If you were to toss a fair coin a given number of times in a row, you would expect to see roughly the same number of heads and tails. If you were to try this out several times, you will obviously get different totals each time; sometimes you will see many more heads, sometimes you will see many more tails. As you run more and more trials, you will find that the cases in which the number of heads and tails are close occur much more frequently than the cases in which one is favored more than the other. In fact, if you were to record the results of hundreds of trials, you will find that the data mimics the probability distribution of the normal distribution, as shown in the simulator below.
Enter the number of times you want to flip the coin in each trial in the first box, and the number of times you want to run this trial in the second box. Click Run Test once to run the first set of trials, then click again to add another set of trials to data you just collected. Notice that as you increase the number of trials (either by increasing the number in the second box or clicking the Run Test button repeatedly), the data comes closer to resembling the probability distribution of the normal distribution (given in red).