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 thez-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.
Accepted Solution
A:
Answer:A. 2.5 standard deviations below the average salary.Step-by-step 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 δδ*Z = X₀ - μ X₀= (δ*Z) + μreplace 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!