Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.Using the empirical rule, what percentage of people have an IQ score between 70 and130?

Answer 1

First, we need to find the z-score value for the given IQs. For IQ 70, we have

$\begin{gathered} z=\frac{X-\mu}{\sigma} \\ z=\frac{70-100}{15} \end{gathered}$

then,

$z=\frac{-30}{15}=-2$

Now, for IQ 130, we have

$\begin{gathered} z=\frac{X-\mu}{\sigma} \\ z=\frac{130-100}{15} \\ z=\frac{30}{15} \\ z=2 \end{gathered}$

This means that the given IQs falls with in 2 standard deviations. Therefore the answer is 95%

$\mu-2\sigma\text{ and }\mu+2\sigma$