Answer :
Final answer:
The correct answer is A. 68%, 95%, 99.7%, which represents the percentage of data within 1, 2, and 3 standard deviations from the mean, respectively, in a bell-shaped distribution according to the Empirical Rule.
Explanation:
The student's question asks about the 68-95-99.7 rule, which is a statistical rule used to predict the dispersion of data in a normal distribution, commonly referred to as the Empirical Rule. For a data set with a bell-shaped distribution:
- Approximately 68% of the data falls within one standard deviation (σ) of the mean (μ).
- Approximately 95% of the data falls within two standard deviations (2σ) of the mean (μ).
- Approximately 99.7% of the data falls within three standard deviations (3σ) of the mean (μ).
Therefore, the correct option that states the percentage of data within 1, 2, and 3 standard deviations of the mean is A. 68%, 95%, 99.7%. This rule is vital to understanding the distribution of data in fields such as statistics and probability.
