Suppose X is a normal random variable with Find P137 X 307

Suppose X is a normal random variable with

Find P(13.7 < X < 30.7).

I understand that it turns into:

-2.13 < x < -.43

But I don\'t know what to do after, can someone help me please? Explain how to solve it from there and why?

Solution

Mean ( u ) =35
Standard Deviation ( sd )=10
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 13.7) = (13.7-35)/10
= -21.3/10 = -2.13
= P ( Z <-2.13) From Standard Normal Table
= 0.01659
P(X < 30.7) = (30.7-35)/10
= -4.3/10 = -0.43
= P ( Z <-0.43) From Standard Normal Table
= 0.3336
P(13.7 < X < 30.7) = 0.3336-0.01659 = 0.317