Standard Deviation and Probability.

What you should be seeing at left is a title, a slider, a box containing three numbers, and a light blue graph. The graph is the normal distribution. Slide the slider about half way over to the right. The graph should now be dark turquoise on the left, and blue on the right. The first of the two numbers is the percentage of the total area under the curve that is blue, ie., the area of the right-tail. The second number is the probability associated with the right-tail (approximate values). If the total area is 1, then p is just the area of the blue (right-tail) part of the graph.

Finally, the value z is the all important z-score (which should make everything clear). It's the number of standard deviations the line between turquoise and blue is from the mean. If you're one standard deviation to the left of the mean, then z = -1, and two standard deviations to the right gives z = +2. The higher the value of z, the smaller the probability associated with the right-tail. By the time you get out to z = 3.6, the probability p = 0.0001 approximately, which means you have about one chance in 10,000 of having a random data point fall beyond z = 3.6. And the probabilities get rapidly smaller thereafter.