Chapter 4 Reinsurance Example on page 9

Hi!

I can't seem to work out the following answer, could you guys please help?

Example on page 9:

I don't understand how to get exp[(-U^2)/2] on the first line of E(z) after substituting u = (X-500)/20

That means σ needs to be 20, how do I get that?

Thank you very much!

 

The claims have a N(500,400) distribution, so σ^2 = 400, and σ = 20.

 

Thank you

Thanks Michael!!