Confidence interval and population. What is the relationship?

Question

Mathematics

Hello! I'm a little misunderstanding the topic with confidence intervals. Suppose there are 10 million inhabitants in a country and I decided to estimate the average height of all inhabitants. I can’t interview everyone, and I decided to take 1000 random groups of 1000 people and get 1000 sample averages of height. Question: Will these sample means be normally distributed about a value approximately equal to the average height in the population? Does the central limit theorem work?

And what about confidence intervals. As I understand it, it is impossible to believe that the value obtained with these sample means is really the average in the general sample. But it is close to it. Therefore, we look at the range that includes 95% of all values ​​and take it as an exhaustive result?

Answer 1

1. Question: Will these sample means be normally distributed around a value approximately equal to the average height in the population?
Answer: Yes
2. Question: Does the central limit theorem work?
Answer: Who canceled it and when?
3. Question: So we look at the range that includes 95% of all values ​​and take it as an exhaustive result?
Answer: We first choose the significance level for non-statistical considerations. It can be 0.95, and 0.9 and 0.0000001 - any. And then we build a confidence interval using the selected significance level.
What is an "exhaustive result" - I have not seen such a term in statistics. Explain.