Question

In a normally distributed population, about 95% of observations lie in the interval of:

• A. \(\mu \pm \sigma\)
• B. \(\mu \pm 2\sigma\)
• C. \(\mu \pm 3\sigma\)
• D. \(\mu \pm 4\sigma\)

Hint:

Empirical rule:
68-95-99.7 rule.
95% in \(\mu \pm 2\sigma\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Normal distribution has specific properties.
The empirical rule describes the data spread.

Step 2: Key Formula or Approach:
Empirical rule:
- 68% within \(\mu \pm 1\sigma\)
- 95% within \(\mu \pm 2\sigma\)
- 99.7% within \(\mu \pm 3\sigma\)

Step 3: Detailed Explanation:
In a normal distribution:
Approximately 68% of data lies within \(\mu \pm 1\sigma\).
Approximately 95% lies within \(\mu \pm 2\sigma\).
Approximately 99.7% lies within \(\mu \pm 3\sigma\).
Thus, 95% lies in \(\mu \pm 2\sigma\).

Step 4: Final Answer:
95% of observations lie in \(\mu \pm 2\sigma\).
Hence, the correct option is (B).