Erdem and Aslı

Difficulty: Medium · Topics: Probability, Statistics, z-Scores

The table shows the mean and standard deviation of a class's maths and geometry exams, and some of Erdem's and Aslı's scores.

Exam Mean Std. dev. Erdem Aslı --- --- --- --- --- Mathematics 80 20 … 90 Geometry 70 5 75 …

I. Erdem came top of the class in geometry.

II. The geometry scores are more spread out.

III. Erdem did better in geometry than Aslı did in maths.

Which of the statements are definitely true?

(The z-score of a value x is z=(x-bar x)/(s), where bar x is the mean and s the standard deviation.)