Question

The total scores on the Medical College Admissions Test (MCAT) in 2013 follow a Normal distribution with mean 25.3 and standard deviation 6.5.

a) what are the median and the first and third quartiles of the MCAT scores? what is the interquartile range?

please i need help!!!

Answer 1

1st quartile (25%) and the 3rd quartile (75%) values are -0.6745 and 0.6745 respectively. Use this formula z= (x-mean)SD -0.6745 = (x-25.3)/6.5.
x=25.3 - 0.6745(6.5) = 25.3 - 4.3843 = 20.9157 1st Quartile
0.6745 = (x - 25.3) 6.5
x = 25.3 + 0.6745 = 25.3 + 4.3843 = 29.6843 3rd quartile
interquartile range is the difference between the 1st quartile and the 4th quartile