AS N goes to infinity you should have via the STRONG Law of large numbers approximately .9N of them containing your parameter.

Here N is the number of confidence intervals you created, not the sample size of each, n.

Hence you have Nn number of observations.

This is a binomial random variable so you expct (.9)(20) of the intervals to contain your parameter.

I had my students do this a year ago.

It really was neat.

I had them generate 100 exponential random variables 100 times.

Each of these confidence interval contained the mean theta or they didn't.

They were each 95 percent CI and every time they redid it via excel, we kept seeing 92-97 percent of them contained the mean.