Use this applet to explore the binomial distribution, the normal distribution and the T distribution. To begin click on a check box and then zoom to the appropriate distribution. Uncheck the box to make that distribution disappear to investigate the other distribution.

Check both the T distribution and the Normal distribution and then zoom to the Normal distribution. You will notice that they are not the same initially. Adjust the degrees of freedom (df) on the T distribution until the T distribution follows the Normal Curve. What was your answer?
What happens to the Normal distribution as the standard deviation (sd) increases?
Adjust the sample size (n) and the probability of success (p) to see how that changes the distribution. What other distribution does the binomial distribution look like?