This Demonstration provides a dynamic supplement to elementary statistics textbooks that show how to use a table of standard normal cumulative probabilities. As you slide along, holding fixed at the upper limit, these probabilities are obtained as the area shown under the curve. Moving to the left, the upper area probability is added to the area to the left of . The probability corresponding to the interval between and is obtained by taking the complement.
You can see that the probability corresponding to the interval is close to 0.5.
This Demonstration also illustrates the 68–95–99.7 rule that, in a normally distributed population, about 68% of the observations fall within one standard deviation, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.