Question

In a Normal distribution, what percentage of data falls within two standard deviations of the mean?

• A. \(68%\)
• B. \(95%\)
• C. \(99.7%\)
• D. \(90%\)

Hint:

Remember the \textbf{68–95–99.7 rule} for Normal distribution: \[ 1\sigma \rightarrow 68%, \qquad 2\sigma \rightarrow 95%, \qquad 3\sigma \rightarrow 99.7% \] It is frequently used in statistics and data analysis.

Answer 1

The Correct Option is B

Concept:
A Normal distribution follows the well-known Empirical Rule (also called the 68–95–99.7 rule). This rule describes how data is distributed around the mean.

• About \(68%\) of the data lies within \(1\) standard deviation of the mean.
• About \(95%\) of the data lies within \(2\) standard deviations of the mean.
• About \(99.7%\) of the data lies within \(3\) standard deviations of the mean.

Step 1: Identify the required interval.
The question asks for the percentage of data within two standard deviations from the mean. \[ \mu - 2\sigma \le X \le \mu + 2\sigma \]
Step 2: Apply the Empirical Rule.
According to the empirical rule: \[ P(\mu - 2\sigma \le X \le \mu + 2\sigma) \approx 95% \] \[ \therefore \text{Approximately } 95% \text{ of the data lies within two standard deviations of the mean.
\]