Question

IQ tests are measured on a scale which is 𝑁(100,225). A woman wants to form an

“Computer Society” which only admits people with the top 1% of IQ scores. What would

she have to set as the cut-off point in the test to allow this to happen?

Answer 1

Let $\Phi(x)$ denote the c.d.f. of standard normal distribution and $\alpha$ denote the desirable cut-off.

In order to admit top 1% one should solve the equation

$\Phi\left(\dfrac{\alpha - 100}{\sqrt{225}}\right) = 0.99,$ so $\alpha = 100 + 15\Phi^{-1}(0.99) \approx 134.895$ .