An incoming MBA student took placement exams in economics and mathematics. In economics, she scored 81 and in math 88. The overall results on the economics exam had a mean of 74 and a standard deviation of 7, while the mean math score was 69, with a standard deviation of 10. Using z-scores, on which exam did she do better compared with the other students?

An incoming MBA student do better in Mathematics exam.

Step-by-step explanation:

We are given that an incoming MBA student took placement exams in economics and mathematics. In economics, she scored 81 and in math 88.

The overall results on the economics exam had a mean of 74 and a standard deviation of 7, while the mean math score was 69, with a standard deviation of 10.

And we have to find that  in which exam did she do better.

Firstly, Let X = results on the economics exam

So, X ~ N()

Also, let Y = results on the mathematics exam

So, Y ~ N()

For finding in which exam did she do better, we will find the z score for both the exams of MBA student because the higher the z score, the better is the student performance in that exam.

The z-score probability distribution is given by;

              Z = ~ N(0,1)

where, = mean score for respective exams

            = standard deviation

Since we are given that the student score 81 in economics exam,

So,  z-score = = 1  {where and }

Since we are given that the student score 88 in mathematics exam,

So,  z-score = = 1.9    {where and }

AS we can clearly see that the z score of Mathematics exam is higher than that of Economics exam, so the student do better in Mathematics exam.