In a normally distributed data set, the percentages of values within specific standard deviations from the mean are well-known:

• Approximately 68% of the values lie within one standard deviation of the mean.
• Approximately 95% of the values lie within two standard deviations of the mean.
• Approximately 99.7% of the values lie within three standard deviations of the mean.

Given this, the correct answer is a) 99.7%.

Would you like more details or have any questions?

Here are some related questions to consider:

1. What percentage of values lies within one standard deviation of the mean?
2. What is the empirical rule and how is it used with normal distributions?
3. How would the percentages change if the distribution were not normal?
4. What is the significance of a Z-score in a normal distribution?
5. How do you calculate the standard deviation of a data set?
6. What percentage of values lies outside three standard deviations from the mean?
7. What does it mean if a value lies more than three standard deviations from the mean?
8. How would you determine if a data set is normally distributed?

Tip: Understanding the properties of normal distribution is crucial for statistical analysis, especially in determining probabilities and making inferences about data.