In 2006 the energy information Administration report that th

In 2006. the energy information Administration report that the mean retail price per gallon of regular grade gasoline was mu =$2.30. Suppose that the standard deviation was sigma = $0.15 and that the retail price per gallon has a bell-shaped distribution. Use empirical rule to answer the following questions. Find the percentage of regular grade gasoline sold between $2.15 and $2.60. Find the interval in which at least 95% of the retail price per gallon of regular grade gasoline will lie.

Solution

Normal Distribution
Mean ( u ) =2.3
Standard Deviation ( sd )=0.15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 2.15) = (2.15-2.3)/0.15
= -0.15/0.15 = -1
= P ( Z <-1) From Standard Normal Table
= 0.15866
P(X < 2.6) = (2.6-2.3)/0.15
= 0.3/0.15 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(2.15 < X < 2.6) = 0.97725-0.15866 = 0.8186                  

b)

(b)
About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.
(u ± 2*s.d)
(2.30 ± 2*0.15 )
(2.30 - 2*0.15 ) , (2.30 + 2*0.15 )
(2, 2.6)