Final answer:
The z-score corresponding to the area P(Z > z) = 0.8686 is approximately -1.12, which indicates that the value is 1.12 standard deviations below the mean of a normal distribution.
Step-by-step explanation:
To find the z-score given the area P(Z > z) = 0.8686, we need to use the z-table which provides the area to the left of the z-score. Because the z-table gives us the left tail probabilities, we want to find the area to the left which is 1 - 0.8686 = 0.1314. Now, we look up this area in the z-table to find the corresponding z-score.
After finding the area in the z-table, we can identify that the z-score closely associated with an area of 0.1314 to the left is approximately -1.12. This z-score indicates that the value is 1.12 standard deviations below the mean of the normal distribution. Remember that z-scores can be negative, indicating that the value is below the mean, or positive, indicating that the value is above the mean.