Question

for a standard normal distribution, which of the following variables always equals 1?
○ $\mu$
○ $\sigma$
○ $x$
○ $z$

Explanation:

Step1: Recall standard normal distribution

A standard normal distribution has a mean ($\mu$) of 0 and a standard deviation ($\sigma$) of 1. The variable $x$ represents a data point, which can take various values. The $z$-score ($z$) is calculated as $z=\frac{x - \mu}{\sigma}$, and it can take different values depending on $x$.

Step2: Analyze each option

• $\mu$: For standard normal, $\mu = 0$, not 1.
• $\sigma$: For standard normal, $\sigma = 1$, this is always true.
• $x$: $x$ can be any real number, not always 1.
• $z$: $z$ can be any real number (e.g., 0, 1, -2), not always 1.

Answer:

$\boldsymbol{\sigma}$ (the option with $\sigma$)