Muscle used for inspiration during quite breathing:

DiaphragmIt is crucial for breathing and respiration.It's responsible for 45% of the air that enters the lungs during quiet breathing.During inhalation, the diaphragm contracts, thus enlarging the thoracic cavity (the external intercostal muscles also paicipate in this enlargement).This reduces intra-thoracic pressure: in other words, enlarging the cavity creates suction that draws air into the lungs.When the diaphragm relaxes, air is exhaled by elastic recoil of the lung and the tissues lining the thoracic cavity in conjunction with the abdominal muscles which act as an antagonist paired with the diaphragm's contraction.