A study generated a normal distribution with a mean value as 200 and standard deviation of 20. 68% of area will fall between
## **Core Concept**
In a normal distribution, about 68% of the data falls within one standard deviation of the mean. This is a fundamental concept in statistics, often referred to as the 68-95-99.7 rule or the empirical rule.
## **Why the Correct Answer is Right**
The correct answer, , represents the range within one standard deviation of the mean. Given that the mean (μ) is 200 and the standard deviation (σ) is 20, one standard deviation below the mean is 200 - 20 = 180, and one standard deviation above the mean is 200 + 20 = 220. Therefore, 68% of the area under the normal distribution curve falls between 180 and 220.
## **Why Each Wrong Option is Incorrect**
- **Option A:** This option suggests a range that is too broad, extending beyond one standard deviation from the mean, which would actually encompass more than 68% of the data.
- **Option B:** This option suggests a range that is too narrow, not covering a full standard deviation from the mean, which would encompass less than 68% of the data.
- **Option D:** This option is incorrect for similar reasons as Option A and B, not accurately representing one standard deviation from the mean.
## **Clinical Pearl / High-Yield Fact**
A key point to remember is the 68-95-99.7 rule:
- About 68% of the data falls within **one standard deviation** of the mean.
- About 95% of the data falls within **two standard deviations** of the mean.
- About 99.7% of the data falls within **three standard deviations** of the mean.
## **Correct Answer:** .