Assume that adults have IQ scores that are normally distribu

Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation of 15. Find the third quartile Q3, which is the IQ score separating the top 25% from the others.

The third quartile, Q3 is (__) round to one deciaml place

Solution

Mean ( u ) =105
Standard Deviation ( sd )=15
Number ( n ) = 1000
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  

P ( Z < x ) = 0.75
Value of z to the cumulative probability of 0.75 from normal table is 0.674
P( x-u/s.d < x - 105/15 ) = 0.75
That is, ( x - 105/15 ) = 0.67
--> x = 0.67 * 15 + 105 = 115.1