Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 6, Problem 101CR
A company uses three different assembly lines—A1, A2 and A3—to manufacture a particular component. Of those manufactured by A1, 5% need rework to remedy a defect, whereas 8% of A2’s components and 10% of A3’s components need rework. Suppose that 50% of all components are produced by A1, 30% are produced by A2 and 20% are produced by A3.
- a. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R) and another for no rework (N). Then enter appropriate probabilities on the branches.
- b. What is the
probability that a randomly selected component came from A1 and needed rework? - c. What is the probability that a randomly selected component needed rework?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
2. Complete a tree diagram with two stages-where the first stage has outcomes A and B and the second stage
has outcomes X and Y-given the following information: Pr[A] = 2/3, Pr[X|A] = 1/7, Pr[B[X] = 49/58,
Pr[Y|B] = 2/9. (Be careful! You do not need all of the preceding information to fill out the tree. Make
sure you know which probabilities tell you something on the tree and which ones do not!)
Answer the following questions:
(a) What is Pr[Y]?
(b) What is Pr[Y|A]?
(c) What is Pr[A|Y]?
Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type.
Suppose a recent study shows that 22% of adults have blood type A, 26% of adults have blood type B, 34% of adults have blood type AB, and 18% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities.
What is the probability that Brian and Jennifer share the same blood type? Give your answer as a decimal, precise to at least two decimal places.
Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type.
Suppose a recent study shows that 22% of adults have blood type A, 26% of adults have blood type B, 34% of adults have blood type AB, and 18% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities.
What is the probability that Brian and Jennifer share the same blood type? Give your answer as a decimal, precise to at least two decimal places.
Chapter 6 Solutions
Introduction To Statistics And Data Analysis
Ch. 6.1 - Define the term chance experiment, and give an...Ch. 6.1 - Define the term sample space, and then give the...Ch. 6.1 - Consider the chance experiment in which the type...Ch. 6.1 - Refer to the chance experiment described in the...Ch. 6.1 - A tennis shop sells five different brands of...Ch. 6.1 - Refer to the chance experiment described in the...Ch. 6.1 - A new model of laptop computer can be ordered with...Ch. 6.1 - A college library has four copies of a certain...Ch. 6.1 - A library has five copies of a certain textbook on...Ch. 6.1 - Suppose that, starting at a certain time,...
Ch. 6.1 - Refer to the previous exercise and now suppose...Ch. 6.1 - A family consisting of three peopleP1, P2, and...Ch. 6.1 - Prob. 13ECh. 6.1 - An engineering construction firm is currently...Ch. 6.1 - For the events described in the previous exercise,...Ch. 6.1 - Consider a Venn diagram picturing two events A and...Ch. 6.3 - A large department store offers online ordering....Ch. 6.3 - Consider the chance experiment described in the...Ch. 6.3 - The manager of an online music store has kept...Ch. 6.3 - Consider the chance experiment described in the...Ch. 6.3 - A bookstore sells two types of books (fiction and...Ch. 6.3 - Consider the chance experiment described in the...Ch. 6.3 - Medical insurance statuscovered (C) or not covered...Ch. 6.3 - Roulette is a game of chance that involves...Ch. 6.3 - Phoenix is a hub for a large airline. Suppose that...Ch. 6.3 - A customer satisfaction survey is planned. The...Ch. 6.3 - A professor assigns five problems to be completed...Ch. 6.3 - Refer to the following information on full-term...Ch. 6.3 - The report Teens, Social Media Technology...Ch. 6.3 - According to The Chronicle for Higher Education...Ch. 6.3 - The same issue of The Chronicle for Higher...Ch. 6.3 - A deck of 52 playing cards is mixed well, and 5...Ch. 6.3 - After all students have left the classroom, a...Ch. 6.3 - Use the information given in the previous exercise...Ch. 6.3 - The student council for a school of science and...Ch. 6.3 - A student placement center has requests from five...Ch. 6.3 - Suppose that a six-sided die is weighted so that...Ch. 6.4 - Two different airlines have a flight from Los...Ch. 6.4 - The article Chances Are You Know Someone with a...Ch. 6.4 - The accompanying data are from the article...Ch. 6.4 - Using the probabilities calculated in the previous...Ch. 6.4 - The following graphical display is similar to one...Ch. 6.4 - The article Americans Growing More Concerned About...Ch. 6.4 - The events E and T are defined as E = the event...Ch. 6.4 - The newspaper article Folic Acid Might Reduce Risk...Ch. 6.4 - Suppose that an individual is randomly selected...Ch. 6.4 - Is ultrasound a reliable method for determining...Ch. 6.4 - The paper Accuracy and Reliability of...Ch. 6.4 - The report 2015 Utah Seat Belt Use Survey (Utah...Ch. 6.4 - The National Highway Traffic Safety Administration...Ch. 6.4 - Use the information given in the previous exercise...Ch. 6.4 - The paper Good for Women, Good for Men, Bad for...Ch. 6.5 - Many fire stations handle emergency calls for...Ch. 6.5 - Refer to the information given in the previous...Ch. 6.5 - The paper Predictors of Complementary Therapy Use...Ch. 6.5 - The report TV Drama/Comedy Viewers and Health...Ch. 6.5 - The report Great Jobs, Great Lives. The...Ch. 6.5 - In a small city, approximately 15% of those...Ch. 6.5 - Jeanie is a bit