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?

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([tex]\mu=74,\sigma^{2} = 7^{2}[/tex])

Also, let Y = results on the mathematics exam

So, Y ~ N([tex]\mu=69,\sigma^{2} = 10^{2}[/tex])

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 = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = mean score for respective exams

[tex]\sigma[/tex] = 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 = [tex]\frac{81-74}{7}[/tex] = 1 {where [tex]\mu=74[/tex] and [tex]\sigma =7[/tex] }

The z-score of Mathematics exam is calculated as;

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

So, z-score = [tex]\frac{88-69}{10}[/tex] = 1.9 {where [tex]\mu=69[/tex] and [tex]\sigma =10[/tex] }

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.