Find the z-scores for which 98% of the distribution's area lies between -z and z.
how is the answer (-2.33, 2.33)?

On a normal or bell shaped curve, these two z scores are symmetric to one another about zero, which is exactly in the center. The area between these two Z scores is equal to .98 These Z scores correspond to percentiles. So the -2.33 represents the .0099 percentile, and 2.33 represents .9901 percentile .9901-.0099 roughly equals .98. 
These Z scores are the result of "normalization." If you haven't gotten into that, I don't think I should explain it here. It requires integration and probably a specific example involving repeated trials of an experiment to explain it thoroughly, but it springs from the central limit theorem.