Question

Family incomes have a mean of $60 000 with a standard deviation of $20 000. The data is normally distributed. A new tax law is designed to help families with incomes between $45 000 and $80 000. What percentage of families will this new law help? Provide evidence of your work by typing out your full solution.

ASP

Answer 1

$\mu=60000 \\ \sigma=20000 \\ P(45000<X<80000) = P(X<80000) -P(X<45000) \\ = P(Z< \frac{80000-60000}{20000}) -P(Z< \frac{45000-60000}{20000}) \\ = P(Z< 1) -P(Z< -0.75) \\ = 0.8413 -0.2266 \\ = 0.6147$

61.47 % of families this new law will help.