Step 1 :The problem is asking for the z-scores that correspond to the middle 68% of a normal distribution. In a standard normal distribution, the middle 68% of data falls between -1 and 1 standard deviations from the mean.
Step 2 :Therefore, the z-scores that separate the middle 68% of the distribution from the rest are \(z_{1} = -1\) and \(z_{2} = 1\).
Step 3 :The negative z-score represents the point below the mean where 16% of the data falls, and the positive z-score represents the point above the mean where 16% of the data falls.
Step 4 :Therefore, the middle 68% of the data falls between these two z-scores.
Step 5 :\(\boxed{z_{1} = -1, z_{2} = 1}\)