Question

On a unit test in a statistics class, the teacher determines that the mean test grade was 77.5 with a standard deviation of 5.2. One test grade has a z-score of 2.4. Which of the following statements gives the best interpretation of this z-
score?

A. This student's test grade was higher than 2.4% of the other students' test grades.

B. This student's test grade was 2.4 standard deviations above the mean test grade.

C. This student's test grade was 2.4 standard deviations below the mean test grade.

D. The student's test grade was lower than 2.4% of the other students' test grades.​

Answer 1

Answer: B. This student's test grade was 2.4 standard deviations above the mean test grade.

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Explanation:

The z score tells us how far away the raw score is from the mean. This distance is in terms of standard deviations.

• z = 1 means we're 1 standard deviation above the mean
• z = 2 means we're 2 standard deviations above the mean

and so on.

Negative z scores indicate the raw score is below the mean.

• z = -1 means we're 1 standard deviation below the mean
• z = -2 means we're 2 standard deviations below the mean

and so on. So that's why z = 2.4 indicates the students test grade was 2.4 standard deviations above the mean.