According to the law of large numbers, what happens to the accuracy of predictions as the sample population increases?

The law of large numbers states that as the size of a sample drawn from a population increases, the sample mean will get closer to the expected value or the population mean. This principle is fundamental in statistics and insurance because it underpins how risks are calculated and managed.

When the sample size is small, random variability can significantly impact the results, leading to less reliable predictions. However, as the sample size increases, the effects of random fluctuations diminish, making the predictions more stable and close to the true population parameters. Thus, with a larger sample, one can expect the predictions about averages or proportions to become more accurate. This reliability is why insurers rely on extensive data when assessing risk and setting premiums, as larger data sets provide a clearer picture of expected outcomes.

Therefore, the assertion that predictions become more accurate with an increasing sample population aligns perfectly with the principles laid out by the law of large numbers.