Final answer:
Human heights within a population usually follow a normal distribution and adhere to the Empirical Rule with the data being bell-shaped and symmetric around the mean. Statistical analysis confirms this, and the normal distribution of the data allows for easier and more reliable statistical inferences.
Step-by-step explanation:
When discussing situations where you can collect data that the Empirical Rule applies to, one can think of human heights within a given population. The distribution of heights is normally distributed, meaning that most people's heights are around the average, with fewer people being extremely tall or extremely short. This follows the Empirical Rule because the data is bell-shaped and symmetric around the mean.
What leads us to believe this situation follows the Empirical Rule is extensive statistical analysis on human heights that has shown it approximates a bell curve. For instance, if you measure the heights of adult men in the U.S., you will find that about 68 percent of them will fall within one standard deviation from the mean height, 95 percent within two standard deviations, and 99.7 percent within three standard deviations.
There are several benefits to having data that are distributed normally. It allows the use of the normal approximation to compute various probabilities and perform other statistical analyses like hypothesis testing or confidence intervals, which are more straightforward and well-supported for normal distributions due to the Central Limit Theorem.