Final answer:
The Empirical Rule applies to bell-shaped and symmetric distributions indicating 68%, 95%, and 99% of data within one, two, and three standard deviations of the mean, respectively, which is crucial for understanding statistical probability.
Step-by-step explanation:
The Empirical Rule applies to distributions that are bell-shaped and symmetric. This rule states that for a normal distribution, which is a type of continuous distribution, about 68 percent of the data falls within one standard deviation of the mean, about 95 percent is within two standard deviations, and more than 99 percent is within three standard deviations of the mean. Such distributions are associated with random variables that follow a normal distribution, represented graphically by a symmetric, bell-shaped curve where the mean, median, and mode coincide. This is a key concept in descriptive statistics and is crucial for understanding probability, statistics, and various applications that involve data analysis.
The empirical rule is practically applied in many scenarios, such as determining the percentage of the population that falls within a certain range of values, assessing probabilities in statistics, and analyzing sample data concerning the population mean. It is also used to contrast theoretical distributions with empirical data obtained from experiments or observations, and to evaluate if a distribution approximates normality. It's important to remember that while theoretically beneficial, the empirical rule is best applied when the sample size is sufficiently large, typically greater than 30, to ensure a close approximation to a normal distribution.