Area under mean +/- 2 SD will include ————% of population.
## **Core Concept**
The question tests understanding of the **68-95-99.7 rule**, also known as the empirical rule, which describes the distribution of data in a normal distribution. This rule states that about 95% of the data falls within two standard deviations (SD) of the mean.
## **Why the Correct Answer is Right**
In a normal distribution, about 95% of the values lie within **two standard deviations (2 SD)** of the **mean**. This is a fundamental concept in statistics and is crucial for understanding how data is distributed. The formula for this range is: **Mean ± 2 SD**. Therefore, the area under the curve within **mean ± 2 SD** includes approximately **95%** of the population.
## **Why Each Wrong Option is Incorrect**
* **Option A:** 68% - This is incorrect because 68% of the population lies within **one standard deviation (1 SD)** of the mean, not two.
* **Option B:** 99.7% - This is incorrect because 99.7% of the population lies within **three standard deviations (3 SD)** of the mean, which is a much broader range.
* **Option D:** 47.5% - This is incorrect as it represents half of the 95% range and does not accurately reflect the total percentage of the population within **mean ± 2 SD**.
## **Clinical Pearl / High-Yield Fact**
A key point to remember is the **68-95-99.7 rule**, which helps in quickly estimating the percentage of data points within a certain range of the mean in a normal distribution. This rule is often used in medical research and practice to understand the distribution of patient data, such as blood pressure or cholesterol levels.
## **Correct Answer:** B. 95%