## Core Concept
The question pertains to the properties of a standard normal distribution, also known as a bell-shaped curve or Gaussian distribution. In statistics, understanding how data points are distributed around the mean is crucial, and the standard deviation (SD) is a key measure of variability. The standard normal distribution is symmetric about its mean, and the area under the entire curve is 1.
## Why the Correct Answer is Right
In a standard normal distribution:
- About 68% of the data falls within 1 standard deviation (SD) of the mean.
- About 95% of the data falls within 2 standard deviations (SD) of the mean.
- About 99.7% of the data falls within 3 standard deviations (SD) of the mean.
This is often referred to as the 68-95-99.7 rule or the empirical rule. Therefore, the mean Β± 2 standard deviations covers approximately 95% of the data points in a standard normal distribution.
## Why Each Wrong Option is Incorrect
- **Option A:** This option is incorrect because it suggests a range that covers less than 95% of the data, which does not align with the 95% coverage for mean Β± 2 SD.
- **Option B:** This option is incorrect because, similar to option A, it does not accurately represent the percentage of data covered by mean Β± 2 SD.
- **Option D:** This option is incorrect because it overestimates the coverage, suggesting a range that would actually cover more than 95% of the data, likely referring to mean Β± 3 SD or another range.
## Clinical Pearl / High-Yield Fact
A key point to remember for exams and clinical practice is the 68-95-99.7 rule. This rule helps in quickly estimating the dispersion of data in a normal distribution. For instance, in clinical research, understanding that 95% of patients will have values within 2 SD of the mean can help in setting normal ranges for laboratory tests.
**Correct Answer: C. 95%**
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