Question
Mike is trying to get into a Medical college for Post-graduation in India. Before applying for any college/university, he needs to take an exam for that particular college/university. Therefore, he decided to take two exams – AIIMS PG and JIPMER PG”. The summary statistics of the results for each exam are given below:
![\[ \begin{tabular}{|c|c|c|c|} \hline _ & Mean & Std. Deviation & Mike's Marks\\ \hline AIIMS PG & 151 & 10 & 172\\ \hline JIPMER PG & 25.1 & 6.4 & 37\\ \hline \end{tabular} \]](https://ehanghalib.com/wp-content/ql-cache/quicklatex.com-b0afe00abdcdd54895db1995e4d79cd4_l3.png "Rendered by QuickLaTeX.com")
Mike took both the exams and scored 172 in AIIMS PG and 37 in JIPMER PG.
Based on the above data, you need to figure out, in which exam did he do relatively better? Explain how did you arrive at this conclusion?
Solution
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Let’s assume that the marks of both exams follow a Gaussian distribution. We will have the probability distribution curve as below:
Standardize the Scores Using z-Score
State the Problem
Now, let’s transform the problem. We need to find the “probability of finding students who scored more marks than Mike”. The stated problem is now in the form of P(X > a).
Thus, we need to find P(z > 2.1) for AIIMS distribution and P(z > 1.86) for JIPMER distribution.
- P(z > 2.1) = 0.017 means that 1.7% students scored better than Mike in AIIMS PG entrance exam.
- P(z > 1.86) = 0.327 means that 3.2% students scored better than Mike in JIPMER PG entrance exam.
Conclusions
- In AIIMS PG entrance exam, Mike scored better than 98.2% of all test-takers.
- In JIPMER PG entrance exam, Mike scored better than 96.8% of all test-takers.
Thus, Sam scored relatively better in AIIMS PG.