Will my baby's lungs be mature?

I'm 37 weeks tomorrow, and in 4 days I am going in for an amnio to check if his lungs are mature, if so they are inducing that night. I'm really anxious and can't find any sites that say when the lungs are fully mature. I'm having a boy. And my dr will not give a steroid shot so please do not mention them, just what week lungs are usually mature at. Thanks!