Let $G$ denote the centroid of triangle $ABC$. If triangle $ABG$ is equilateral with side length 2, then determine the perimeter
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In a normal distribution, the median is the same as the mean (25.3). The first quartile is the value of 
such that
You have
For the standard normal distribution, the first quartile is about
, and by symmetry the third quartile would be 
. In terms of the MCAT score distribution, these values are
The interquartile range (IQR) is just the difference between the two quartiles, so the IQR is about 8.8.
The central 80% of the scores have z-scores
such that
That leaves 10% on either side of this range, which means
You have
Converting to MCAT scores,
So the interval that contains the central 80% is
(give or take).
You have
For the standard normal distribution, the first quartile is about
The interquartile range (IQR) is just the difference between the two quartiles, so the IQR is about 8.8.
The central 80% of the scores have z-scores
That leaves 10% on either side of this range, which means
You have
Converting to MCAT scores,
So the interval that contains the central 80% is