About the standard gaussian distribution

First of all I have to apologize because my english is horrible. 

I am working in a basic and practical statistic course. 

I will speak about confidence intervals, of course. 

But when I was preparing this chapter I had a doubt: I wonder if it has sence today to explain the confidence intervals for a mean in terms of the standard normal distribution. 

If we show that the mean follows a normal distribution with variance/n then it is easy to explain (and to understand) that the confidence interval is due to two percentiles, the percentile alpha/2 and the percentile 1-alpha/2 from a normal distribution with the sample mean and the sample variance/n. 

I think that the standard gaussian distribution was usefull when we had to calculate CI in the past. 
That is, it was a simple way to have all possibilities in a single table (in paper). 

But now, we have R functions that let us to obtain the exact values for any normal distribution. 

I think that is not necessary to explain how to work with transformations if we can explain that a CI is simply to identify percentiles. 

What do you think?

Thanks

PD I know that the normal distribution for CI need some hipothesis. But I have focused the question

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David Monterde

Lo dif?cil se hace. 
Lo imposible se intenta. 
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