Question

The ASQ​ (American Society for​ Quality) regularly conducts a salary survey of its​ membership, primarily quality management professionals. Based on the most recently published mean and standard​ deviation, a quality control specialist calculated the​z-score associated with his own salary and found it was minus2.50. What is his​ salary?A. 2.5 standard deviations below the average salary.B. 2 and a half times less than the average salary.C. 2.5 standard deviations above the average salary.D. 2 and a half times more than the average salary.

Answer 1

A. 2.5 standard deviations below the average salary.

Explanation:

Hello!

Usually, when you calculate a probability of an X₀ value from a normally distributed variable you need to standardize it to reach the proper value. In this case, you already have the Z-value and need to reverse the standardization to obtain the X₀ value.

Z= X₀ - μ

δ

δ*Z = X₀ - μ

X₀= (δ*Z) + μ

replace Z= -2.50

X₀= (δ*-2.50) + μ

X₀= μ - (δ*2.50)

You can replace the Z value any time. I've just choose to do it at the end because it's more confortable for me.

I hope it helps!