In this packet, we will be introduced to the following terms:
Some terms that should already be known are:
Source: Greene
This shows a fun demonstration on how the central limit theorem works.
Source: YouTube
Let's look at the random variable X = year on a penny. It is pretty safe to assume that this will not be normally distributed. There will be plenty of old pennies, plenty of new pennies, and plenty inbetween. But, if we take a large random sample of pennies, calculate the average year of all those pennies, repeat this many times, and graph our results, the distribution will now appear normal! This is the beauty of the central limit theorem. Regardless of the underlying distribution of the original population, the new sampling distribution will be normal as long as you take large enough samples.
Another tangible example of the central limit theorem would be the length of words in a book. This is not a normal distribution either; it is in fact right skewed. The shortest words will be 1 letter (a, I) there will be a peak around 4 letters, and it can go as high as 10, 12, or more. But the central limit theorem applies to this situation as well. If we take a large random sample of words, find the average length, repeat this many times, and graph the results, the distribution will now be normal.
Can you come up with your own example of a distribution that the central limit theorem can be applied to?
Source: Greene
