What is the value corresponding to a z-score of 3 when the mean is 8 and the standard deviation is 2?

• A. 12
• B. 14
• C. 10
• D. 16

Answer: (B)

The z-score tells how many standard deviations a value is from the mean. To find the actual value when you know the mean, standard deviation, and z-score, use X = mu + z*sigma. With mu = 8, sigma = 2, and z = 3, you get X = 8 + 3×2 = 14. So the value is 14. For reference, 12 would be 2 standard deviations above the mean, 10 would be 1 standard deviation above, and 16 would be 4 standard deviations above.