If the mean is 50 and the standard deviation is 5, a value of 60 corresponds to which z-score?

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (B)

Using the standardization concept, a z-score shows how many standard deviations a value is from the mean: z = (X − μ)/σ. Here, μ = 50 and σ = 5, and X = 60, so z = (60 − 50)/5 = 10/5 = 2. That means 60 is two standard deviations above the mean. To see why other z-scores don’t fit: a z-score of 1 would place X at 55, a z-score of 3 would place X at 65, and a z-score of 4 would place X at 70.