A fast-food restaurant chain with 700 outlets in the United States describes the geographic location of itsrestaurants with the accompanying table of percentages. A restaurant is to be chosen at random from the 700 totest market a new style of chicken. Given that the restaurant is located in the eastern United States, what is theprobability it is located in a city with a population of at least 10,000? $\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Region }\\\begin{array} { r r r r r c } \hline & & \text { NE } & \text { SE } & \text { SW } & \text { NW } \\\hline & < 10,000 & 10 \% & 6 \% & 3 \% & 0 \% \\\text { Population of City } 10,000 &- 100,000 & 15 \% & 5 \% & 12 \% & 5 \% \\& > 100,000 & 20 \% & 4 \% & 9 \% & 11 \%\end{array}\end{array}$

Question

A fast-food restaurant chain with 700 outlets in the United States describes the geographic location of itsrestaurants with the accompanying table of percentages. A restaurant is to be chosen at random from the 700 totest market a new style of chicken. Given that the restaurant is located in the eastern United States, what is theprobability it is located in a city with a population of at least 10,000? $\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Region }\
\begin{array} { r r r r r c } 
\hline & & \text { NE } & \text { SE } & \text { SW } & \text { NW } \
\hline & < 10,000 & 10 \% & 6 \% & 3 \% & 0 \% \
\text { Population of City } 10,000 &- 100,000 & 15 \% & 5 \% & 12 \% & 5 \% \
& > 100,000 & 20 \% & 4 \% & 9 \% & 11 \%
\end{array}
\end{array}$

A) 0.733
B) 0.543
C) 0.44
D) 0.267

Quizplus · Accepted Answer

The probability that a randomly chosen restaurant is located in a city with a population of at least 10,000, given it is in the eastern United States (NE or SE), is calculated by adding the percentages of restaurants in cities with populations of 10,000-100,000 and those in cities with populations of more than 100,000, then dividing by the total percentage of restaurants in the eastern United States. For NE and SE, the percentages are 15% + 20% for NE and 5% + 4% for SE. The total for the eastern United States is 10% + 15% + 20% + 6% + 5% + 4% = 60%. The probability is then (15% + 20% + 5% + 4%) / 60% = 44% / 60% = 0.733.

A Fast-Food Restaurant Chain with 700 Outlets in the United