Answer:
Therefore, the z-score that corresponds to the cumulative area 0.1515 is approximately -1.035.
Explanation:
To find the z-score that corresponds to a cumulative area of 0.1515, we can use the standard normal table.
First, we look for the closest entry in the table to the given area. In this case, the closest entry is 0.1517, which corresponds to a z-score of -1.04.
Since the given area is not exactly in the table, we use the z-score halfway between the corresponding z-scores for the two closest entries.
The closest entry with a smaller area is 0.1492, which corresponds to a z-score of -1.04. The closest entry with a larger area is 0.1531, which corresponds to a z-score of -1.03.
Since the given area is halfway between these two entries, we take the average of the corresponding z-scores: (-1.04 + -1.03) / 2 = -1.035.
Therefore, the z-score that corresponds to the cumulative area 0.1515 is approximately -1.035.