Pre-Test

For a standard normal distribution, which of the following variables always equals 0?

A. [tex] \mu [/tex]
B. [tex] \sigma [/tex]
C. [tex] x [/tex]
D. [tex] z [/tex]



Answer :

To solve this problem, let's analyze the characteristics of a standard normal distribution. A standard normal distribution is a special case of the normal distribution, which has specific parameters:

1. Mean (μ): The average or the central value of the distribution.
2. Standard Deviation (σ): A measure of the spread or dispersion of the distribution.

In a standard normal distribution, the values of the parameters are defined as follows:

- The mean (μ) is always equal to 0.
- The standard deviation (σ) is always equal to 1.

Now, let's understand the other variables mentioned:

- x: This represents a data point or a value on the horizontal axis of the distribution. It varies depending on the distribution and does not have a fixed value.

- z: This represents the z-score, which is the number of standard deviations a data point (x) is from the mean (μ). For a standard normal distribution, z can have any real number value, as it measures how far and in which direction a point deviates from the mean.

Given these definitions, we can determine which variable always equals 0:

- μ (Mean): Always 0 in a standard normal distribution.
- σ (Standard Deviation): Always 1 in a standard normal distribution, not 0.
- x (Data Point): Variable and does not always equal 0.
- z (Z-score): Variable and does not always equal 0.

Hence, the correct choice is:

[tex]\[ \mu \][/tex]

The mean (μ) of a standard normal distribution always equals 0.