[shellysharma]

[jcaron2]

You want to know the area under the normal (Gaussian) curve to the left of the point at 2 standard deviations below the average (which would be like a z-score of -2). However, the z-score chart is only for positive values of z, so you just need to realize that the normal curve is symmetric. The area to the left of z = -2 is exactly the same as the area to the right of z = +2. So now if you go to the chart, you'll see that for a z-score of 2, the value of p is 0.4772. That means that between z = 0 (at the center of the normal curve) and z = 2, the area under the curve is 0.4772. So how much area remains to the right of z = 2? Well, we know that the total area under the normal curve is 1.0, and it's symmetric, so the total area to the right of the mean (z = 0) is 0.5. Since the area between z = 0 and z = 2 accounts for 0.4772 out of the total, the remaining area, to the right of z = 2, must be 0.5 - 0.4772 = 0.0228. And, as we discussed before, that also means that the area to the left of z = -2 would likewise be 0.0228.

So that's your answer. The probability of being 2 or more standard deviations below the mean is 2.28%.