In a study of factors that influence brand switching by a certain demographic, the following factors were identified as being significant as judged by 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 The results of the survey follow. Factor 1 2 3 4 5 6 7 8 Respondents (%) 68.6 60.2 22.8 20.6 16.6 16.6 14.9 6.9 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%, and let C denote the set of factors that had a response less than 25%. Find the following. (a) n(A), n(B), n(C) n(A) = n(B) = n(C) = (b) n(A ∩ B) (e) n(Ac ∩ Cc) (f) n[(A ∪ B) ∩ C]

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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In a study of factors that influence brand switching by a certain demographic, the following factors were identified as being significant as judged by 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

The results of the survey follow.

Factor 1 2 3 4 5 6 7 8
Respondents (%) 68.6 60.2 22.8 20.6 16.6 16.6 14.9 6.9

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%, and let C denote the set of factors that had a response less than 25%. Find the following.

(a)    
n(A), n(B), n(C)

n(A) =  
n(B) =  
n(C) =  

(b)    
n(A ∩ B)


(e)    
n(Ac ∩ Cc)



(f)    
n[(A ∪ B) ∩ C]
 
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