The question is will the bare spots be covered by the already growing grass?

Okay So after a lot of research, and finally deciding to fill my back yard with lush grass. and went with the most expensive seed I could afford to cover a 100sqft area and got 4lbs I am having problems with huge bare spots. It has been well over a month since getting the ground ready, pretty much leveled slightly tilled in products suggested after getting soil tested, and sewing the seed mix. Not very satisfied with the results with big patches I though buying high grade seeds would yield better results. the first 2 weeks I watered for about 10-13 minutes in the morning and about 7 minutes around 1pm to keep the ground moist. after 3 weeks I cut back to a 6 min in the morning and 6 in the afternoon. I mowed at week 4 (gas was about 3 inches) the highest setting on my mower (it took about half a inch or less) , then dropped it and mowed again 6 days later.