A standard normal distribution has
**Core Concept**
A standard normal distribution, also known as a z-distribution, is a probability distribution where the mean (μ) is equal to 0 and the standard deviation (σ) is equal to 1. This distribution is crucial in statistics and is used to compare the results of different samples.
**Why the Correct Answer is Right**
The standard normal distribution is characterized by its mean (μ) and standard deviation (σ). In this distribution, the mean (μ) is indeed equal to 0, which represents the center of the distribution. The standard deviation (σ) is also equal to 1, which indicates that about 68% of the data points fall within one standard deviation of the mean (i.e., between -1 and 1). This distribution is symmetrical and bell-shaped, allowing for easy calculation of probabilities and percentiles.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because a standard normal distribution does not have a mean of 1. The mean of a standard normal distribution is always 0.
**Option C:** This option is incorrect because the mean of a standard normal distribution is not larger than its standard deviation. In fact, the standard deviation is equal to 1, making it equal to the mean.
**Option D:** This option is partially correct in stating that all scores are within one standard deviation of the mean. However, it is not specific to a standard normal distribution, which is characterized by a mean of 0 and a standard deviation of 1.
**Clinical Pearl / High-Yield Fact**
A standard normal distribution is often used in statistical analysis to standardize data and compare results across different studies. This is particularly useful in pharmacology when comparing the efficacy of different treatments.
**✓ Correct Answer: B. A mean of 0 and a standard deviation of 1**