In a normal curve, the area of one standard deviation around the mean includes which of the following per cent of values in a distribution –
**Core Concept**
In probability theory and statistics, a normal curve is a continuous 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. The standard deviation is a measure of the amount of variation or dispersion from the average.
**Why the Correct Answer is Right**
The area under the normal curve within one standard deviation from the mean includes approximately 68.27% of the total area under the curve. This is because the normal curve is symmetric, and the mean, one standard deviation, and two standard deviations from the mean divide the curve into four equal parts. The area within one standard deviation from the mean represents about two-thirds of the total area under the curve. This concept is crucial in understanding the central limit theorem and the standard normal distribution.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not accurately represent the percentage of values within one standard deviation of the mean in a normal distribution.
**Option C:** This option is incorrect because it is an overestimation of the values within one standard deviation of the mean in a normal distribution.
**Option D:** This option is incorrect because it does not accurately represent the percentage of values within one standard deviation of the mean in a normal distribution.
**Clinical Pearl / High-Yield Fact**
Remember that in a normal distribution, about 68% of the values lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% lie within three standard deviations.
**Correct Answer:** C. 68.27%