# Adding normal distribution - z-scores

1. Jun 5, 2012

### blumfeld0

Hi -

I have a quick question. I understand that the sum of two normal distributions is a normal distribution. Now let's say I have the z-score from one normal distribution and the z-score of another set of data that is also normally distributed and a third and a fourth etc.

I just want to know if it is mathematically allowed to ADD the z-scores together? I do not care too much about the probability (p-value). I would like to know if it is allowed and are there any internet references on this topic?

Thank you very much.

2. Jun 5, 2012

### Stephen Tashi

You didn't specify what you meant by "mathematically allowed", but I can't think of any reasonable interpretation of those words where the answer would be "yes". So let's say the answer is "no".

If you have a specific question, perhaps you should give a very specific example to explain what you mean.

3. Jun 5, 2012

### chiro

One thing about the z-scores is that we assume this relates to a N(0,1) distribution. If you different distributions corresponding to N(0,1) together, you end up getting something relating to N(0,m) where m is the number of distributions and because of this, you are no longer dealing with something that a z-score should correspond to.