What percentage of the area of the standard normal distribution is between z = -2.00 and z = +2.00? How do you know this?
play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
and you can see how it works.
To determine the percentage of the area between z = -2.00 and z = +2.00 on the standard normal distribution curve, we can utilize a Z-table or a statistical software.
Using a Z-table, you can find the area under the curve by looking up the corresponding Z-scores. The Z-table provides the area to the left of a given Z-score. In this case, we want to find the area between z = -2.00 and z = +2.00, so we need to find the area to the left of z = +2.00 and subtract the area to the left of z = -2.00.
Typically, Z-tables provide values in terms of positive Z-scores. However, we can use the symmetry of the standard normal distribution to our advantage. Since the standard normal distribution is symmetric around zero, the area to the left of z = -2.00 is equal to the area to the right of z = +2.00.
Hence, to find the total area between -2.00 and +2.00 on the standard normal distribution, we can determine the area to the left of +2.00 and subtract it from 1 (since the total area under the curve is always 1).
Using a Z-table, we find that the area to the left of z = +2.00 is approximately 0.9772. Subtracting this value from 1, we get:
1 - 0.9772 ≈ 0.0228
Therefore, approximately 2.28% of the area under the standard normal distribution curve lies between z = -2.00 and z = +2.00.