Question

a survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. complet
origin \tdriver
\tstudent \tstaff
american \t105 \t106
european \t31 \t13
asian \t55 \t49

a) what percent of all the cars surveyed were foreign?
41.2 %
(round to one decimal place as needed.)
b) what percent of the american cars were owned by students?
49.8 %
(round to one decimal place as needed.)
c) what percent of the students owned american cars?
55 %
(round to one decimal place as needed.)
d) what is the marginal distribution of origin?
origin \tmarginal
american \t58.8 %
european \t12.3 %
asian \t28.9 %
(round to one decimal place as needed.)
e) what are the conditional distributions of origin by driver classification?
origin \tstudent \tstaff
american \t% \t%
european \t% \t%
asian \t% \t%
(round to one decimal place as needed.)

Explanation:

Part e)

First, we calculate the total number of students and staff separately.

Step 1: Calculate total for Students

Total students = 105 (American) + 31 (European) + 55 (Asian) = 191

Step 2: Calculate total for Staff

Total staff = 106 (American) + 13 (European) + 49 (Asian) = 168

Now, we find the percentage for each origin within each driver group.

For American cars:

Step 3: Student - American

Percentage = $\frac{105}{191} \times 100 \approx 55.0\%$

Step 4: Staff - American

Percentage = $\frac{106}{168} \times 100 \approx 63.1\%$

For European cars:

Step 5: Student - European

Percentage = $\frac{31}{191} \times 100 \approx 16.2\%$

Step 6: Staff - European

Percentage = $\frac{13}{168} \times 100 \approx 7.7\%$

For Asian cars:

Step 7: Student - Asian

Percentage = $\frac{55}{191} \times 100 \approx 28.8\%$

Step 8: Staff - Asian

Percentage = $\frac{49}{168} \times 100 \approx 29.2\%$

Answer:

Origin	Student (%)	Staff (%)
European	16.2	7.7
Asian	28.8	29.2