Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Title: Understanding Factors Influencing Brand Switching**
**Introduction:**
In a study of factors that influence brand switching by a certain demographic, the following factors were identified as significant based on the responses of the 439 participants in the survey:
1. Better price
2. Friend's recommendation
3. Seeing others use it
4. Interesting packaging
5. Buzz—people talking about the brand
6. An advertisement
7. Press stories
8. Entertainer/sports celebrity endorsement
**Survey Results:**
The results of the survey are shown in the table below:
| Factor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|--------|------|-------|-------|-------|-------|-------|-------|-------|
| Respondents (%) | 68.8 | 60.4 | 22.8 | 20.8 | 16.8 | 14.7 | 6.7 |
**Questions:**
Consider the following definitions:
- Let \( A \) denote the set of factors that had a response greater than 20%.
- Let \( B \) denote the set of factors that had a response between 15% and 25%.
- Let \( C \) denote the set of factors that had a response less than 25%.
Based on these definitions, answer the following questions:
(a) Determine \(n(A)\), \(n(B)\), and \(n(C)\).
\( n(A) = \)
\( n(B) = \)
\( n(C) = \)
(b) Compute \( n(A \cap B) \).
\( n(A \cap B) = \)
(c) Compute \( n(A^c \cap C) \).
\( n(A^c \cap C) = \)
(d) Compute \( n(A \cap B^c) \).
\( n(A \cap B^c) = \)
(e) Compute \( n(A^c \cap C^c) \).
\( n(A^c \cap C^c) = \)
(f) Compute \( n[(A \cup B) \cap C] \).
\( n[(A \cup B) \cap C] = \)
---
**Graph/Diagram Explanation:**
The provided table categorizes the](https://content.bartleby.com/qna-images/question/6e1b5fc2-7275-49e6-a434-e3b12d2d745f/2ab4d0f2-c5d4-4038-9e92-d339429793ae/agjg9ak_processed.jpeg)
Transcribed Image Text:**Title: Understanding Factors Influencing Brand Switching**
**Introduction:**
In a study of factors that influence brand switching by a certain demographic, the following factors were identified as significant based on the responses of the 439 participants in the survey:
1. Better price
2. Friend's recommendation
3. Seeing others use it
4. Interesting packaging
5. Buzz—people talking about the brand
6. An advertisement
7. Press stories
8. Entertainer/sports celebrity endorsement
**Survey Results:**
The results of the survey are shown in the table below:
| Factor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|--------|------|-------|-------|-------|-------|-------|-------|-------|
| Respondents (%) | 68.8 | 60.4 | 22.8 | 20.8 | 16.8 | 14.7 | 6.7 |
**Questions:**
Consider the following definitions:
- Let \( A \) denote the set of factors that had a response greater than 20%.
- Let \( B \) denote the set of factors that had a response between 15% and 25%.
- Let \( C \) denote the set of factors that had a response less than 25%.
Based on these definitions, answer the following questions:
(a) Determine \(n(A)\), \(n(B)\), and \(n(C)\).
\( n(A) = \)
\( n(B) = \)
\( n(C) = \)
(b) Compute \( n(A \cap B) \).
\( n(A \cap B) = \)
(c) Compute \( n(A^c \cap C) \).
\( n(A^c \cap C) = \)
(d) Compute \( n(A \cap B^c) \).
\( n(A \cap B^c) = \)
(e) Compute \( n(A^c \cap C^c) \).
\( n(A^c \cap C^c) = \)
(f) Compute \( n[(A \cup B) \cap C] \).
\( n[(A \cup B) \cap C] = \)
---
**Graph/Diagram Explanation:**
The provided table categorizes the
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