Bundle: Understandable Statistics: Concepts And Methods, 12th + Jmp Printed Access Card For Peck's Statistics + Webassign Printed Access Card For ... And Methods, 12th Edition, Single-term
12th Edition
ISBN: 9781337758925
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5.4, Problem 18P
Engineering: Cracks Henry Petroski is a professor of civil engineering at Duke University. In his book To Engineer Is Human: The Role of Failure in Successful Design, Professor Petroski says that up to 95% of all structural failures, including those of bridges, airplanes, and other commonplace products of technology, are believed to be the result of crack growth. In most cases, the cracks grow slowly. It is only when the cracks reach intolerable proportions and still go undetected that catastrophe can occur. In a cement retaining wall, occasional hairline cracks are normal and nothing to worry about. If these cracks are spread out and not too close together, the wall is considered safe. However, if a number of cracks group together in a small region, there may be real trouble. Suppose a given cement retaining wall is considered safe if hairline cracks are evenly spread out and occur on the average of 4.2 cracks per 30-foot section of wall.
- (a) Explain why a Poisson
probability distribution would be a good choice for the random variable r = number of hairline cracks for a given length of retaining wall. - (b) In a 50-foot section of safe wall, what is the probability of three (evenly spread-out) hairline cracks? What is the probability of three or more (evenly spread-out) hairline cracks?
- (c) Answer part (b) for a 20-foot section of wall.
- (d) Answer part (b) for a 2-foot section of wall. Round λ to the nearest tenth.
- (e) Consider your answers to parts (b), (c), and (d). If you had three hairline cracks evenly spread out over a 50-foot section of wall, should this be cause for concern? The probability is low. Could this mean that you are lucky to have so few cracks? On a 20-foot section of wall [part (c)], the probability of three cracks is higher. Does this mean that this distribution of cracks is closer to what we should expect? For part (d), the probability is very small. Could this mean you are not so lucky and have something to worry about? Explain your answers.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Suppose that the chance that an elementary student eats hot lunch is 30 percent. What’s the chance that, among 20 randomly selected students, between 6 and 8 students eat hot lunch (inclusive)?
Bob’s commuting times to work are varied. He makes it to work on time 80 percent of the time. On 12 randomly selected trips to work, what’s the chance that Bob makes it on time at least 10 times?
Your chance of winning a small prize in a scratch-off ticket is 10 percent. You buy five tickets. What’s the chance you will win at least one prize?
Chapter 5 Solutions
Bundle: Understandable Statistics: Concepts And Methods, 12th + Jmp Printed Access Card For Peck's Statistics + Webassign Printed Access Card For ... And Methods, 12th Edition, Single-term
Ch. 5.1 - Statistical Literacy Which of the following are...Ch. 5.1 - Statistical Literacy Which of the following are...Ch. 5.1 - Statistical Literacy Consider each distribution....Ch. 5.1 - Prob. 4PCh. 5.1 - Prob. 5PCh. 5.1 - Statistical Literacy Consider the probability...Ch. 5.1 - Basic Computation: Expected Value and Standard...Ch. 5.1 - Basic Computation: Expected Value For a...Ch. 5.1 - Critical Thinking: Simulation We can use the...Ch. 5.1 - Marketing: Age What is the age distribution of...
