Question

Which one of the following would be a correct interpretation if you have a z-score of $+2.0$ on an exam?

a. It means that you missed two questions on the exam.

b. It means that you got twice as many questions correct as the average student.

c. It means that your grade was 2 points higher than the mean grade on this exam.

d. It means that your grade was in the upper $2\%$ of all grades on this exam.

e. It means that your grade is 2 standard deviations above the mean for this exam.

Short answer

This indicates that your exam mark is 2 standard deviations above the mean.

Step-by-step solution

Given information

The following options are

a. It means that you missed two questions on the exam.

b. It means that you got twice as many questions correct as the average student.

c. It means that your grade was 2 points higher than the mean grade on this exam.

d. It means that your grade was in the upper 2% of all grades on this exam.

e. It means that your grade is 2 standard deviations above the mean for this exam.

Explanation for correct option

The Z score is the number of standard deviations a score deviates from the mean.

As a result, the best solution is (e)

Explanation for incorrect option

Option a. It means that you missed two questions on the exam is not correct interpretation if you have a z-score of +2.0 on an exam .

b. It means that you got twice as many questions correct as the average student is not correct interpretation if you have a z-score of +2.0 on an exam .

c. It means that your grade was 2 points higher than the mean grade on this exam is not correct interpretation if you have a z-score of +2.0 on an exam .

d. It means that your grade was in the upper 2% of all grades on this exam is not correct interpretation if you have a z-score of +2.0 on an exam .

e. It means that your grade is 2 standard deviations above the mean for this exam is not correct interpretation if you have a z-score of +2.0 on an exam .