Atmospheric pressure and inspired oxygen pressure fall roughly linearly with altitude to be 50% of the sea level value at 5500 m and only 30% of the sea level value at 8900 m (the height of the summit of Everest).
During active climbing, oxygen saturation drops, because red blood cells go through the lungs more quickly when you exercise. There isn't enough time for them to equalize with the oxygen in your lungs.
