Survival from lung cancer
What proportion of lung cancer patients survive five years after diagnosis?
How many patient records must be examined to be 95% confident that we are within 0.02 of the correct value?
The diagram finds the sample size by a trial-and-error method. For any values of n and p, it finds the width of the resulting confidence interval.
Solving an equation
You could also mention that, provided n is reasonably large, the equations can be solved to give