Mean + 1.96 SD include following % of values in a distribution: September 2012
**Core Concept**
In statistics, the mean (+/- 1.96 standard deviations) represents the range within which 95% of the values in a normal distribution lie. This concept is crucial in understanding the relationship between the mean, standard deviation, and the percentage of values in a distribution.
**Why the Correct Answer is Right**
The formula for calculating the percentage of values within a specific range in a normal distribution is based on the z-score. The z-score represents the number of standard deviations from the mean. In this case, a z-score of 1.96 corresponds to the 95th percentile, meaning that 95% of the values in the distribution lie within 1.96 standard deviations of the mean. This is because the area under the normal curve between z-scores of -1.96 and 1.96 is approximately 0.95, or 95%.
**Why Each Wrong Option is Incorrect**
**Option A:**
This option does not specify the correct percentage of values included within the range. The correct percentage is 95%, not 90%.
**Option B:**
This option is incorrect as it does not specify the correct z-score. The z-score of 2.58 corresponds to a different percentage of values in the distribution.
**Option C:**
This option is incorrect as it does not specify the correct percentage of values included within the range. The correct percentage is 95%, not 99%.
**Clinical Pearl / High-Yield Fact**
It's essential to remember that the 95% confidence interval (mean +/- 1.96 SD) is a widely used statistical tool in medical research to estimate the population mean based on a sample mean.
**Correct Answer: D. 95% of the values in a distribution.**