The Standard Normal Probability Distribution

B

The standard normal probability distribution has a mean of 0 and std. deviation of 1.

The standard normal probability distribution, also known as the standard normal distribution or the Z-distribution, is a specific type of probability distribution. It is a continuous probability distribution that has a bell-shaped curve, symmetric around the mean.

The standard normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean represents the center of the distribution, and the standard deviation measures the spread or dispersion of the data.

According to the question, we need to determine the characteristics of the standard normal probability distribution. The options provided are as follows:

A. A mean of 0 and any standard deviation B. A mean of 0 and a standard deviation of 1 C. Any mean and a standard deviation of 1 D. A mean of 1 and any standard deviation E. None of these answers are correct

To identify the correct answer, we need to understand the properties of the standard normal distribution. In the standard normal distribution, the mean is always 0 (μ = 0), and the standard deviation is always 1 (σ = 1). This means that option B, which states a mean of 0 and a standard deviation of 1, accurately describes the standard normal distribution.

Option A suggests that the standard normal distribution can have any standard deviation, which is incorrect. The standard normal distribution always has a standard deviation of 1.

Option C suggests that the standard normal distribution can have any mean, which is also incorrect. The mean of the standard normal distribution is always 0.

Option D states a mean of 1, which is incorrect. The mean of the standard normal distribution is always 0.

Therefore, the correct answer is option B: "A mean of 0 and a standard deviation of 1." This accurately describes the characteristics of the standard normal probability distribution.