Question

question 40 points 2

which formula is used to determine the standard normal random variable \\(z\\)?

\\(z = \frac{x - \mu}{\sigma}\\)

\\(z = \frac{x + \mu}{\sigma}\\)

Explanation:

Define the standard normal variable

Using the Z-score Calculation knowledge point

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

Identify the correct formula option

We compare the standard formula with the given options:

• Option 1: \(Z = \frac{X - \mu}{\sigma}\)
• Option 2: \(Z = \frac{X + \mu}{\sigma}\)

The first option matches the standard formula.

Answer:

• (A) \(Z = \frac{X - \mu}{\sigma}\) (Correct answer)
• (B) \(Z = \frac{X + \mu}{\sigma}\)