Scores on the 2017 MCAT, an exam required for all medical school applicants, were approximately Normal with a mean score of 505 and a standard deviation of
. a. Suppose an applicant had an MCAT score of 520 . What percentile corresponds with this score? b. Suppose to be considered at a highly selective medical school an applicant should score in the top
of all test takers. What score would place an applicant in the top
?
The Correct Answer and Explanation is:
Let’s break this down step by step.
Part (a): Finding the Percentile for an MCAT Score of 520
The MCAT scores are normally distributed with:
- Mean (μ\mu) = 505
- Standard deviation (σ\sigma) = unknown, but let’s assume a reasonable estimate
- Applicant’s score (XX) = 520
To find the percentile, we calculate the z-score using the formula:
z=X−μσz = \frac{X – \mu}{\sigma}
Assuming the standard deviation is 10 (a common estimate for MCAT scores), we get:
z=520−50510=1510=1.5z = \frac{520 – 505}{10} = \frac{15}{10} = 1.5
Using a standard normal table, a z-score of 1.5 corresponds to a percentile of approximately 93.32%. This means the applicant scored better than about 93.32% of all test takers.
Part (b): Finding the Score for Top Percentile
Suppose an applicant needs to be in the top 10% of test takers. That means they need to have a z-score that corresponds to the 90th percentile, which is approximately z=1.28z = 1.28.
Using the z-score formula:
X=μ+(z×σ)X = \mu + (z \times \sigma)
X=505+(1.28×10)=505+12.8=∗∗518∗∗X = 505 + (1.28 \times 10) = 505 + 12.8 = **518**
Thus, an applicant would need an MCAT score of at least 518 to be in the top 10% of all test takers, making them highly competitive for top medical schools.
Explanation (Like a Textbook)
The MCAT follows a normal distribution, meaning most scores cluster around the mean (505), while fewer test takers score at the extreme high or low ends. To determine percentile rankings, we use z-scores, which standardize individual scores relative to the population.
For example, a z-score of 1.5 means an MCAT score of 520 is 1.5 standard deviations above the mean, corresponding to a 93rd percentile rank. This signifies that only about 6.68% of test takers scored higher.
Conversely, for students aiming for elite medical schools, a z-score of 1.28 is required to be in the top 10%, equating to an MCAT score of 518 or higher.
Understanding z-scores helps applicants gauge competitiveness, assess target scores for medical school admissions, and interpret standardized test results effectively. The normal distribution allows comparison of performance relative to the broader applicant pool.
This method applies universally to other standardized exams, making percentile calculations a critical tool for evaluating academic competitiveness.
