Question

d. Imagine that instead of 100 points, you generated 1000 uniformly random points Then, data you generated was transformed into 100 new data points, each new data point representing the average of ten of the 1000 uniformly random points. Point 1 is the average of the first ten, the second is the average of the second ten, etc, generating 100 new points. The histogram of the 100 points appears normally distributed, not uniformly, and is shown below. State the theorem that governs this phenomenon and explain it in your own words. Histogram 25 20 15 웁 10 Frequency Average Data Packets Per Hr (Bin)

Answer 1

The Theorem that governs this phenomenon:

Central Limit Theorem

Explanation:
Sampling Distribution of Sample Means is Normal Distribution, irrespective of the shape of the population.

Here, the population is Uniform Distribution.

By Central Limit Theorem, the Sampling Distribution of the 100 Sample Means is Normal Distribution.