A random variable Z that is normally distributed with mean μ = 0 and standard deviation σ = 1 is said to have the ____________________.

Verified step by step guidance

1. Recognize that the problem describes a random variable Z with mean \( \mu = 0 \) and standard deviation \( \sigma = 1 \).
2. Recall that a normal distribution with mean 0 and standard deviation 1 is a special type of normal distribution.
3. This special normal distribution is known as the standard normal distribution.
4. The standard normal distribution is often denoted by \( Z \) and is used as a reference to calculate probabilities and percentiles for any normal distribution by standardizing.
5. Therefore, the blank should be filled with "standard normal distribution".

Key Concepts

Normal Distribution

The normal distribution is a continuous probability distribution characterized by its symmetric, bell-shaped curve. It is defined by two parameters: the mean (μ), which determines the center, and the standard deviation (σ), which measures the spread. Many natural phenomena follow this distribution.

Standard Normal Distribution

The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. It serves as a reference distribution for standardizing other normal variables, allowing for easier calculation of probabilities and use of standard normal tables.

Random Variable

A random variable is a numerical outcome of a random phenomenon. It can be discrete or continuous, and in this context, Z is a continuous random variable that follows a specific probability distribution, such as the standard normal distribution.