40 weeks and stilll waiting!

So I called the hospital this morning, they told me Ill be 41 weeks on the 17th and only then, they will check my cervix, make an ultrasound and monitoring to check if everything is ok! They told me if you are not ready yet, you will be sent home until you reach 42 weeks! And ONLY then, you May be induced! As it is a first pregnancy, they want to let nature do its role! Anyone experienced or is experiencing this?!