Using the Standard Normal Table determine the proportion of

Using the Standard Normal Table, determine the proportion of the area under the normal curve that falls between z = -.30 and z = -.80.

       .1702
       -.1702
       .4060
       -.4060

Solution

Normal Distribution
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

To find P(a < = Z < = b) = F(b) - F(a)
P(X < -0.3) = (-0.3-0)/1
= -0.3/1 = -0.3
= P ( Z <-0.3) From Standard Normal Table
= 0.38209
P(X < -0.8) = (-0.8-0)/1
= -0.8/1 = -0.8
= P ( Z <-0.8) From Standard Normal Table
= 0.21186
P(-0.3 < X < -0.8) = 0.21186-0.38209 = -0.1702