# Is sample standard deviation a valid approximation of population standard deviation for z-scores?

Given a Normal distributions for the population and my sample, a population mean of mu, and a sample standard deviation of s, if I want to find the area under the population curve from x to infinity, is it valid to say that s = sigma (population standard deviation) here? In other words, can I say that z=(x-mu)/s=(x-mu)/sigma or would I maybe have to calculate this as a t-score and use the degrees of freedom in the sample to find the area under the curve?

## 1 Answer

I orginally misread your qustion, therefore it deleted my (wrong) comment.

Anyway, since you don't know the population variance you would need to use the t-test.

• Just to clarify, I am not trying to perform a t-test here, and this has nothing to do with the sampling distribution of the mean. I simply have a sample standard deviation and want to calculate a z- or maybe t-score but generalize that to the population. Given this information, would you still say that a t-model is most appropriate here? – user110737 Apr 2 '16 at 22:07
• @jt2000, you have estimated the standard deviation, so the same rule applies. Use the T-score – Repmat Apr 3 '16 at 17:51