zbird2134

The Z table values for "2" and "3" under the zero column are 0.9772 and 0.9987. Since this question is asking about "at least" 2 or 3 standard deviations, you're looking for the area under the tails on either side of the mean. Which means one minus the area under the curve, times two.

So for 2 standard deviations, the area under the curve based on the Z table value is 0.9772. Which implies area under the tail is (1 - 0.9772) = 0.0228. Ultimately, area under the both the tails, because the normal distribution is symmetrical, is (2 * 0.0228) = 0.0456.

Hope this helps.