Question

Assume that adults have IQ scores that are normally distribüted with a mean of 104.6 and a standard deviation 15.8.Find the first quartile Q.which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.)The first quartile ls:

Answer 1

The z-score in which the bottom 25% lies is equal to -0.67.

Given a mean score of 104.6 and a standard deviation of 15.6

$\begin{gathered} X=\mu+(-0.67)\sigma \\ \text{Substitute} \\ \mu=104.6,\sigma=15.6 \\ \\ X=104.6+(-0.67)(15.6) \\ X=104.6-10.452 \\ X=94.148 \end{gathered}$

Rounding to one decimal place, the score separating the bottom 25% or the first quartile is 94.1.