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

question 178

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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 Swedish households are either very wealthy (income at least $100,000) or very poor (income at most $12,000) Express your answer to the nearest 1%.  Country  U.S.  Canada  Switzerland  Germany  Sweden  Mean  household  income $38,000$35,000$39,000$34,000$32,000 Standard  deviation $21,000$17,000$16,000$14,000$11,000\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}

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Definitions:

Cartilaginous Fishes

A class of fishes that have skeletons made entirely out of cartilage, rather than bone.

Jawless Fishes

A group of fish that lack a true jaw, represented by modern lampreys and hagfishes, belonging to the superclass Agnatha.

Myxini

A class of jawless marine animals known as hagfishes, characterized by their slimy skin and primitive features.

Petromyzontida

An order of jawless fish, also known as lampreys, characterized by their eel-like appearance and parasitic or non-parasitic lifestyle.

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