A new car that is a gas and electricpowered hybrid has recen

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 60 miles and a standard deviation of 5 miles. Find the probability of the following events. Use Excel to obtain more accuracy. The car travels more than 65 miles per gallon. Probability = The car travels less than 54 miles per gallon. Probability = The car travels between 56 and 66 miles per gallon. Probability =

Solution

Mean ( u ) =60
Standard Deviation ( sd )=5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)              
P(X > 65) = (65-60)/5
= 5/5 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587                  
b)
P(X < 54) = (54-60)/5
= -6/5= -1.2
= P ( Z <-1.2) From Standard Normal Table
= 0.1151  
c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 56) = (56-60)/5
= -4/5 = -0.8
= P ( Z <-0.8) From Standard Normal Table
= 0.21186
P(X < 66) = (66-60)/5
= 6/5 = 1.2
= P ( Z <1.2) From Standard Normal Table
= 0.88493
P(56 < X < 66) = 0.88493-0.21186 = 0.6731