Assume that adults have IQ scores that are normally distribu

Assume that adults have IQ scores that are normally distributed with a mean of 107 and a standard deviation of 15. Find the third quartile Q_3, which is the IQ score separating the top 25% from the others.

Solution

Normal Distribution
Mean ( u ) =107
Standard Deviation ( sd )=15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.25
Value of z to the cumulative probability of 0.25 from normal table is 0.67
P( x-u/ (s.d) > x - 107/15) = 0.25
That is, ( x - 107/15) = 0.67
--> x = 0.67 * 15+107 = 117.11