Question

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)?

  

Answer 1

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%