The average human has a density of 945kg/m^3 after inhaling and 1020kg/m^3 after exhaling.
Without making any swimming movements, what percentage of the human body would be above the surface in the Dead Sea ( a body of water w/ a density of about 1230kg/m^3)?
You can only ask one question at a time so I edited accordingly. What you are looking at here is buoyancy. If something denser than the water in the Dead Sea is placed on its surface it will sink. If something less dense than the water in the Dead Sea is placed on its surface it will float. The ratio of the two densities will determine what percentage of the object will be below the water level and above the water level. So in the case of inhaling (more air is present on the lungs thus making the human body less dense overall), divide the two ratios to get 945/1230 = 76.8%. This is the percentage below the surface of the water so subtract from one to get the percentage above the surface of the water: 1-0.768 = 23.2%. In the case of exhaling, the ratio is 1020/1230 = 82.9% below the surface and 1-0.829 = 17.1% above the surface. This makes sense that taking a deep breath causes more of the body to rise above the water versus exhaling. The answers are summarized below: