Question

Assume that adults have IQ scores that are normally distributed with a mean of 100 and standard deviation of 15 (as on the Wechsler test). Find the probability that 1. a randomly selected adult has an IQ greater than 120

Answer 1

The Solution:

Given:

$\begin{gathered} X=120 \\ \mu=100 \\ \sigma=15 \end{gathered}$

We are required to find the probability that the adult selected has IQ greater than 120.

By the Z-statistic formula, we have:

$Z=\frac{X-\mu}{\sigma}=\frac{120-100}{15}=\frac{20}{15}=\frac{4}{3}=1.3333$

From the Z score tables, we have:

$P(Z>1.3333)=0.0912\approx0.091$

Therefore, the correct answer is 0.091