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. Find the percent of canadian families which earned an after-tax income of $69,000 or more. $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \
\hline \begin{array} { c }
\text { Mean Household } \
\text { Income }
\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \
\hline \text { Standard Deviation } & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \
\hline
\end{array}$$
A)5%
B) 95%
C) 47.5%
D) 2.5%
E) 99.7%

Question

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. Find the percent of canadian families which earned an after-tax income of $69,000 or more. $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \
\hline \begin{array} { c } 
\text { Mean Household } \
\text { Income }
\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \
\hline \text { Standard Deviation } & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \
\hline
\end{array}$$  
A)5%
B) 95%
C) 47.5%
D) 2.5%
E) 99.7%

Quizplus · Accepted Answer

To find the percent of Canadian families earning $69,000 or more, we calculate the z-score using the formula $$z = \frac{X - \mu}{\sigma}$$, where $X = 69,000$, $\mu = 35,000$ (mean for Canada), and $\sigma = 17,000$ (standard deviation for Canada). Plugging in the values, we get $$z = \frac{69,000 - 35,000}{17,000} = 2$$. A z-score of 2 corresponds to the upper tail of the normal distribution, which is approximately 2.5% of the area under the curve. This means that about 2.5% of Canadian families earned $69,000 or more.

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