Question

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 77 and a standard deviation of 10. The scores on the calculus final are also approximately normally distributed, with a mean of 83 and a standard deviation of 14. A student scored 81 on the chemistry final and 81 on the calculus final. Relative to the students in each respective class, in which subject did the student do better?

Answer 1

Answer:

Student do better in Chemistry subject.

Step-by-step explanation:

We are given that at a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 77 and a standard deviation of 10. The scores on the calculus final are also approximately normally distributed, with a mean of 83 and a standard deviation of 14.

A student scored 81 on the chemistry final and 81 on the calculus final.

And we have to find that  in which subject did the student do better.

Firstly, Let X = scores on the chemistry final exam

So, X ~ N($\mu=77,\sigma^{2} = 10^{2}$)

Also, let Y = scores on the calculus final exam

So, Y ~ N($\mu=83,\sigma^{2} = 14^{2}$)

For finding in which subject did the student do better, we will find the z score for both the exams of student because the higher the z score, the better is the student perform 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 subjects

            $\sigma$ = standard deviation

• The z-score of Chemistry final exam is calculated as;

Since we are given the student score of 81 on the chemistry final exam,

So,  z-score = $\frac{81-77}{10}$ = 0.4  {where $\mu=77$ and $\sigma =10$ }

• The z-score of Calculus final exam is calculated as;

Since we are given the student score of 81 on the calculus final exam,

So,  z-score = $\frac{81-83}{14}$ = -0.143     {where $\mu=83$ and $\sigma =14$ }

AS we can clearly see that the z score of Chemistry final exam is higher than that of Calculus exam so the student do better in Chemistry subject exam.