On a standardized exam, the scores are normally distributed with a mean of 105 and a standard deviation of 20. Find the z-score of a person who scored 140 on the exam.
To find the z-score, we use the formula:
z = (X - μ) / σ
where:
z is the z-score
X is the raw score (140 in this case)
μ is the mean (105)
σ is the standard deviation (20)
Plugging in the values:
z = (140 - 105) / 20
z = 35 / 20
z = 1.75
Therefore, the z-score of a person who scored 140 on the exam is 1.75.