On a standardized exam, the scores are normally distributed with a mean of 180 and a standard deviation of 20. Find the z-score of a person who scored 135 on the exam.
To find the z-score of a person who scored 135 on the exam, we can use the formula:
z = (x - μ) / σ
where:
z = z-score
x = score (135 in this case)
μ = mean (180)
σ = standard deviation (20)
Plugging in the values, we get:
z = (135 - 180) / 20
z = -45 / 20
z = -2.25
Therefore, the z-score of a person who scored 135 on the exam is -2.25.