Question

for a standard normal distribution, which of the following variables always equals 0?
○ μ
○ σ
○ x
○ z

Explanation:

Step1: Recall standard normal distribution properties

A standard normal distribution has a mean ($\mu$) of 0 and a standard deviation ($\sigma$) of 1. The variable \( x \) represents a data point, \( z \) is the z - score.

Step2: Analyze each option

• For \( \mu \): In a standard normal distribution, the mean \( \mu = 0 \).
• For \( \sigma \): In a standard normal distribution, the standard deviation \( \sigma=1

eq0 \).

• For \( x \): \( x \) can take various values depending on the data, it is not always 0.
• For \( z \): The z - score \( z=\frac{x - \mu}{\sigma}\), and \( z \) can take different values depending on \( x \), it is not always 0.

Answer:

\(\mu\) (the first option: \(\boldsymbol{\mu}\))