Confidence interval given the population mean and standard deviation Say we have a normal distribution with mean 10 and standard deviation 5. How do I get a two sided and one sided (left/right) 90% confidence interval using this?
This is the actual question I am trying to answer:
We have a normal process with mean 10 and standard deviation 5. 

We want to test whether or not the values 15, 12, and 4 come from this process.

Are those three values in a 90% symmetric about the mean confidence interval?
Are those three values in a 90% one-sided to the left confidence interval?

Everything about confidence intervals I see online refers to cases where the population mean is unknown, and you create a confidence interval using the sample mean, sample standard deviation, and sample size. I can't find anything when you have the population mean and standard deviation and then want a confidence interval for the data.

@Abso, what the question is describing is not a 90% confidence interval, it is a 90% margin of error around a particular hypothesis.  It is unfortunate that the question uses this term incorrectly.  As you and Alexis have correctly stated, the confidence interval is for making inference on an unknown mean.  The confidence interval is a set of hypotheses for which the observed data are within a 90% margin of error.
