50/250 = 25% >> 5%! You should be using a Finite Population Correction Factor.

Sample Mean Standard Error is

It's not exactly the book's answer, but it's much closer. There are also some rounding issues going on. If I round the normalized deviations to only two decimal places, I match the book exactly.

Never forget the Finite Population Correction Factor, otherwise your sample size calculation may require you to sample more than 100% of the population. That's no good, right?