Final answer:
The Z-score corresponding to a cumulative area of 0.94 is found by identifying the area in the Standard Normal Table closest to 0.94 or by using a calculator with the invNorm function. It is approximately 1.555.
Step-by-step explanation:
To find the Z-score that corresponds to a cumulative area of 0.94 using a Standard Normal Table or technology, one needs to look up the area closest to 0.94 in the body of the table and then identify the corresponding Z-score. When we refer to a cumulative area of 0.94 in a normal distribution, it indicates that 94% of the data falls below this Z-score, and 6% falls above it. To find this value, one can also use technology such as a TI-83, 83+, or 84+ calculator with the command invNorm(0.94,0,1). The result will provide the Z-score where the area to the left is 0.94.
For example, if using a Z-table, the cumulative area to the left of Z-score 1.55 is approximately 0.9394, and for Z-score 1.56, it's approximately 0.9406. Since 0.94 is between these two areas, the Z-score we are looking for is also between 1.55 and 1.56. Hence, the Z-score that corresponds to a cumulative area of 0.94 is approximately 1.555.