SOLUTION: Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.45 with a standard deviation of $.20 and that the retail price per gallon has a b

Algebra ->  Statistics  -> Density-curves-and-normal-distributions -> SOLUTION: Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.45 with a standard deviation of $.20 and that the retail price per gallon has a b      Log On


   

Question 1184185: Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.45 with a standard deviation of $.20 and that the retail price per gallon has a bell shaped distribution. What percentage of a regular grade gasoline sold for more than $3.85 per gallon
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
population mean = 3.45
population standard deviation = .20

z = (x - m) / s
z is the z-score
x is the raw score
m is the raw mean
s is the standard deviation.

formula becomes:

z = (3.85 - 3.45) / .2 = 2.

area to the right of a z-score of 2 is equal to .022750062.

that's the probability of the price of gasoline being greater than 3.85.

the probability of .022750062 rounds to .0228 as shown in the following diaplay of the z-score calculator by david m. lane.



the z-score calculator can work off the mean and standard deviation to give you the raw score, as shown.

the z-score calculator gives you the z-score if the mean is set to 0 and the standard deviation is set to 1.

here's the display when looking for the z-score.