Question 12 of 20 10.0 Points In February 2002 the Argentine peso lost 70% of it
ID: 3225982 • Letter: Q
Question
Question 12 of 20
10.0 Points
In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported.
Number of Products Purchased
Brands Purchased
Fewer
Same
More
Total
Same
10
14
24
48
Changed
262
82
8
352
Total
272
96
32
400
What is the probability that a consumer selected at random purchased fewer products than before?
What is the probability that a consumer selected at random purchased the same number or more products than before?
What is the probability that a consumer selected at random purchased fewer products than before and changed brands?
Given that a consumer changed the brands, what then is the probability that the consumer purchased fewer products than before?
Question 12 of 20
10.0 Points
In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported.
Number of Products Purchased
Brands Purchased
Fewer
Same
More
Total
Same
10
14
24
48
Changed
262
82
8
352
Total
272
96
32
400
What is the probability that a consumer selected at random purchased fewer products than before?
Explanation / Answer
from the table we get-
total number of consumers is 400
out of which 272 consumers purchased fewer products than before.
hence the probability that a ranodmly selected consumer will purchase fewer products than before is 272/400=0.68 [answer]
96 consumers purchased same number of products and 32 consumers purchased more number of products.
so total number of consumers who purchased sme number or more products than before is 96+32=128
hence the probability that a consumer selected at random purchased the same number or more products than before is 128/400=0.32 [answer]
out of the 272 consumers who purchased fewer products , 262 of them changed brands and 10 stick to the same brand
so the probability that a consumer selected at random purchased fewer products than before and changed brands is 262/400=0.655 [answer]
there are 352 consumers who changed brands out of which 262 consumers purchased fewer brands
so P[consumer purchased fewer products than before | consumer changed brands]
=P[ consumer purchased fewer products and changed brands]/P[consumer changed brands]
=(262/400)/(352/400)=262/352=0.7443182 [answer]
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