Simulation: samples from normal (µ = 12, σ = 2)

This diagram demonstrates that for 95% CIs:

Click Expanded summary scale then click Accumulate and take 100-200 sample.

The red intervals do not include 12 — click on any interval to see the corresponding sample. Explain that the sample values are sometimes a bit high (or low) by chance.

In practice, we only have a single sample. We cannot tell whether it is one of the 'lucky 95%' whose CIs include µ, but we are 95% confident that it is.