Statistics: normal distributions homework help needed!?

[person]

Find the z-score for which 5% of the distribution's area lies between -z and z.

I do not know where to start with this confusing problem.
I need an explanation of how you solved the problem.
Heather, your help is very good, but I am still wondering how you got the 52.5% and 48.5%

This is where I'm lost, the rest I can follow.