According to the American Automobile Association (AAA), the mean cost of a gallon of regular unleaded fuel in 2007 was $2.835. AAA noted that the standard deviation of the fuel price was $0.15. A random sample of n=100 gas stations is selected and the mean gas price is analyzed.

Question

According to the American Automobile Association (AAA), the mean cost of a gallon of regular unleaded fuel in 2007 was $2.835. AAA noted that the standard deviation of the fuel price was $0.15. A random sample of n=100 gas stations is selected and the mean gas price is analyzed.
What is the probability that the mean fuel cost is between $2.84 and $2.86?

MathGuru · Answer

Use z-scores.

Formula for this problem:

z = (x - mean)/(sd/√n)

Find two z-scores, using 2.84 for x and also 2.86 for x. Mean = 2.835 and sd = 0.15. Sample size n = 100.

Once you find the two z-scores, use a z-distribution table to determine your probability between the two z-scores.