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=(X-\mu)/(\sigma) \\ z=(70-100)/(15) \end{gathered}`

then,

`z=(-30)/(15)=-2`

Now, for IQ 130, we have

`\begin{gathered} z=(X-\mu)/(\sigma) \\ z=(130-100)/(15) \\ z=(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`