In a standard deviation of 2, confidence limit is
**Core Concept**
The 68-95-99.7 rule, also known as the empirical rule, describes the distribution of data in a normal distribution. It states that about 68.3% of the data falls within one standard deviation of the mean, about 95.4% of the data falls within two standard deviations, and about 99.7% of the data falls within three standard deviations.
**Why the Correct Answer is Right**
The correct answer is B. 95.40% because it corresponds to the 95% confidence interval, which is the range within which 95% of the data points are expected to fall. This is a critical concept in statistics, particularly in hypothesis testing and confidence intervals. When a standard deviation of 2 is given, it implies that 95% of the data points lie within two standard deviations of the mean. This is where the concept of the 68-95-99.7 rule comes into play.
**Why Each Wrong Option is Incorrect**
**Option A:** 68.30% is incorrect because it corresponds to the 68% confidence interval, which is the range within which 68% of the data points are expected to fall. This is the proportion of data points within one standard deviation of the mean, not two.
**Option C:** 99.70% is incorrect because it corresponds to the 99.7% confidence interval, which is the range within which 99.7% of the data points are expected to fall. This is the proportion of data points within three standard deviations of the mean, not two.
**Option D:** 76.20% is incorrect because it is not a valid confidence interval. The proportions of data points within one, two, and three standard deviations of the mean are 68.3%, 95.4%, and 99.7%, respectively.
**Clinical Pearl / High-Yield Fact**
A key takeaway from the 68-95-99.7 rule is that about 95% of the data points lie within two standard deviations of the mean. This is a fundamental concept in statistics that has far-reaching implications in medicine, particularly in hypothesis testing and confidence intervals.
**β Correct Answer: B. 95.40%**