The average price for a gallon of gasoline in the United States is $3.73 and in
ID: 3135176 • Letter: T
Question
The average price for a gallon of gasoline in the United States is $3.73 and in Russia it is $3.40 (Bloomberg Businessweek, March 5–March 11, 2012). Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $.25 in the United States and a standard deviation of $.20 in Russia. a. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon? b. What percentage of the gas stations in Russia charge less than $3.50 per gallon? c. What is the probability that a randomly selected gas station in Russia charged more than the mean price in the United States?
Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 3.5
u = mean = 3.73
s = standard deviation = 0.25
Thus,
z = (x - u) / s = -0.92
Thus, using a table/technology, the left tailed area of this is
P(z < -0.92 ) = 0.17878638 [ANSWER]
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B)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 3.5
u = mean = 3.4
s = standard deviation = 0.2
Thus,
z = (x - u) / s = 0.5
Thus, using a table/technology, the left tailed area of this is
P(z < 0.5 ) = 0.691462461 = 69.15% [ANSWER]
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c)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 3.73
u = mean = 3.4
s = standard deviation = 0.2
Thus,
z = (x - u) / s = 1.65
Thus, using a table/technology, the right tailed area of this is
P(z > 1.65 ) = 0.049471468 [ANSWER]
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