This applet is designed to help you understand and investigate the calculation of probabilities from a Normal distribution. The screen starts with a Standard Normal distribution ( the variate, X ~ N(0,1) ).
You can drag the two red circles to the left and right, to see how the probability (the area under the curve) changes as you move the boundaries.
Clicking "Invert" enables you to look at the areas outside the boundaries. Clicking "Reset" returns to the start position.

You can use the boxes at the bottom of the page to vary the mean and standard deviation of the distribution. Underneath the graph you will then see the new distribution of the variate X, and the probability calculations from that new distribution.
Checking the "Symmetric" box at the top constrains the distribution to being symmetric about the mean.
BEWARE! Although the probabilities are rounded to 4 dp they are not guaranteed to be accurate. You will need tables or special calculators to get more accurate values.