forgetful, and if she doesnt make...Ch. 6.5 - Consider a system consisting of four components,...Ch. 6.5 - Consider the system described in the previous...Ch. 6.5 - In a January 2016 Harris Poll, each of 2252...Ch. 6.5 - Consider the following events: T = event that a...Ch. 6.5 - The following case study was reported in the...Ch. 6.5 - Three friends (A, B, and C) will participate in a...Ch. 6.5 - A store sells two different brands of dishwasher...Ch. 6.5 - The National Public Radio show Car Talk used to...Ch. 6.5 - Refer to the previous exercise. Suppose now that...Ch. 6.6 - A university has 10 vehicles available for use by...Ch. 6.6 - Prob. 70ECh. 6.6 - There are two traffic lights on Darlenes route...Ch. 6.6 - Let F denote the event that a randomly selected...Ch. 6.6 - According to a July 31, 2013 posting on cnn.com, a...Ch. 6.6 - Suppose that Blue Cab operates 15% of the taxis in...Ch. 6.6 - A large cable company reports the following: 80%...Ch. 6.6 - Refer to the information given in the previous...Ch. 6.6 - The authors of the paper Do Physicians Know When...Ch. 6.6 - A study of how people are using online services...Ch. 6.6 - The report Twitter in Higher Education: Usage...Ch. 6.6 - Use the information given in the previous exercise...Ch. 6.6 - Prob. 81ECh. 6.6 - Use the table of estimated probabilities from the...Ch. 6.6 - Suppose that we define the following events: C =...Ch. 6.6 - The article U.S. Investors Split Between Digital...Ch. 6.6 - Prob. 85ECh. 6.6 - The paper referenced in the previous exercise also...Ch. 6.6 - In an article that appears on the web site of the...Ch. 6.7 - The report Airline Quality Rating 2016...Ch. 6.7 - Five hundred first-year students at a state...Ch. 6.7 - Use the information given in the previous exercise...Ch. 6.7 - The table given below describes (approximately)...Ch. 6.7 - On April 1, 2010, the Bureau of the Census in the...Ch. 6.7 - Refer to the information given in the previous...Ch. 6.7 - Refer to the information given in Exercises 6.92...Ch. 6 - False positive results are not uncommon with...Ch. 6 - A company uses three different assembly linesA1,...Ch. 6 - Consider the following information about...Ch. 6 - Use the information given in the previous exercise...Ch. 6 - Use the information given in exercise 6.102 to...Ch. 6 - Prob. 105CRCh. 6 - The following table summarizing data on smoking...Ch. 6 - A study of the impact of seeking a second opinion...Ch. 6 - A company sends 40% of its overnight mail parcels...Ch. 6 - Prob. 109CRCh. 6 - Prob. 110CRCh. 6 - In a school machine shop, 60% of all machine...Ch. 6 - There are five faculty members in a certain...Ch. 6 - The general addition rule for three events states...Ch. 6 - A theater complex is currently showing four...Ch. 6 - Prob. 117CRCh. 6 - Suppose that a box contains 25 light bulbs, of...Ch. 6 - Return to Exercise 6.118, and suppose that 4 bulbs...Ch. 6 - A transmitter is sending a message using a binary...
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
- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2arrow_forwardBrian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type. Suppose a recent study shows that 28% of adults have blood type A, 21% of adults have blood type B, 34% of adults have blood type AB, and 17% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities. What is the probability that Brian and Jennifer share the same blood type? Give your answer as a decimal, precise to at least two decimal places. ?(Brian and Jennifer have the same blood type) = Suppose a county’s recent health report gives a pet allergy prevalence of 0.15 for kids. There is a new at-home test kit for pet allergies on the market that provides families with a convenient way to test if children have a pet allergy. The…arrow_forwardConsider there are only two computer companies in a country. The companies are named “Dude” and “Imac”. Each year, company Dude keeps 1/5th of its customers, while the rest switch to Imac. Each year, Imac keeps 1/3rd of its customers, while the rest switch to Dude. If in 2002, Dude has 1/6th of the market and Imac has 5/6th of the market, what is the distribution of the market share between the two companies in 2003. (Hint: you can cast this as a matrix multiplication problem)arrow_forward
- Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type. Suppose a recent study shows that 21% of adults have blood type A, 34% of adults have blood type B, 38% of adults have blood type AB, and 7% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities. What is the probability that Brian and Jennifer share the same blood type? Give your answer as a decimal, precise to at least two decimal places. ?(Brian and Jennifer have the same blood type)P(Brian and Jennifer have the same blood type) =arrow_forwardLet's assume that there are 500 people in a population. The researcher has access to all 500 participants, and sends a questionnaire that is accessed by a hyperlink. Of the 500 possible subjects, 485 complete it. Does this mean that the results generated from this study will be highly-accurate? What might cause the study to be unreliable?arrow_forwardIII. A researcher is interested in what type of bait attracts the most moths. The number of moths in a trap was recorded for traps that were in different locations, and used different baits. The data is in the file Trap.csv, with the following columns: Column 1. Moths: The number of moths in the trap Column 2. Location: The location of the trap on a tree Top, Middle, Lower, Ground. - Column 3. Bait: Chemical The bait used - Scent, Sugar, (a) Plot the interaction plot. Does there appear to be an interaction effect? Explain your answer. (b) Find the group means for Location. (c) Find the group means for Bait. (d) Find the group means for all treatment levels. (e) Do you believe that the number of moths trapped is different for all Locations? Explain.arrow_forward
