That's n=500 trials, with probability of a "success" (i.e., heads) in ONE trial as 0.5 and a standard deviation as 


 
where 


We consider "between them to mean exclusive of 200 and 300, so to use the
normal approximation we exclude 200, by taking the lower bound on the upper
side of 200, as 200.5, and the upper bound on the lower side of 300, as 299.5.
us.  You can find the z-scores and look up the answer on a normal table, if
you aren't allowed to use technology.

It comes out as 0.999990455 with technology.

Common sense tells us that it's extremely likely. The probability rounds to 1.
So it's almost certain that you'll get somewhere between those numbers of heads.

Edwin