Question

An advertising company plans to market a product to low-income families. A study states that for a particular area the mean income per family is $25,174 and the standard deviation is $8,700. If the company plans to target the bottom 18% of the families based on income, find the cutoff income. Assume the variable is normally distributed.

Answer 1

`\begin{gathered} \text{ A percentile rank of 18 has a z-score of -0.915},\text{ with that we can use it along} \\ \text{ with the other given} \\ z=-0.915 \\ \mu=25174 \\ \sigma=8700 \\ \text{ We use the formula for getting the z-score and substitute} \\ z=(x-\mu)/(\sigma) \\ -0.915=(x-25174)/(8700) \\ (-0.915)(8700)=x-25174 \\ -7960.50=x-25174 \\ 25174-7960.50=x \\ 17213.50=x \\ x=17213.50 \\ \text{ The target cutoff is \$17213.50} \end{gathered}`