In February 2002 the Argentine peso lost 70% of its value compared to the United
ID: 2958380 • Letter: I
Question
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. Use the following data to answer questions 9 through 12.
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
18. The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank. _______
Explanation / Answer
This is the second problem since you didn't put te questions for the first.
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assume that it is normally distributed:
The probability of having an average of greater than 28, is the same as having a total of more than 840.
The consumption of each car is a random variable. The sum of random variables is also a random variable and has a mean equal to the sum of their means and a variance equal to the sum of their variances.
Let X~N(25.9, 90.25)
Let Y = 30X
Then:
Y~N(30×25.9, 30×90.25)
Y~N(777, 2707.5)
This means Y has a mean of 777 and a standard deviation of 52.033643
P(Y>840) 0.000327
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