Big baby

So I went to my 37wk appt this past Wednesday and got a US and was told my baby was 8lb4oz and her head was at 9.3cm! The dr said I could possibly be having a 9.5 lb baby! My husband and I are both tall. My mom told me I was 9lb 12oz (had natural) and my husband was 8lb 4oz. My question is what are the chances of having a c-section vs a natural birth? Did anyone go through this?

The dr said we'll try natural first but c-section isn't out of the picture. My hips aren't that big either.