Español Quality control: A population of 611 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the following table. A wafer is chosen at random from the population. Write your answer as a fraction or a decimal, rounded to four decimal places, Lot Conforming Nonconforming A 97 15 B 166 41 C 254 38 Send data to Excel (a) What is the probability that the water is from Lot A? (b) What is the probability that the wafer is nonconforming? (c) What is the probability that the wafer is from Lot A and is nonconforming? (d) Given that the water is from Lot A, what is the probability that it is nonconforming? (e) Given that the wafer is nonconforming, what is the probability that it is from Lot A7 (f) Let E, be the event that the water comes from Lot A, and let E, be the event that the wafer is nonconforming. Are E, and E, independent? Part: 0/6 Part 1 of 6 The probability that the wafer is from Lot A is 0.1833 Part: 1/6 Part 2 of 6 The probability that the water is nonconforming is 0.1538 Part: 2/6 Part 3 of 6 The probability that the wafer is from Lot A and is nonconforming is 0.0245 G
Español Quality control: A population of 611 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the following table. A wafer is chosen at random from the population. Write your answer as a fraction or a decimal, rounded to four decimal places, Lot Conforming Nonconforming A 97 15 B 166 41 C 254 38 Send data to Excel (a) What is the probability that the water is from Lot A? (b) What is the probability that the wafer is nonconforming? (c) What is the probability that the wafer is from Lot A and is nonconforming? (d) Given that the water is from Lot A, what is the probability that it is nonconforming? (e) Given that the wafer is nonconforming, what is the probability that it is from Lot A7 (f) Let E, be the event that the water comes from Lot A, and let E, be the event that the wafer is nonconforming. Are E, and E, independent? Part: 0/6 Part 1 of 6 The probability that the wafer is from Lot A is 0.1833 Part: 1/6 Part 2 of 6 The probability that the water is nonconforming is 0.1538 Part: 2/6 Part 3 of 6 The probability that the wafer is from Lot A and is nonconforming is 0.0245 G
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Probability and Statistics Exercise
**Part 3 of 6:**
- **Question:** The probability that the wafer is from Lot A and is nonconforming is:
- **Answer:** 0.0245
This part likely investigates the combined probability of two events: the wafer being from Lot A and the wafer being nonconforming.
**Part 3 of 6:**
- **Question:** The probability that the wafer is nonconforming given that it is from Lot A is:
- **Answer:** 0.0245
This part explores the conditional probability, specifically the likelihood that the wafer is nonconforming under the condition that it comes from Lot A.
**Part 4 of 6:**
- **Question:** The probability that the wafer is nonconforming given that it is from Lot A is:
- **Answer:** 0.0245
Similar to the previous part, this question examines the conditional probability of the wafer being nonconforming, given it is from Lot A.
**Part 5 of 6:**
- **Question:** The probability that the wafer is from Lot A given that it is nonconforming is:
- **Answer:** 0.0245
This question shifts focus to the Bayesian probability, determining the likelihood that a wafer is from Lot A, given that it is nonconforming.
**Part 6 of 6:**
- **Question:** The events \(E_1\) and \(E_2\) are [Select from a dropdown] independent.
- **Answer:** not
In this part, the question addresses the independence of two events. It concludes that \(E_1\) and \(E_2\) are **not** independent.
#### Diagrams and Graphs Explanation
For this particular image, no diagrams, graphs, or charts were provided. The detailed progression bars visible on each part indicate progress tracking, showing how far along the user is within the transition from part 3 to part 6.
**Note for Teachers:**
When explaining these concepts, consider utilizing visual aids like Venn diagrams or probability trees to better illustrate conditional and Bayesian probabilities. Examples for independent and dependent events can further elucidate the definitions and differences in practice.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd990cdd-ee11-4e18-b5de-3c59c3ecfc2c%2F7f0e2953-e107-43ca-886d-6a2b1f4e7821%2Fkv1sdi8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics Exercise
**Part 3 of 6:**
- **Question:** The probability that the wafer is from Lot A and is nonconforming is:
- **Answer:** 0.0245
This part likely investigates the combined probability of two events: the wafer being from Lot A and the wafer being nonconforming.
**Part 3 of 6:**
- **Question:** The probability that the wafer is nonconforming given that it is from Lot A is:
- **Answer:** 0.0245
This part explores the conditional probability, specifically the likelihood that the wafer is nonconforming under the condition that it comes from Lot A.
**Part 4 of 6:**
- **Question:** The probability that the wafer is nonconforming given that it is from Lot A is:
- **Answer:** 0.0245
Similar to the previous part, this question examines the conditional probability of the wafer being nonconforming, given it is from Lot A.
**Part 5 of 6:**
- **Question:** The probability that the wafer is from Lot A given that it is nonconforming is:
- **Answer:** 0.0245
This question shifts focus to the Bayesian probability, determining the likelihood that a wafer is from Lot A, given that it is nonconforming.
**Part 6 of 6:**
- **Question:** The events \(E_1\) and \(E_2\) are [Select from a dropdown] independent.
- **Answer:** not
In this part, the question addresses the independence of two events. It concludes that \(E_1\) and \(E_2\) are **not** independent.
#### Diagrams and Graphs Explanation
For this particular image, no diagrams, graphs, or charts were provided. The detailed progression bars visible on each part indicate progress tracking, showing how far along the user is within the transition from part 3 to part 6.
**Note for Teachers:**
When explaining these concepts, consider utilizing visual aids like Venn diagrams or probability trees to better illustrate conditional and Bayesian probabilities. Examples for independent and dependent events can further elucidate the definitions and differences in practice.
Transcribed Image Text:### Quality Control in Semiconductor Wafers
#### Overview
A population of 611 semiconductor wafers is sorted into three lots. The wafers are categorized by lot and by whether they conform to a thickness specification. The table below provides data on the number of wafers in each category. A wafer is chosen at random from the population.
#### Data Table
| Lot | Conforming | Nonconforming |
|-----|------------|---------------|
| A | 97 | 15 |
| B | 166 | 41 |
| C | 254 | 38 |
#### Questions
(a) What is the probability that the wafer is from Lot A?
(b) What is the probability that the wafer is nonconforming?
(c) What is the probability that the wafer is from Lot A and is nonconforming?
(d) Given that the wafer is from Lot A, what is the probability that it is nonconforming?
(e) Given that the wafer is nonconforming, what is the probability that it is from Lot A?
(f) Let \(E_1\) be the event that the wafer comes from Lot A, and let \(E_2\) be the event that the wafer is nonconforming. Are \(E_1\) and \(E_2\) independent?
#### Answers and Explanations
**Part 1:**
*Question*: What is the probability that the wafer is from Lot A?
*Answer*: The probability that the wafer is from Lot A is \(\frac{112}{611} \approx 0.1833\).
**Part 2:**
*Question*: What is the probability that the wafer is nonconforming?
*Answer*: The probability that the wafer is nonconforming is \(\frac{94}{611} \approx 0.1538\).
**Part 3:**
*Question*: What is the probability that the wafer is from Lot A and is nonconforming?
*Answer*: The probability that the wafer is from Lot A and is nonconforming is \(\frac{15}{611} \approx 0.0245\).
**Part 4:**
*Question*: Given that the wafer is from Lot A, what is the probability that it is nonconforming?
*Answer*: The probability that a wafer is nonconforming given that it is from Lot A is \(\frac{15}{112
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman