True statement about standard normal curve:
**Core Concept**
The standard normal curve, also known as the z-distribution, is a bell-shaped probability distribution with a mean of 0 and a standard deviation of 1. It is used to standardize scores and calculate probabilities in statistics and research.
**Why the Correct Answer is Right**
The standard normal curve has a symmetrical distribution around its mean, resulting in equal distribution on either side of the curve. This means that for every point to the left of the mean, there is a corresponding point to the right of the mean, maintaining the balance and symmetry of the curve. The standard normal curve is defined by the equation `f(z) = (1/β(2Ο)) * e^(-z^2/2)`, where `z` represents the number of standard deviations from the mean. This equation ensures that the area under the curve is equal on both sides of the mean.
**Why Each Wrong Option is Incorrect**
**Option B:** The total area under the standard normal curve is actually 1, not 2, as it represents the entire probability distribution.
**Option C:** The mean of the standard normal curve is 0, not 1, as it is a standardized distribution with a mean of 0 and a standard deviation of 1.
**Option D:** The standard deviation of the standard normal curve is 1, not 0, as it is a key parameter defining the distribution.
**Clinical Pearl / High-Yield Fact**
When working with the standard normal curve, remember that it is a standardized distribution with a mean of 0 and a standard deviation of 1. This allows for easy comparison and calculation of probabilities across different datasets.
**β Correct Answer: A. Equal distribution on either side of the curve**