Classifying [mean,stdev] data

I have a large dataset and each item is either of type A or type B. My data is a [mean,stdev] pair. What would be a good approach to classifying this data?

I know that one approach if I had a bunch of points I wanted to classify would be to take the mean and stdev and use it to model the pdf with a guassian classifier.

However, since each "point" in my dataset is a [mean,stdev] pair (which itself implicitly defines some distribution) I'm curious as to a way to build a classifier for this type of data.

Hopefully that made sense.

Cheers