G'Day Markus.
I've attached an Excel spreadsheet that should let you calculate what you want to know. It's overkill for your needs, but I had it handy. Used to do these calculations all the time for work, for furnaces and pneumatic conveying, ventilation, and dust extraction systems, because Oberon (where I live and worked) is +1100m.
Typically here at +1100m, on average the air is 7°C cooler than sea level due solely to altitude. So standard atmospheric density at sea level is 1.2 kg/m3 at 21°C. where in Oberon is it 1.08 kg/m3 @14°C.
Not only is the air less dense at altitude, but you aren't looking through the thickest part of it! The densest kilometre isn't in the way in Oberon, for example. This is worth at least 1 magnitude in naked eye visibility. When I first returned to Oberon, I noted that I could regularly see M7 stars or better with the naked eye, where at sea level M6 is considered the limit in a dark site.
For more information (if you need it) search for the US Standard Atmosphere. It may have NASA or NOAA in the title as well. It should give you a table of atmospheric temperatures, pressures and densities all way up through the stratosphere. I have it in one of my Fan Engineering texts that are buried somewhere...
Al.
Al.