In a population of 200 people with normal distribution. How many people would be included in 1 SD ?
## Core Concept
In a normal distribution, about 68% of the data falls within one standard deviation (SD) of the mean. This is a fundamental principle in statistics, often referred to as the 68-95-99.7 rule.
## Why the Correct Answer is Right
The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. Specifically, about 68% of the data falls within 1 SD of the mean, about 95% falls within 2 SDs, and about 99.7% falls within 3 SDs. Therefore, in a population of 200 people with a normal distribution, approximately 68% of them would be included in 1 SD.
## Why Each Wrong Option is Incorrect
**Option A:** This option is incorrect because it suggests a calculation that does not align with the 68% figure provided by the empirical rule.
**Option B:** This option is incorrect because it suggests 95%, which is the percentage of data that falls within 2 SDs of the mean, not 1 SD.
**Option D:** This option is incorrect because it suggests 99.7%, which is the percentage of data that falls within 3 SDs of the mean, not 1 SD.
## Clinical Pearl / High-Yield Fact
A key point to remember is the 68-95-99.7 rule for normal distributions. This rule helps in quickly estimating the spread of data in a population. For instance, knowing that about 68% of the population falls within 1 SD of the mean can be useful in various medical and research contexts for understanding the distribution of measurements or outcomes.
## Correct Answer Line
**Correct Answer: C. 136**