The area under the standard normal curve between two identical z-scores, in this case, Z₁=1.67 and Z2=1.67, is actually zero since there is no range between them. Generally, one could find the area between different z-scores by looking them up in the z-table and subtracting to find the difference.
To find the area under the standard normal curve between the given z-values of Z₁=1.67 and Z2=1.67, you effectively are looking for the area between the same point, which is zero. However, when finding the area between two different z-scores, you would use a standard normal probability table (z-table) or a calculator function such as invNorm. Since the same z-score is given twice, this suggests no actual range, and therefore, the area calculation is unnecessary for this specific example.
For a general calculation between different z-values, you would look up each z-score's associated area to the left in the z-table, and subtract the smaller area from the larger area to find the area between the two z-scores. The z-table reveals cumulative probabilities, which represent the area under the curve to the left of a given z-value.