Area under Normal curve with ±1 SD:
**Core Concept**
The normal distribution, also known as the Gaussian distribution or bell curve, is a probability distribution that is symmetric about the mean. The standard deviation (SD) is a measure of the amount of variation or dispersion from the average. The area under the normal curve represents the probability of a value occurring within a given range.
**Why the Correct Answer is Right**
The area under the normal curve within ±1 SD of the mean is approximately 68.27%. This is because the normal distribution is symmetric, and the area under the curve within one standard deviation of the mean captures nearly two-thirds of the total area under the curve. The mean (μ) and standard deviation (σ) define the position and spread of the normal distribution, respectively.
**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because the area under the normal curve within ±1 SD is not 50%. This option reflects a misunderstanding of the symmetry of the normal distribution.
**Option B:** Incorrect because the area under the normal curve within ±1 SD is not 90%. This option overestimates the proportion of the area captured within one standard deviation of the mean.
**Option C:** Incorrect because the area under the normal curve within ±1 SD is not 85%. This option underestimates the proportion of the area captured within one standard deviation of the mean.
**Clinical Pearl / High-Yield Fact**
In a normal distribution, approximately 68.27% of data points lie within ±1 SD of the mean, 95.45% lie within ±2 SD, and 99.73% lie within ±3 SD. This knowledge is essential for understanding the spread of data in various medical and statistical contexts.
**Correct Answer: D. 68.27%**