Given a population with mean $\mu$ = $100$ and standard deviation $\sigma$ = $20$, what is the z-score of a value $x$ = $140$?

• A. $1$
• B. $2$
• C. $4$
• D. $0.5$

Answer: (B)

Verified step by step guidance

1. Identify the given values: the population mean \( \mu = 100 \), the population standard deviation \( \sigma = 20 \), and the value \( x = 140 \) for which we want to find the z-score.
2. Recall the formula for the z-score, which measures how many standard deviations a value is from the mean: \[ z = \frac{ x - \mu }{ \sigma } \]
3. Substitute the given values into the formula: \[ z = \frac{ 140 - 100 }{ 20 } \]
4. Simplify the numerator by subtracting the mean from the value: \[ 140 - 100 = 40 \]
5. Divide the result by the standard deviation to find the z-score: \[ z = \frac{ 40 }{ 20 } \]