Let X be normally distributed with mean μ and standard deviation σ 0. Which of the following is true about the z value corresponding to a given x value?
A) A positive z = (x - μ)/σ indicates how many standard deviations x is above μ.
B) A negative z = (x - μ)/σ indicates how many standard deviations x is below μ.
C) The z value corresponding to x = μ is zero.
D) All of the above.

Question

Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is true about the z value corresponding to a given x value?
A) A positive z = (x - μ)/σ indicates how many standard deviations x is above μ.
B) A negative z = (x - μ)/σ indicates how many standard deviations x is below μ.
C) The z value corresponding to x = μ is zero.
D) All of the above.

Quizplus · Accepted Answer

A) This is true. A positive z-value means that x is above the mean, and the magnitude of the z-value tells us how many standard deviations x is above the mean.

B) This is also true. A negative z-value means that x is below the mean, and the magnitude of the z-value tells us how many standard deviations x is below the mean.

C) This is true as well. The z-value corresponding to x = μ is (μ - μ) / σ = 0 / σ = 0.

Therefore, all three statements are true, and the answer is D.

Let X Be Normally Distributed with Mean μ and Standard