Answer:
(a) 169
(b) 341
(c) 125
(d) 87
Step-by-step explanation:
Consider the Venn diagram below.
The total number of shoppers surveyed is, N = 428.
Number of shoppers who made a purchase, n (P) = 216
Number of shoppers who were satisfied with the service they received,
n (S) = 294
Number of shoppers who made a purchase but were not satisfied with the service, [tex]n(S^{c}\cap P)[/tex] = 47
(a)
The number of shoppers who made a purchase and were satisfied with the service = n (S ∩ P)
[tex]n(S\cap P)=n(P)-n(S^{c}\cap P)\\=216-47\\=169[/tex]
(b)
The numbers of shoppers who made a purchase or were satisfied with the service = n (P ∪ S)
[tex]n(P\cup S)=n(P)+n(S)-n(P\cap S)\\=n(P)+n(S)-n(S\cap P)\\=216+294-169\\=341[/tex]
(c)
The numbers of shoppers who were satisfied with the service but did not make a purchase = [tex]n(S\cap P^{c})[/tex]
[tex]n (S\cap P^{c} ) = n (S) - n (S \cap P)\\=294-169\\=125[/tex]
(d)
The number of shoppers who were not satisfied and did not make a purchase = [tex]n(S^{c}\cap P^{c})[/tex]
[tex]n(S^{c}\cap P^{c})=N-n(S\cup P)\\=N-n(P\cup S)\\=428-341\\=87[/tex]
