SHOW YOUR WORK, AND EXPLAIN: According to the American Automobile Association (A
ID: 3058452 • Letter: S
Question
SHOW YOUR WORK, AND EXPLAIN: According to the American Automobile Association (AAA), the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was $3.65 (AAA Fuel Gauge Report). Assume that the standard deviation of such costs is $.15. Suppose that a random sample of n = 100 gas stations is selected from the population and the cost per gallon of regular unleaded fuel is determined for each. Consider x, the sample mean cost per gallon.
a. Calculate mx and x
b. What is the approximate probability that the sample has a mean fuel cost between $3.65 and $3.67?
c. What is the approximate probability that the sample has a mean fuel cost that exceeds $3.67?
Explanation / Answer
SHOW YOUR WORK, AND EXPLAIN: According to the American Automobile Association (AAA), the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was $3.65 (AAA Fuel Gauge Report). Assume that the standard deviation of such costs is $.15. Suppose that a random sample of n = 100 gas stations is selected from the population and the cost per gallon of regular unleaded fuel is determined for each. Consider x, the sample mean cost per gallon.
a. Calculate mx and x
b. What is the approximate probability that the sample has a mean fuel cost between $3.65 and $3.67?
c. What is the approximate probability that the sample has a mean fuel cost that exceeds $3.67?
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