Question

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?

Answer 1

Answer:

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($\mu=74,\sigma^{2} = 7^{2}$)

Also, let Y = results on the mathematics exam

So, Y ~ N($\mu=69,\sigma^{2} = 10^{2}$)

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 = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean score for respective exams

            $\sigma$ = standard deviation

• The z-score of Economics exam is calculated as;

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

So,  z-score = $\frac{81-74}{7}$ = 1  {where $\mu=74$ and $\sigma =7$ }

• The z-score of Mathematics exam is calculated as;

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

So,  z-score = $\frac{88-69}{10}$ = 1.9    {where $\mu=69$ and $\sigma =10$ }

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.