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Complete 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?(to 4 decimals)
Answer:
0.1788
Explanation:
We solve this question using z score formula.
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
a. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon?(to 4 decimals)
For the United States
x is the raw score = $3.50
μ is the population mean = Average price for a gallon of gasoline in the United States is $3.73
σ is the population standard deviation = standard deviation of $.25 in the United States = $0.25
z score = $3.50 - $3.73/$0.25
=-0.92
Determining the Probability value from Z-Table:
P(x ≤ 3.50) = P(x < 3.5) = P(z = -0.92)
= 0.17879
Approximately to 4 decimal places = 0.1788
Therefore, the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon is 0.1788