Question 1011624
Ho: p is <+0.50
Ha:p>0.50.  The Ho includes LESS than 0.50 because correctly predicting the sex of the baby should be at least 50%.  Given that interpretation, there is no need to do the test on a probability of 36.2%.
============
If one expands the criteria that it is not random, that can be done, but the comment of "no ability to predict the sex of their baby" might be better written solely as "not random"
Ho: p=0.50
Ha:p NE 0.50
alpha=0.05
z=(phat-p)/sqrt{p*(1-p)}/n
reject if |z|>1.96
=0.362-0.5/sqrt{.362*.638)/160; 58/160 is closest to 36.2%.
=-0.138/0.0380
= -3.63
Reject Ho; their choices are worse than random.