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.
<em>Firstly, Let X = scores on the chemistry final exam</em>
<em>So, X ~ N(</em><em>)</em>
<em>Also, let Y = scores on the calculus final exam</em>
<em>So, Y ~ N(</em><em>)</em>
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 = ~ N(0,1)
where, = mean score for respective subjects
= standard deviation
- <u>The z-score of Chemistry final exam is calculated as;</u>
Since we are given the student score of 81 on the chemistry final exam,
So, z-score = = 0.4 {where
and
}
- <u>The z-score of Calculus final exam is calculated as;</u>
Since we are given the student score of 81 on the calculus final exam,
So, z-score = = -0.143 {where
and
}
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.