A survey of automobiles parked in student and staff lots at a large university classified the brands by region of origin,as seen in the table. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Driver }\\$
$6854\begin{array}{c} Origin &\begin{array}{|l|cc|} \hline& \text { Student } & \text { Staff } \\\hline \text { North American } & 91 & 90 \\\text { European } & 31 & 16 \\\text { Asian } & 68 & 54 \\\hline\end{array}\end{array}$ What is the marginal distribution of origin?

A) 52% North American,13% European,35% Asian
B) 56% North American,10% European,34% Asian
C) 54% Students,46% Staff
D) 107% North American,16% European,54% Asian
E) 48% North American,16% European,36% Asian

Question

A survey of automobiles parked in student and staff lots at a large university classified the brands by region of origin,as seen in the table.

\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Driver }\\

6854\begin{array}{c} Origin &\begin{array}{|l|cc|} \hline& \text { Student } & \text { Staff } \\\hline \text { North American } & 91 & 90 \\\text { European } & 31 & 16 \\\text { Asian } & 68 & 54 \\\hline\end{array}\end{array}

What is the marginal distribution of origin?

A) 52% North American,13% European,35% Asian
B) 56% North American,10% European,34% Asian
C) 54% Students,46% Staff
D) 107% North American,16% European,54% Asian
E) 48% North American,16% European,36% Asian

Caroline Ayman · Accepted Answer

Final Answer : A, Explanation :   To find the marginal distribution of origin, add the totals for each origin across both student and staff, then divide by the grand total. North American:   91 + 90 = 181 91+90=181 91 + 90 = 181  , European:   31 + 16 = 47 31+16=47 31 + 16 = 47  , Asian:   68 + 54 = 122 68+54=122 68 + 54 = 122  . Grand total:   181 + 47 + 122 = 350 181+47+122=350 181 + 47 + 122 = 350  . Percentages: North American   181 / 350 = 51.7 % 181/350=51.7\% 181/350 = 51.7%  , European   47 / 350 = 13.4 % 47/350=13.4\% 47/350 = 13.4%  , Asian   122 / 350 = 34.9 % 122/350=34.9\% 122/350 = 34.9%  . Rounded: 52% North American, 13% European, 35% Asian.

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