Final answer:
The empirical rule allows for a comparison between empirical findings and expectations for a normal distribution. Differences can indicate non-normal data, small samples, or outliers. Larger sample sizes tend to provide a better approximation of true probabilities.
Step-by-step explanation:
The empirical rule, also known as the 68-95-99.7 rule, applies to a normal distribution and states that about 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three. Comparing empirical findings to those expected based on the empirical rule can determine whether the observed data follow a normal distribution. If the results significantly differ, it may be due to the data not being normally distributed, the sample size being too small, or the presence of outliers. In the case of repeatedly picking two candies, the empirical probability can change with increased trials due to a larger sample providing a better approximation of the true probability. When comparing data, if the empirical results differ greatly from the theoretical expectations, it might indicate something unexpected about the effectiveness of a product or a different distribution than initially assumed.