Final answer:
Option (A), The Law of Large Numbers explains why increasing sample size leads to a sample mean that closely approximates the population mean. It's a central concept in probability and statistics.
Step-by-step explanation:
The principle that explains why, as the number of observations drawn increases, the sample mean of the observed values gets closer to the mean μ of the population is the Law of Large Numbers. This statistical theorem states that as a sample size grows, its mean will get closer and closer to the average of the whole population.
If a student were to flip a coin a few times, they might not get a 50/50 distribution of heads and tails due to chance. However, if they were to flip the coin thousands, or better yet, millions of times, the proportion of heads to tails would likely get very close to 1:1, reflecting the true probability.