How to determine the width of the zone of acceptance in hypothesis testing?

[amberglo]

First and foremost, I am terrible in Stats so bear w/ me on this one. This is my question, if anyone has an idea on how to figure out this problem that would be great! Here it is: Suppose you flip a coin 100 times and you want to test the hypothesis that the coin is fair, making sure there is less than a 5 percent chance of erroneously rejecting the fair coin hypothesis. How wide should the zone of acceptance be? How wide should the zone be if you flip the coin 5 times?

 

[CRGreathouse]

What you want is a range balanced around the mean which has cumulative probability 95%. The chance of 2 or 3 heads out of 5 flips is
((5 choose 2) + (5 choose 3)) / 2^5 = 20/32
The chance of 1 to 4 heads is
((5 choose 1) + (5 choose 2) + (5 choose 3) + (5 choose 4)) / 2^5 = 30/32

With 100 flips, you are probably intended to use the normal curve as an approximation rather than the explicit binomial formula, although either would work.