Ch. 5.1 - Marketing: Income What is the income distribution...Ch. 5.1 - History: Florence Nightingale What was the age...Ch. 5.1 - Fishing: Trout The following data are based on...Ch. 5.1 - Criminal Justice: Parole USA Today reported that...Ch. 5.1 - Prob. 15PCh. 5.1 - Prob. 16PCh. 5.1 - Expected Value: Life Insurance Jim is a...Ch. 5.1 - Expected Value: Life Insurance Sara is a...Ch. 5.1 - Prob. 19PCh. 5.1 - Prob. 20PCh. 5.1 - Combination of Random Variables: Insurance Risk...Ch. 5.2 - Statistical Literacy What does the random variable...Ch. 5.2 - Prob. 2PCh. 5.2 - Statistical Literacy For a binomial experiment,...Ch. 5.2 - Prob. 4PCh. 5.2 - Interpretation Suppose you are a hospital manager...Ch. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.2 - Critical Thinking According to the college...Ch. 5.2 - Prob. 10PCh. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - Prob. 17PCh. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - Prob. 22PCh. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - Prob. 26PCh. 5.2 - Binomial Distribution Table: Symmetry Study the...Ch. 5.2 - Prob. 28PCh. 5.2 - Prob. 29PCh. 5.2 - In each of the following problems, the binomial...Ch. 5.2 - Prob. 31PCh. 5.2 - Prob. 32PCh. 5.3 - Statistical Literacy What does the expected value...Ch. 5.3 - Statistical Literacy Consider two binomial...Ch. 5.3 - Basic Computation: Expected Value and Standard...Ch. 5.3 - Basic Computation: Expected Value and Standard...Ch. 5.3 - Critical Thinking Consider a binomial distribution...Ch. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 8PCh. 5.3 - Critical Thinking Consider a binomial distribution...Ch. 5.3 - Prob. 10PCh. 5.3 - Sports: Surfing In Hawaii, January is a favorite...Ch. 5.3 - Quality Control: Syringes The quality-control...Ch. 5.3 - Private Investigation: Locating People Old Friends...Ch. 5.3 - Ecology: Hawaiian Tsunamis A tidal wave or tsunami...Ch. 5.3 - Education: Illiteracy USA Today reported that...Ch. 5.3 - Rude Drivers: Tailgating Do you tailgate the car...Ch. 5.3 - Hype: Improved Products The Wall Street Journal...Ch. 5.3 - Prob. 18PCh. 5.3 - Prob. 19PCh. 5.3 - Defense: Radar Stations The probability that a...Ch. 5.3 - Criminal Justice: Jury Duty Have you ever tried to...Ch. 5.3 - Public Safety: 911 Calls The Denver Post reported...Ch. 5.3 - Law Enforcement: Property Crime Does crime pay?...Ch. 5.3 - Prob. 24PCh. 5.3 - Prob. 25PCh. 5.3 - Prob. 26PCh. 5.3 - Prob. 27PCh. 5.3 - Critical Thinking Let r be a binomial random...Ch. 5.4 - Statistical Literacy For a binomial experiment,...Ch. 5.4 - Statistical Literacy When using the Poisson...Ch. 5.4 - Critical Thinking Suppose we have a binomial...Ch. 5.4 - Critical Thinking Suppose we have a binomial...Ch. 5.4 - Prob. 5PCh. 5.4 - Prob. 6PCh. 5.4 - Prob. 7PCh. 5.4 - Prob. 8PCh. 5.4 - College: Core Requirement Susan is taking Western...Ch. 5.4 - Law: Bar Exam Bob is a recent law school graduate...Ch. 5.4 - Sociology: Hawaiians On the leeward side of the...Ch. 5.4 - Prob. 12PCh. 5.4 - Prob. 13PCh. 5.4 - Archaeology: Artifacts At Burnt Mesa Pueblo, in...Ch. 5.4 - Ecology: River Otters In his doctoral thesis, L....Ch. 5.4 - Law Enforcement: Shoplifting The Denver Post...Ch. 5.4 - Prob. 17PCh. 5.4 - Engineering: Cracks Henry Petroski is a professor...Ch. 5.4 - Prob. 19PCh. 5.4 - Earthquakes: San Andreas Fault USA Today reported...Ch. 5.4 - Prob. 21PCh. 5.4 - Prob. 22PCh. 5.4 - Prob. 23PCh. 5.4 - Prob. 24PCh. 5.4 - Prob. 25PCh. 5.4 - Prob. 26PCh. 5.4 - Prob. 27PCh. 5.4 - Prob. 28PCh. 5.4 - Prob. 29PCh. 5.4 - Prob. 30PCh. 5.4 - Prob. 31PCh. 5.4 - Prob. 32PCh. 5.4 - Prob. 33PCh. 5 - Prob. 1CRPCh. 5 - Prob. 2CRPCh. 5 - Prob. 3CRPCh. 5 - Prob. 4CRPCh. 5 - Prob. 5CRPCh. 5 - Prob. 6CRPCh. 5 - Prob. 7CRPCh. 5 - Prob. 8CRPCh. 5 - Prob. 9CRPCh. 5 - Airlines: On-Time Arrivals Consumer Reports rated...Ch. 5 - Prob. 11CRPCh. 5 - Prob. 12CRPCh. 5 - Prob. 13CRPCh. 5 - Prob. 14CRPCh. 5 - Prob. 15CRPCh. 5 - Prob. 16CRPCh. 5 - Prob. 17CRPCh. 5 - Prob. 18CRPCh. 5 - Prob. 19CRPCh. 5 - Prob. 20CRPCh. 5 - Prob. 2DHCh. 5 - Prob. 2LCCh. 5 - Prob. 4LCCh. 5 - Prob. 1UTCh. 5 - Prob. 2UTCh. 5 - Prob. 3UTCh. 5 - Prob. 4UTCh. 5 - Prob. 5UTCh. 5 - Prob. 6UTCh. 5 - Binomial Distributions Although tables of binomial...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Suppose that 60 percent of families own a pet. You randomly sample four families. What is the chance that two or three of them own a pet?arrow_forwardIf 40 percent of university students purchase their textbooks online, in a random sample of five students, what’s the chance that exactly one of them purchased their textbooks online?arrow_forwardA stoplight is green 40 percent of the time. If you stop at this light eight random times, what is the chance that it’s green exactly five times?arrow_forward
