In this video there is an explanation of why CLT is so important in statistics. One of the problems formulated in the video is:
Suppose salaries at a very large corporation have a mean of 62,000 and a standard deviation of 32,000.
Problem: If a single employee is randomly selected, what is the probability their salary exceeds 66,000?
Here we can't use CLT and consider our distribution is normal and easily calculate the probability. Now my question is how can we solve this problem then? (Imagine that a not-normal distribution of salaries is given.