Question

The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline was $3.51 . Suppose that the standard deviation was $0.10 and that the retail price per gallon has a bell-shaped distribution. (Hint: You must use the empirical rule for this problem. )

a. What percentage of regular grade gasoline sold between $3.31 and $3.71 per gallon (to 1 decimal)?

b. What percentage of regular grade gasoline sold between $3.31 and $3.61 per gallon (to 1 decimal)?

c. What percentage of regular grade gasoline sold for more than $3.71 per gallon (to 1 decimal)?

Answer 1

Ans:

The 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

a)

3.31 and 3.71 are 2 standard deviations below and above the mean respectively.

So,

95.0% of regular grade gasoline sold between $3.31 and $3.71 per gallon.

b)3.31 and 3.61 are 2 standard deviations below and one standard deviation above the mean respectively.

percentage of regular grade gasoline sold between $3.31 and $3.61 per gallon

=(0.95/2)+(0.68/2)

=0.475+0.34=0.815 or 81.5%

c)2.5% of regular grade gasoline sold for more than $3.71 per gallon.