Quick questions on Confidence intervals for a population mean (QCE Specialist Mathematics Unit 4)

A confidence interval for $\mu$ (with known population standard deviation $\sigma$) is

The correct interpretation refers to the method over repeated sampling. A $95\%$ confidence level means that if many samples were taken and an interval constructed from each, about $95\%$ of those intervals would contain the true mean $\mu$. It does not mean there is a $95\%$ probability that $\mu$ lies in this particular interval: $\mu$ is a fixed number, and any single interval either contains it or does not. The confidence is in the long-run reliability of the procedure.

We are $95\%$ confident that the true mean height of the population lies between about $170.0$ cm and $174.0$ cm. If we repeated this sampling procedure many times, roughly $95\%$ of the intervals produced would contain the true mean height.