Question 1162759
If the population is normally distributed, then the sampling distribution of both will be normal.
If the population is not normally distributed, then it depends. 
Because the z-table is being used, and because sigma and not s is used, I would assume normality in the population and the answer is Yes.

z=(57-55)/4.6/sqrt(37)
=2*sqrt(37)/4.6=2.64
So between 55 (z=0) and 57 (z=2.6446) that probability is 0.4959