Quick questions on Statistical inference - TCE Mathematics Specialised (Tasmania)

A confidence interval gives a range of plausible values for $\mu$. Using the normal model for $\bar{X}$, a confidence interval for the population mean is $$\bar{x} \pm z \,\frac{\sigma}{\sqrt{n}},$$where$z$is the critical value for the chosen confidence level. The common values are$z = 1.96$for 95 percent and$z = 2.576$ for 99 percent confidence.

The confidence level describes the long-run reliability of the method: if we repeated the sampling many times and built an interval each time, about 95 percent of those intervals would contain the true $\mu$. It is not a probability statement about $\mu$ for one fixed interval.