- Exercise 10.3.4: Selecting coders for 3 different projects. i About (a) A manager must select three coders from her group to write three different software projects. There are 7 junior and 3 senior coders in her group. The first project can be written by any of the coders. The second project must be written by a senior person and the third project must be written by a junior person. How many ways are there for her to assign the three coders to the projects if no person can be assigned to more than one project?arrow_forwardData was collected for 40 randomly selected trees growing in the median strip of a busy freeway. The height of each tree (in inches) was recorded. Data was recorded to the nearest whole inch. The data is summarized in the histogram below. Based on this histogram, determing the minimum and maximum possible tree heights for the recorded data. Note: Each class contains its lower class boundary, but not its upper class boundary.Minimum tree height = inchesMaximum tree height = inchesarrow_forwardOtitis media, or middle ear infection, is initially treated with an antibiotic. Researchers have compared two antibiotics, A and B, for their cost effectiveness. A is inexpensive, safe, and effective. B is also safe. However, it is considerably more expensive and it is generally more effective. Use the tree diagram to the right (where the costs are estimated as the total cost of medication, office visit, ear check, and hours of lost work) to answer the following. a. Find the expected cost of using each antibiotic to treat a middle ear infection. A tree diagram has a root that splits into 2 branches labeled A and B. Primary branch A splits into 2 secondary branches labeled 0.80 Cure 59.30 dollars and 0.20 No cure 96.15 dollars. Primary branch B splits into two secondary branches labeled 0.90 Cure 69.15 dollars and 0.10 No cure 106.00 dollars.0.800.200.900.10 b. To minimize the total expected cost, which antibiotic should be chosen? a. The expected cost of…arrow_forward
- Otitis media, or middle ear infection, is initially treated with an antibiotic. Researchers have compared two antibiotics, A and B, for their cost effectiveness. A is inexpensive, safe, and effective. B is also safe. However, it is considerably more expensive and it is generally more effective. Use the tree diagram to the right (where the costs are estimated as the total cost of medication, office visit, ear check, and hours of lost work) to answer the following. a. Find the expected cost of using each antibiotic to treat a middle ear infection. b. To minimize the total expected cost, which antibiotic should be chosen? a. The expected cost of using antibiotic A is S (Round to the nearest cent as needed.) D w an example Get more help ww O Search e ( *** O 19 'C Clear all 0.70 Cure $59.30 A 0.30 No cure $96.15 0.85, Care $69.15 B 0.15 No cure $106.00 Check answer 2:17 PM 12/15/2022arrow_forwardOtitis media, or middle ear infection, is initially treated with an antibiotic. Researchers have compared two antibiotics, A and B, for their cost effectiveness. A is inexpensive, safe, and effective. B is also safe. However, it is considerably more expensive and it is generally more effective. Use the tree diagram to the right (where the costs are estimated as the total cost of medication, office visit, ear check, and hours of lost work) to answer the following. a. Find the expected cost of using each antibiotic to treat a middle ear infection. 0.75 , Cure $59.30 A 0.25 No cure $96.15 0.85, Cure $69.15 No cure $106.00 0.15 b. To minimize the total expected cost, which antibiotic should be chosen? a. The expected cost of using antibiotic A is $ (Round to the nearest cent as needed.)arrow_forwardA scientist is interested in whether stretching before running 5 kilometers will improve a runner’s time. The scientist decides that an experimental study is the best method to use to answer the question. One group of runners will run a 5-kilometer race without stretching, and a second group of runners will follow a specific stretching routine before running the race. The finishing times will be recorded, along with the group type for each runner. Assuming this group is representative of all adults who followed a specific stretching routine before running, use a normal distribution to estimate the probability that a randomly-selected adult could complete the race in fewer than 20 minutes after stretching. **THIS IS THE FULL QUESTION AND THIS IS NOT GRADED ***arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
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
Bayes' Theorem 1: Introduction and conditional probability; Author: Dr Nic's Maths and Stats;https://www.youtube.com/watch?v=lQVkXfJ-rpU;License: Standard YouTube License, CC-BY
What is Conditional Probability | Bayes Theorem | Conditional Probability Examples & Problems; Author: ACADGILD;https://www.youtube.com/watch?v=MxOny_1y2Q4;License: Standard YouTube License, CC-BY
Bayes' Theorem of Probability With Tree Diagrams & Venn Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=OByl4RJxnKA;License: Standard YouTube License, CC-BY
Bayes' Theorem - The Simplest Case; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XQoLVl31ZfQ;License: Standard Youtube License