Question

State a real-life problem, and formulate it for the following:

Use of CLT to approximate probabilities associated with a discrete distribution.

Answer 1

Follwoing is the example for real life example of use of CLT with discrete distribution -

Polls are in isolated numbers hence it is the case of discrete distribution.

Suppose we are pollsters trying to guess who will win in the election A or B. We take a poll and find that in our sample, people 58% of people would vote for candidate A over candidate B. Of course, we have only observed a small sample of the overall population, so we’d like to know if our result can be said to hold for the entire population, and if it can’t, we’d like to know how large the error might be. The central limit theorem tells us that if we ran the poll over and over again, the resulting guesses would be normally distributed around the true population value. Then we can ask: alright, suppose the true percentage of voters preferring candidate A was 50% or less; how likely would it be that we would observe a sample with 58% preferring A? Since we know what type of a distribution our estimate comes from, we can make an educated guess about that probability, and if it is very low, we can conclude that we are confident that candidate A is winning.