Find the area under the standard normal curve over the inter

Find the area under the standard normal curve over the interval z = -0.23 to z = 0.23. Compute probabilities using the standard normal table in Round the answer to four decimal places.

Solution

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 < -0.23) = (-0.23-0)/1
= -0.23/1 = -0.23
= P ( Z <-0.23) From Standard Normal Table
= 0.40905
P(X < 0.23) = (0.23-0)/1
= 0.23/1 = 0.23
= P ( Z <0.23) From Standard Normal Table
= 0.59095
P(-0.23 < X < 0.23) = 0.59095-0.40905 = 0.1819