In a normal surve, what percent of the values will be included in the area between two standard detions on either side of the mean (x+- ….) ?
**Core Concept**
Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In a normal distribution, the mean, median, and mode are all equal.
**Why the Correct Answer is Right**
About 68% of the values in a normal distribution lie within one standard deviation of the mean. This is because the area under the normal curve between the mean and one standard deviation above it is equal to the area between the mean and one standard deviation below it. The sum of these two areas is approximately 68% of the total area under the curve. The remaining 32% of the data points are distributed in the tails of the distribution, more than one standard deviation away from the mean.
**Why Each Wrong Option is Incorrect**
**Option A:** This option would imply that 95% of the values lie within one standard deviation of the mean, which is incorrect. While 95% of the data points do lie within two standard deviations of the mean, only 68% lie within one standard deviation.
**Option B:** This option would imply that 32% of the values lie within one standard deviation of the mean, which is incorrect. As mentioned earlier, 68% of the data points lie within one standard deviation of the mean.
**Option D:** This option is not provided.
**Clinical Pearl / High-Yield Fact**
Remember the 68-95-99.7 rule, also known as the empirical rule, which states that in a normal distribution:
- About 68% of the data points lie within one standard deviation of the mean.
- About 95% of the data points lie within two standard deviations of the mean.
- About 99.7% of the data points lie within three standard deviations of the mean.
**Correct Answer: C. 68%.**