The total scores on the Medical College Admission Test MCAT

The total scores on the Medical College Admission Test (MCAT) follow a Normal distribution with mean 25.9 and standard deviation 6.6.

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

Solution

FIRST QUARTILE:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.25      
          
Then, using table or technology,          
          
z =    -0.67448975      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    25.9      
z = the critical z score =    -0.67448975      
s = standard deviation =    6.6      
          
Then          
          
x = critical value =    21.44836765   [ANSWER, Q1]

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MEDIAN:

The median of a normal distribution is simply the mean.

Thus,

median = mean = 25.9 [answer]

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THIRD QUARTILE:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.75      
          
Then, using table or technology,          
          
z =    0.67448975      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    25.9      
z = the critical z score =    0.67448975      
s = standard deviation =    6.6      
          
Then          
          
x = critical value =    30.35163235   [ANSWER, Q3]