Final answer:
To calculate the total area under the normal curve for the given z-scores, find the area to the left of z=-1.56 and the area to the right of z=2.56 by using the Z-table or statistical software, then sum these two areas.
Step-by-step explanation:
To find the area under the normal curve to the left of z=-1.56, you need to use a Z-table or other statistical tools such as a calculator or software that can calculate this value. Once you find the area to the left of z=-1.56, you will have the first part of the answer. To find the area to the right of z=2.56, you need to calculate or find the area to the left of this z-score (using the Z-table or other tools) and then subtract this value from 1, since the total area under the normal distribution is 1. The sum of these two areas will give the combined area under the normal curve for the specified z-scores.
For example, If a Z-table indicates that the area to the left of z=-1.56 is 0.0594, then this is the first part of your answer. If the table shows the area to the left of z=2.56 is 0.9949, then the area to the right of z=2.56 is 1 - 0.9949 = 0.0051. The total area sought would be 0.0594 (left of -1.56) + 0.0051 (right of 2.56), which equals 0.0645.