Step 1: Understanding the Question
The question asks for the proportion of data in a Normal distribution that lies in the interval from two standard deviations below the mean to two standard deviations above the mean, i.e., \( (\mu - 2\sigma, \mu + 2\sigma) \).
Step 2: Key Formula or Approach
This question relates to the Empirical Rule, also known as the 68–95–99.7 rule, which is a key property of the Normal distribution.
Step 3: Detailed Explanation
The Empirical Rule states the approximate percentage of data within certain ranges around the mean (\(\mu\)) for a Normal distribution with standard deviation (\(\sigma\)):
Approximately 68% of the data falls within one standard deviation of the mean (\(\mu \pm \sigma\)).
Approximately 95% of the data falls within two standard deviations of the mean (\(\mu \pm 2\sigma\)).
Approximately 99.7% of the data falls within three standard deviations of the mean (\(\mu \pm 3\sigma\)).
The question specifically asks for the percentage within two standard deviations.
Step 4: Final Answer
According to the Empirical Rule, approximately 95% of the data falls within two standard deviations of the mean.