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

question 85

Short Answer

If we model after-tax household income with 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 normal, and round all percentages to the nearest whole number. What percentage of U.S. households had an income of $50,000 or more Express your answer to the nearest 1%. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\\hline \begin{array} { l } \text { Mean } \\\text { household } \\\text { income }\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\\hline \begin{array} { l } \text { Standard } \\\text { deviation }\end{array} & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\\hline\end{array}$$
__________% of households

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Definitions:

Defined Benefit Pension Plan

A retirement plan where an employer promises a specified pension payment upon retirement, based on the employee's earnings history, tenure of service, and age.

Retired Employees

Individuals who have ended their professional career and are no longer working, often receiving pensions or living off retirement savings.

Employer Responsibility

The obligations and duties of an employer towards their employees, which can include providing a safe working environment and fair pay.

After-Tax Rate

The rate of return on an investment after accounting for taxes.