Q. 6.56 - Elementary Statistics

Question

Why is the standard normal curve sometimes referred to as the z-curve?

Step-by-Step Solution

Answer

In the standard normal curve, a dummy variable $z-$ has been used. So, it referred to as the z-curve.

Step 1: Concept Introduction

In conventional normal distributions, a normal curve is known as the normal random variable, such as a $z-$score.

The following equation can be used to convert any normal random variable $X$into a$z$ score:

$Z=\frac{(X-\mu )}{\sigma }$

Step 2: Explanation

We refer to the $z$ scores on the horizontal axis of the standard normal curve as $z$ scores since the standard normal curve represents a normally distributed variable.

This shows that the $z-$curve is sometimes indicated as standard normal curve.