(a)What percentage of regular grade gasoline sold between $2.66 and $4.26 per gallon?Since it is given that the retail price per gallon of gas has a bell-shaped distribution, the empirical rule can be applied.The empirical rule uses standard deviations about the mean to describe the percentage of the data that will lie within a given range. Therefore, we must first determine how many standard deviations above and below the mean $2.66 and $4.26 are. It is given that the mean is $3.46 and the standard deviation is $0.40.The number of standard deviations, z, a value is from the mean can be found using the following formula. If we are given a value that is smaller than the mean, use the following.

z =

mean given value

standard deviation

If the given value is larger than the mean, use the following.

z =

given value mean

standard deviation

The difference between the mean and the smaller value, $2.66, is $0.80. How many standard deviations, z, below the mean is $2.66?

z	=	mean smaller value standard deviation
	=	3.46 0.40
	=

The difference between the larger value, $4.26, and the mean is $0.80. How many standard deviations above the mean is $4.26?

z	=	larger value mean standard deviation
	=	4.26 0.40
	=