Working with the standard normal distribution in R couldn’t be easier. The only change you make to the four norm functions is to not specify a mean and a standard deviation — the defaults are 0 and 1.
Here are some examples:
> dnorm(0)
[1] 0.3989423
> pnorm(0)
[1] 0.5
> qnorm(c(.25,.50,.75))
[1] -0.6744898 0.0000000 0.6744898
> rnorm(5)
[1] -0.4280188 -0.9085506 0.6746574 1.0728058 -1.2646055
This also applies to the tigerstats functions:
> pnormGC(c(-1,0),region="between")
[1] 0.3413447
> qnormGC(.50, region = "below")
[1] 0
To standardize a set of scores so that you can compare them to other sets of scores, you convert each one to a z-score. The formula for converting a score to a z-score (also known as a standard score) is 
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