A 95% confidence for the mean μ is given by (-2.14,3.07).
There’s no probability, where does the probability come in?
it comes in from random sampling. The fact that if you select a random sample and compute your estimator and if you got to do it again or if someone else did it, they’re going to get a different estimator based on the randomness of the sample.
Collect your sample.
Estimate the parameter.
Return a confidence interval.
If you did this again, you would not get the same results! Different samples and different confidence intervals.
Multiple samples give multiple confidence intervals.
95% of them will correctly capture μ and 5% miss it.