To answer this question we will compute the z-score.
Recall that the z-score can be computed using the following formula:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where }\mu\text{ is the mean, }\sigma\text{ is the standard deviation, and x is the observed value.} \end{gathered}[/tex]Substituting μ=55000, σ=15000, and x=20000 we get:
[tex]z=\frac{20000-55000}{15000}=-\frac{35000}{15000}=-2.3\bar{3}.[/tex]Now, the percentage of the population that lives in poverty is:
[tex]P(z<-2.3\bar{3})=0.0098153\cdot100percent=0.98153\text{percent}.[/tex]Now, we know that the new tax law is expected to benefit middle-income families that have an income between $50,000 to $60,000, using the z-score formula we get:
[tex]\begin{gathered} z=\frac{50000-55000}{15000}=-\frac{5000}{15000}=-0.3\bar{3}, \\ z=\frac{60000-55000}{15000}=\frac{5000}{15000}=0.3\bar{3}\text{.} \end{gathered}[/tex]Then, the percentage of the population that will be benefited from the law is:
[tex]P(-0.3\bar{3}Answer:
The percentage of the population that lives in poverty is 0.98153%.
The percentage of the population that will be benefited from the law is 26.112%.
