Question

# The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline...

The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline was \$3.56. Suppose that the standard deviation was \$.10 and that the retail price per gallon has a bell-shaped distribution.

NOTE: Please use empirical rule approximations for this problem.

a. What percentage of regular grade gasoline sold between \$3.46 and \$3.66 per gallon (to 1 decimal)?

b. What percentage of regular grade gasoline sold between \$3.46 and \$3.76 per gallon (to 1 decimal)?

c. What percentage of regular grade gasoline sold for more than \$3.76 per gallon (to 1 decimal)?

Empirical rule states that for a normal distribution:

68% of the data will fall within one standard deviation of the mean.

95% of the data will fall within two standard deviations of the mean.

Almost all (99.7%) of the data will fall within three standard deviations of the mean.

( 3.46 , 3.66 )

= ( 3.36 , 3.76 )

=( 3.26 , 3.86 )

a)

The score 3.46 and 3.66 are within one standard deviation of the mean.

Percentage of regular grade gasoline sold between 3.46 and 3.66 = 68%

b)

The score 3.76 is 2 standard deviation above the mean and the score 3.46 is one standard deviation below the mean.

Percentage of regular grade gasoline sold between 3.46 and 3.76 = 95/2 + 68/2 = 81.5%

c)

The score 3.76 is two standard deviation above the mean.

Percentage of regular grade gasoline sold for more than 3.76 = (100 - 95)/2 = 2.5%

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