1. I assumed the first one was binomial, so i used binomcdf(100, 0.6, 60) on my caluclator and got a 53.79% chance. Not totally sure on this one, but this is what I got.
2. It's given that it's normal, so use normalcdf(-infinity, 299, 300, 3) (or you could use a table but thats very tedious). Comes out to 36.944% - This means that 36.944% of bottles will contain less than 299mL. This one is definitely right.
3. I multiplied the distribution by 6 (so it would be ~ Nor(1800, 18)), and I decided to look for 1794. I believe this should be the same probability (someone can correct me if I'm wrong). I plugged in normalcdf(-infinity, 1794, 1800, 18), and I got 36.944%
Edit: I did all this in AP Stats like a couple months ago, so my memory is hazy. This is what I got though. I don't think #3 is right.