Summarize the implications of the central limit theorem. Identify what you believe to be the most important application of it. Explain your position, providing examples where possible.

The central limit theorem is a principle in probability theory that states that the distribution of sample means will eventually approximate a normal distribution as the sample size becomes larger. This means that, the more samples we collect, the closer we would get to a normal distribution, also known as "bell curve."

What I believe is the most important application of it is when we want to obtain information on a particular group of people that is very large. For example, if we want to know the heights of all girls in the sophomore year of high school. As the girls are the same age and gender, their heights are likely to be similar. However, we could approximate the mean accurately by sampling at least 30 of them and using the principle of the central limit theorem.