Answered

The total scores on the Medical College Admission Test (MCAT) follow a Normal distribution with mean 25.9 and standard deviation 6.4 .

What are the median and the first and third quartiles of the MCAT scores?

Verified Answer :

A normal distribution follows a z-score pattern. 
In a normal distribution, 50% of the data is on the left side of the peak, and 50% is on the right side. In other words, the mean is the median in a normal distribution.
The first quartile on a normal curve is where 25% or .25 represents the area under the curve to the left of the line. 
So, you go to the z-score table, find where the area is .250
you should get a z-score of -.68
This means that the first quartile is .68 standard deviations away from the mean.
To calculate, Q1=25.9-.68(6.4)=21.548
For Q3 similar procedure. Find on z-score chart where the area under the curve=.75 (zscore of .67) and calculate accordingly
Q3=25.9+.67(6.4)=30.188
in summary:

Q1=21.548
Median/Mean=25.9
Q3=30.188