residents of neighborhood own more than one car but one of t

residents of neighborhood own more than one car but one of their cars is chosen as main family car. the age of these family vehicles can be modeled by a normal distribution with mean 2 years and standard deviation 6 months. what percentage of vehicles is between 1 and 3 years old?

Solution

Mean ( u ) =2
Standard Deviation ( sd )= 6 months = 0.5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 1) = (1-2)/0.5
= -1/0.5 = -2
= P ( Z <-2) From Standard Normal Table
= 0.02275
P(X < 3) = (3-2)/0.5
= 1/0.5 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(1 < X < 3) = 0.97725-0.02275 = 0.9545 ~ 95.45% are in between 1 to 3