- If 10 percent of the parts made by a certain company are defective and have to be remade, what is the chance that a random sample of four parts has one that is defective?arrow_forwardQuestion 4 Fourteen individuals were given a complex puzzle to complete. The times in seconds was recorded for their first and second attempts and the results provided below: 1 2 3 first attempt 172 255 second attempt 70 4 5 114 248 218 194 270 267 66 6 7 230 219 341 174 8 10 9 210 261 347 218 200 281 199 308 268 243 236 300 11 12 13 14 140 302 a. Calculate a 95% confidence interval for the mean time taken by each individual to complete the (i) first attempt and (ii) second attempt. [la] b. Test the hypothesis that the difference between the two mean times for both is 100 seconds. Use the 5% level of significance. c. Subsequently, it was learnt that the times for the second attempt were incorrecly recorded and that each of the values is 50 seconds too large. What, if any, difference does this make to the results of the test done in part (b)? Show all steps for the hypothesis testarrow_forwardQuestion 3 3200 students were asked about the importance of study groups in successfully completing their courses. They were asked to provide their current majors as well as their opinion. The results are given below: Major Opinion Psychology Sociology Economics Statistics Accounting Total Agree 144 183 201 271 251 1050 Disagree 230 233 254 227 218 1162 Impartial 201 181 196 234 176 988 Total 575 597 651 732 645 3200 a. State both the null and alternative hypotheses. b. Provide the decision rule for making this decision. Use an alpha level of 5%. c. Show all of the work necessary to calculate the appropriate statistic. | d. What conclusion are you allowed to draw? c. Would your conclusion change at the 10% level of significance? f. Confirm test results in part (c) using JASP. Note: All JASP input files and output tables should be providedarrow_forward
- Question 1 A tech company has acknowledged the importance of having records of all meetings conducted. The meetings are very fast paced and requires equipment that is able to capture the information in the shortest possible time. There are two options, using a typewriter or a word processor. Fifteen administrative assistants are selected and the amount of typing time in hours was recorded. The results are given below: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 typewriter 8.0 6.5 5.0 6.7 7.8 8.5 7.2 5.7 9.2 5.7 6.5 word processor 7.2 5.7 8.3 7.5 9.2 7.2 6.5 7.0 6.9 34 7.0 6.9 8.8 6.7 8.8 9.4 8.6 5.5 7.2 8.4 a. Test the hypothesis that the mean typing time in hours for typewriters is less than 7.0. Use the 1% level of significance. b. Construct a 90% confidence interval for the difference in mean typing time in hours, where a difference is equal to the typing time in hours of word processors minus typing time in hours of typewriter. c. Using the 5% significance level, determine whether there is…arrow_forwardIllustrate 2/7×4/5 using a rectangular region. Explain your work. arrow_forwardWrite three other different proportions equivalent to the following using the same values as in the given proportion 3 foot over 1 yard equals X feet over 5 yardsarrow_forward
- 2. An experiment is set up to test the effectiveness of a new drug for balancing people's mood. The table below contains the results of the patients before and after taking the drug. The possible scores are the integers from 0 to 10, where 0 indicates a depressed mood and 10 indicates and elated mood. Patient Before After 1 4 4 2 3 3 3 6 4 4 1 2 5 6 5 6 1 3 7 4 7 8 6 9 1 4 10 5 4 Assuming the differences of the observations to be symmetric, but not normally distributed, investigate the effectiveness of the drug at the 5% significance level. [4 Marks]arrow_forward3. (i) Consider the following R code: wilcox.test(UK Supermarkets $Salary ~ UKSupermarkets $Supermarket) (a) Which test is being used in this code? (b) What is the name of the dataset under consideration? How would be adapt this code if we had ties? What other command can be used which deals with ties? (ii) Consider the following R code: install packages("nortest") library(nortest) lillie.test (Differences) (a) Assuming the appropriate dataset has been imported and attached, what is wrong with this code? (b) If this code were to be corrected, what would be determined by run- ning it? [3 Marks]arrow_forward1. (i) Explain the difference in application between the Mann-Whitney U test and the Wilcoxon Signed-Rank test, i.e. in which scenarios would each test be used? (ii) What is the main procedure underlying these nonparametric tests? [3 Marks]arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY