I've tried so many things but I never get the correct answer. Here's an example:

For $\displaystyle Y \sim B(20,0.4)$ Find $\displaystyle P(3<Y<13)$ using a normal approximation

This is what I do:

$\displaystyle \mu=np=(20)(0.4)=8$

$\displaystyle \sigma^2=np(1-p)=20(0.4)(0.6)=4.8$

But at this point, I get in a mess.

The correct answer is 0.9596

Thanks in advance for any replies.