Here we have an unknown population mean , and a known standard deviation based on a simple random sample of size n, which we are also given.
Since our sample is large enough (usually n > 30 will suffice), we consider the sample mean normally distributed, with the same expectation for the population mean , but with standard error . We standardize and get a random variable
that depends on the population mean parameter (which is to be estimated), but with a normal distribution independent of . Thus, we can find the range endpoints -z and z, independent of the population mean parameter, which is the range that Z falls somewhere in between with 95% probability. So we set the following equation up:
(which you could have looked up easily enough (or had it memorized)
So now we have