standard normal distribution

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I have a problem in how to approximate ''by a standard normal distribution''.
In the book named ''risk analysis in finance and insurance'', by Melnikov
( you can find the pdf form on http://wafaa-sherif.com/new/ar/wp-conte ... urance.pdf ), page 137, a solved problem is presented.
The part that confuses me is:
'' Since the total number of policy holders is reasonably large, then the quantity (S - E(S)) / √(V(S) can be accurately approximated by a standard normal distribution. Hence we obtain the equation.. ''
What I ask for is a really detailed explanation of how that approximation was done. Any indication on this topic will be helpful.

Thanks a lot..!!