SOLUTION: use normal approximation and find the probability of getting between 200 and 300 heads in 500 tosses of a fair coin.

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Question 1149774: use normal approximation and find the probability of getting between 200 and 300 heads in 500 tosses of a fair coin.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
That's n=500 trials, with probability of a "success" (i.e., heads) in ONE trial as 0.5 and a standard deviation as 

mean+=+mu+=+np+=+500%2A0.5=250
matrix%281%2C2%2C+standard%2C+deviation%29=sigma=sqrt%28npq%29 
where q=1-p+=+1-0.5+=+0.5
sqrt%28npq%29=sqrt%28500%2A0.5%2A0.5%29=11.18033989

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