A random variable that has a mean of 0 and a standard deviation of 1 is called what?

A random variable that has a mean of 0 and a standard deviation of 1 specifically defines what is known as a standard normal probability distribution. This distribution is a special case of the normal distribution, which is characterized by its bell-shaped curve and symmetrical property. The standard normal distribution serves as a basis for conducting hypothesis tests and creating confidence intervals in statistics.

The mean of 0 indicates that the distribution is centered at the origin, and a standard deviation of 1 means the spread of the data around the mean follows a specific scale where roughly 68% of the data falls within one standard deviation from the mean. This particular configuration, where both the mean and standard deviation are standardized, makes it particularly useful for standardizing scores from different normal distributions to a common scale, allowing for easier comparison and analysis.

Other distributions mentioned have different characteristics. For instance, a standard uniform distribution has equal probabilities across a defined range but is not centered at zero with a standard deviation of one. The normal probability distribution refers to the broader class of distributions that can have varying means and standard deviations, while a uniform probability distribution features different properties altogether, lacking the characteristic bell shape and standard deviation that is integral to the normal distributions.