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.

Question

25-10-2022
Mathematics

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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.

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CannonD149997 CannonD149997 · Answer 1 · 2022-10-25T13:55:12+02:00

[tex]\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=\frac{x-\mu}{\sigma} \\ -0.915=\frac{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}[/tex]