If We Model After-Tax Household Income by a Normal Distribution

Short Answer

If we model after-tax household income by a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is bell-shaped and symmetric. If we define a "rich" household as one whose after-tax income is at least 1.3 standard deviations above the mean, find the household income of a rich family in Germany. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\\hline \begin{array} { c } \text { Mean Household } \\\text { Income }\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\\hline \text { Standard Deviation } & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\\hline\end{array}$$ ​
The household income of a rich family in Germany is __________ or __________ (more or less).