 11.8 - For the data sets in Exercises 1926, (a) Draw a...Ch. 11.8 - Prob. 20ECh. 11.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 11.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 11.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 11.8 - Prob. 24ECh. 11.8 - Prob. 25ECh. 11.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 11.8 - Prob. 27ECh. 11.8 - Prob. 28ECh. 11.8 - Prob. 29ECh. 11.8 - Design your own correlation problem. Think of two...Ch. 11.8 - Prob. 31ECh. 11.8 - Prob. 32ECh. 11.8 - Prob. 33ECh. 11.8 - Prob. 34ECh. 11.8 - Prob. 35ECh. 11.8 - Prob. 36ECh. 11.8 - Prob. 37ECh. 11.8 - Prob. 38ECh. 11.8 - Prob. 39ECh. 11.8 - Prob. 40ECh. 11 - A sporting goods store kept a record of sales of...Ch. 11 - The data set shown below represents the time in...Ch. 11 - During June, a local theater company recorded the...Ch. 11 - Construct a bar graph for the number of homicides...Ch. 11 - Draw a pie chart for the data in Exercies 4....Ch. 11 - Draw a histogram and frequency polygon for the...Ch. 11 - Prob. 7RECh. 11 - The data below are the number of U.S. citizens (in...Ch. 11 - Twelve batteries were tested to see how many hours...Ch. 11 - In your own words, explain the difference between...Ch. 11 - The data below are the number of beds at the eight...Ch. 11 - Which data set do you think would have a greater...Ch. 11 - For the census data in Problem 8, (a)Find the...Ch. 11 - Find the quartiles for the data in Problem 8, then...Ch. 11 - Find the area under the standard normal...Ch. 11 - A doctor has treated 45 male patients this week....Ch. 11 - For a data set with 90 values that is normally...Ch. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - The average weight of an airline passengers...Ch. 11 - The average cost of Cheetah brand running shoes is...Ch. 11 - Prob. 24RECh. 11 - A study is done to see whether there is a...Ch. 11 - Prob. 26RECh. 11 - Prob. 1CTCh. 11 - Prob. 2CTCh. 11 - Prob. 3CTCh. 11 - Prob. 4CTCh. 11 - Prob. 5CTCh. 11 - Prob. 6CTCh. 11 - These temperatures were recorded in Pasadena for a...Ch. 11 - Prob. 8CTCh. 11 - Prob. 9CTCh. 11 - Prob. 10CTCh. 11 - A major brand of potato chips sells its product in...Ch. 11 - A study is conducted to determine the relationship...
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- Use the method of undetermined coefficients to solve the given nonhomogeneous system. dx dt = 2x + 3y − 8 dy dt = −x − 2y + 6 X(t) =arrow_forwardAs discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk. (a) Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%. Assume that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let ds ≥ R − Rs with ds ≥ 0. Then make the objective function: Min 1 5 5 s = 1 ds2. Let FS = proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV = proportion of portfolio invested in the large-cap value fund…arrow_forwardCalculus lll May I please have the blank lines completed, and final statement defined as a result? Thank you for the support!arrow_forward
- For each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram? A 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92 B 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91 C 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93 D 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardProblem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forward
- The Course Name Real Analysis please Solve questions by Real Analysisarrow_forwardWe consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forward
- In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forward
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