There are two college entrance exams that are often taken by students, Exam A and Exam B. The composite score on Exam A is approximately normally distributed with mean 20.5 and standard deviation 4.9. The composite score on Exam B is approximately normally distributed with mean 1022 and standard deviation 214. Suppose you scored 27 on Exam A and 1209 on Exam B. Which exam did you score better on? Justify your reasoning using the normal model.

Answer: Exam A

Step-by-step explanation:

We must analyze how far are you from the mean in both cases, where the "step" that we will use to measure is the standard deviation.

In exam A, the mean is 20.5 and the standard deviation is 4.9.

If you scored a 27; then you need to see:

20.5 + 4.9 = 25.4

20.5 + 4.9 + 4.9 = 30.3

So you are within two times the standard deviation (more than the mean).

In the B exam, the mean is 1022 and the standard deviation is 214, where you scored 1209.

1022 + 214 = 1236

So in this exam, you are by one standard deviation away from the media.

With this, you can see that you did score better in exam A.