On a standardized exam, the scores are normally distributed with a mean of 40 and a standard deviation of 5. Find the z-score of a person who scored 27 on the exam.
To find the z-score, we use the formula:
z = (x - μ) / σ
Where:
- x = score
- μ = mean
- σ = standard deviation
In this case, x = 27, μ = 40, and σ = 5.
z = (27 - 40) / 5
z = (-13) / 5
z = -2.6
The z-score of a person who scored 27 on the exam is -2.6.