Question

If I toss a fair coin 800 times, what can be said about the likely proportion of tosses that will land on heads?

Answer 1

Assuming each flip is independent, if you flip a coin with a probability of landing heads pp, nntimes, the probability distribution over the number of successes k is the binomial distribution, NOT the normal curve.

The expectation of the binomial distribution is  

Assuming the coin is fair (p=0.5), then you get

800*0.5 = 400

So, of all the possibilities of how many times heads will appear, 400 is most likely.

Note,

The probability of getting exactly 400 is about 2.5%.