I was looking at a past exam for a subject I am taking and cam across this question:

confidence interval for cluster sample-sfexam.jpg

The question then asks me to give a 95% confidence interval for the total number of university students in Carlton North.

I know how to find confidence intervals for normal distributions, but I don't think this data is normally distributed: most university students live either with their parents (mostly 1 student) or in a shared house (mostly >=4 students) so the tails will be large. The sample also seems to be too small to apply any central limit theorem type thingy.

The other method I know for finding confidence intervals is the bootstrap, but our calculators have to have their memory cleared to be taken to the exam, and I don't think we are expected to write a program for bootstrapping in the exam.

Have I missed something really obvious?