Chapter 3, Problem 28E

(a)

To determine

To find: the percent of all the cars surveyed were foreign.

Answer to Problem 28E

40.9%

Explanation of Solution

Given:

	Student	Staff
American	107	105
European	33	12
Asian	55	47

Calculation:

The total number of foreign cars is 45+102=147.

Also the total number of cars = 359.

Therefore, the percent of all the cars surveyed which were foreign is

  $\begin{array}{c}\frac{\text{Number of foreign cars}}{\text{Total}\text{number of cars}}=\frac{147}{359}\times 100\\ =40.9\%\end{array}$

Therefore, the percent of foreign cars is 40.9%

(b)

To determine

To find: the percent of the American cars were owned by students.

Answer to Problem 28E

50.5%

Explanation of Solution

Given:

	Student	Staff
American	107	105
European	33	12
Asian	55	47

Calculation:

Total number of American cars = 212.

The total number of American cars owned by students = 107.

Therefore, the percent of American cars were owned by students is

  $\begin{array}{c}\frac{\text{Number of student owned American cars}}{\text{Total}\text{number of American cars}}=\frac{107}{212}\times 100\\ =50.5\%\end{array}$

Therefore, the percentage of American cars owned by students is 50.5%

(c)

To determine

To find: the percent of the students owned American cars.

Answer to Problem 28E

54.9%

Explanation of Solution

Given:

	Student	Staff
American	107	105
European	33	12
Asian	55	47

Calculation:

Total number of student cars = 195.

Total number of American cars owned by students = 107

So, the percent of student owned American cars is

  $\begin{array}{c}\frac{\text{Number of student owned American cars}}{\text{Total}\text{number of American cars}}=\frac{107}{195}\times 100\\ =54.9\%\end{array}$

Therefore, the percentage of student owned American cars is 54.9%

(d)

To determine

To find: the marginal distribution of origin.

Explanation of Solution

Given:

	Student	Staff
American	107	105
European	33	12
Asian	55	47

Calculation:

The marginal distribution

For American cars:

  $\begin{array}{c}\frac{\text{Total}\text{number of American origin cars}}{\text{Total}\text{number of cars}}=\frac{212}{359}\times 100\\ =59.1\%\end{array}$

For European cars:

  $\begin{array}{c}\frac{\text{Total}\text{number of European origin cars}}{\text{Total}\text{number of cars}}=\frac{45}{359}\times 100\\ =12.5\%\end{array}$

For Asian cars:

  $\begin{array}{c}\frac{\text{Total}\text{number of Asian origin cars}}{\text{Total}\text{number of cars}}=\frac{102}{359}\times 100\\ =28.4\%\end{array}$

Therefore, there are 59.1% of American origin cars 12.5% of European origin and 28.4% of Asian origin cars.

(e)

To determine

To find: the conditional distributions of origin by driver classification.

Explanation of Solution

Given:

	Student	Staff
American	107	105
European	33	12
Asian	55	47

Calculation:

Driver origin		Student	Staff	Total
	American	$\frac{107}{212}\times 100\%=50.5\%$	$\frac{105}{212}\times 100\%=49.5\%$	100%
	European	$\frac{33}{45}\times 100\%=73.3\%$	$\frac{12}{45}\times 100\%=26.7\%$	100%
	Asian	$\frac{55}{102}\times 100\%=53.9\%$	$\frac{47}{102}\times 100\%=46.1\%$	100%

(f)

To determine

To Explain: that the origin of the car is independent of the type of driver.

Explanation of Solution

Given:

	Student	Staff
American	107	105
European	33	12
Asian	55	47

If the origin of the car is European than there is 73.3% driver were students where only 26.7% driver were staff. Where in other origins both types of driver are almost same percentage

Therefore the origin of the car is not independent of the type of driver.