MATH IN OUR WORLD (VALUE EDITION)
4th Edition
ISBN: 9781266216855
Author: sobecki
Publisher: MCG
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Chapter 11.6, Problem 2E
To determine
To write: The properties of a normal curve.
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In Problems 1 and 2 find the eigenfunctions and the equation that
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1. y" + Ay = 0, y'(0) = 0, y(1) + y'(1) = 0
A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts?
1. Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 44, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the answer of the second part.)
2. Compute the probability of a value greater than 55.0.
Use the same formula, x=55 and subtract the answer from 1.
3. Compute the probability of a value between 52.0 and 55.0.
(The question requires finding probability value between 52 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 52, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
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Assume that you fancy polynomial splines, while you actually need ƒ(t) = e²/3 – 1 for t€ [−1, 1].
See the figure for a plot of f(t).
Your goal is to approximate f(t) with an inter-
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The special case of d 0 is trivial: the only
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thus constant po,0 for all t = [−1, 1].
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The d+1 basis functions bd,k (t) form a ba-
sis Bd {ba,o(t), ba,1(t), bd,d(t)} of the
function space of all possible sα (t) functions.
Clearly, you wish to find out, which of them
given a particular maximal degree d is the
best-possible approximation of f(t) in the least-
squares sense.
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Chapter 11 Solutions
MATH IN OUR WORLD (VALUE EDITION)
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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- If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…arrow_forwardFind the closed formula for each of the following sequences (a_n)_n>=1 by realting them to a well known sequence. Assume the first term given is a_1 d. 5,23,119,719,5039 i have tried finding the differnces and the second difference and i still dont see the patternarrow_forwardSolve the differential equation by variation of parameters 3x2y" + 7xy' + y = x2 - xarrow_forward
- An image processor considered a 750×750 pixels large subset of an image and converted it into gray-scale, resulting in matrix gIn - a false-color visualization of gIn is shown in the top-left below. He prepared a two-dim. box filter f1 as a 25×25 matrix with only the 5×5 values in the middle being non-zero – this filter is shown in the top-middle position below. He then convolved £1 with itself to get £2, before convolving £2 with itself to get f3. In both of the steps, he maintained the 25×25 size. Next, he convolved gIn with £3 to get gl. Which of the six panels below shows g1? Argue by explaining all the steps, so far: What did the image processor do when preparing ₤3? What image processing operation (from gin to g1) did he prepare and what's the effect that can be seen? Next, he convolved the rows of f3 with filter 1/2 (-1, 8, 0, -8, 1) to get f4 - you find a visualization of filter f 4 below. He then convolved gIn with f4 to get g2 and you can find the result shown below. What…arrow_forwardClient 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127arrow_forward3ur Colors are enchanting and elusive. A multitude of color systems has been proposed over a three-digits number of years - maybe more than the number of purposes that they serve... - Everyone knows the additive RGB color system – we usually serve light-emitting IT components like monitors with colors in that system. Here, we use c = (r, g, b) RGB with r, g, bЄ [0,1] to describe a color c. = T For printing, however, we usually use the subtractive CMY color system. The same color c becomes c = (c, m, y) CMY (1-c, 1-m, 1-y) RGB Note how we use subscripts to indicate with coordinate system the coordinates correspond to. Explain, why it is not possible to find a linear transformation between RGB and CMY coordinates. Farbenlehr c von Goethe Erster Band. Roſt einen Defte mit fergen up Tübingen, is et 3. Cotta'fden Babarblung. ISIO Homogeneous coordinates give us a work-around: If we specify colors in 4D, instead, with the 4th coordinate being the homogeneous coordinate h so that every actual…arrow_forward
- Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?arrow_forwardYou manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1 Port 2 Port 3 400 110 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in £ to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 £45 Port 2 £20 £28 Port 3 £13 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form) indicating what each variable represents.arrow_forwarda) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? x1 12 23 81 82 83 S4 $1 -20 1 1 0 0 0 3 82 3 0 -2 0 1 2 0 6 12 1 1 -3 0 0 1 0 2 84 -3 0 2 0 0 -1 1 4 2 -2 0 11 0 0 -4 0 -8 b) Solve the following linear program using the 2-phase simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. maximize 21 - - 2x2 + x3 - 4x4 subject to 2x1+x22x3x4≥ 1, 5x1+x2-x3-4 -1, 2x1+x2-x3-342, 1, 2, 3, 4 ≥0.arrow_forward
- Suppose we have a linear program in standard equation form maximize c'x subject to Ax=b, x≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.arrow_forward(a) For the following linear programme, sketch the feasible region and the direction of the objective function. Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. maximize +22 subject to 1 + 2x2 ≤ 4, 1 +3x2 ≤ 12, x1, x2 ≥0 (b) For the following linear programme, sketch the feasible region and the direction of the objective function. Explain, making reference to your sketch, why this linear programme is unbounded. maximize ₁+%2 subject to -2x1 + x2 ≤ 4, x1 - 2x2 ≤4, x1 + x2 ≥ 7, x1,x20 Give any feasible solution to the linear programme for which the objective value is 40 (you do not need to justify your answer).arrow_forwardfind the domain of the function f(x)arrow_forward
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