Q2 Homework Answers

Above are the numbers (in millions) of persons in the population. The data was taken from the recent US Census. Create a univariate frequency / percentage distribution for each question. To make it easy to find the values, each question number corresponds to number on the table where the requested value is located.

1. What percent of total population are Males?

2. What percent of total population are Caucasian?

3. What percent of total population are Eligible drivers?

4. What percent of eligible drivers had face-to-face contact with police?

5. What percent of those who had contact with police were for motor-vehicle stop?

6. What percent of eligible drivers were actually drivers (total drivers)?

7. What percent of total drivers were stopped?

Problem A 1 through 7 answers

1. What percent of total population are Males? To work this problem you construct a univariate frequency distribution that uses both categories of “gender.”

N = 281.4, K = 2

Male / pop = (138.0 / 281.4) = .4904

Female / pop = (143.4 / 281.4) = .5095

Frequency Proportion Percentage

Male 138.0 0.490 49%

Female 143.4 0.510 51%

Total 281.4

Answer: 49% of total population are Males.

2. What percent of total population are Whites? To work this problem you construct a univariate frequency distribution that uses three categories of “race.” (White, Blacks, or other Ethnicity)

N = 281.4, K = 3

White / total pop = (211.4 / 281.4) = .7512

Black / total pop = (34.6 / 281.4) = .1229

Other / total pop = (35.4 / 281.4) = .1257

Frequency Proportion Percentage

White 211.4 0.751 75%

Black 34.6 0.123 12%

Other 35.4 0.126 13%

Total 281.4

Answer: 75% of total population are White.

3. What percent of total population are Eligible drivers? To work this problem you construct a univariate frequency distribution that uses both categories of “eligibility.” (eligible or not eligible).

N = 281.4, K = 2

eligible drivers age 16 and over / total pop = (209.3 / 281.4) = .7437

not eligible – Not yet age 16 / total pop = (72.1 / 281.4) = .2562

Frequency Proportion Percentage

Eligible 209.3 0.744 74%

Not Eligible 72.1 0.256 26%

Total 281.4

Answer: 74% of total population are Eligible drivers.

4. What percent of eligible drivers had face-to-face contact with police? To work this problem you construct a univariate frequency distribution that uses two categories of “eligible contact.”

N = 209.3, K = 2

Eligible had contact / Eligible = (43.8 / 209.3) = .2093

Eligible no Contact / Eligible = (165.5 / 209.3) = .7907

Frequency Proportion Percentage

Contact 43.8 0.209 21%

No contact 165.5 0.791 79%

Total 209.3

Answer: 21% of eligible drivers had face-to-face contact with police

5. What percent of those who had contact with police were for motor-vehicle stop? To work this problem you construct a univariate frequency distribution that uses two categories of “contact for stop.”

N = 43.8, K = 2

MV stop / had contact = (22.7 = / 43.8) = .5182

Contact not MV stop / had contact = (21.1 = / 43.8) = .4817

Frequency Proportion Percentage

Contact MV Stop 22.7 0.518 52%

Contact Other 21.1 0.482 48%

Total 43.8

Answer: 52% of those who had contact with police were for motor-vehicle stop

6. What percent of eligible drivers were actually drivers? To work this problem you construct a univariate frequency distribution that uses two categories of “drivers.”

N = 209.3, K = 2

total drivers / eligible drivers = (187.3 / 209.3) = .8948

eligible not drivers / eligible drivers = (22 / 209.3) = .1051

Frequency Proportion Percentage

Drivers 187.3 0.895 89%

Not drivers 22.0 0.105 11%

Total 209.3

Answer: 89% of eligible drivers were actually drivers.

7. What percent of total drivers were stopped? To work this problem you construct a univariate frequency distribution that uses two categories of “stopped drivers.”

N = 187.3, K = 2

Total stopped / total drivers = (19.3 / 187.3) = .1030

Not stopped / total drivers = (168.0 / 187.3) = .8969

Frequency Proportion Percentage

Stopped 19.3 0.103 10%

Not Stopped 168.0 0.897 90%

Total 187.3

Answer: 10% of total drivers were stopped.

Problem B

Total US population (Total Pop) 281.4

White 211.4

Black 34.6

Other 35.4

Total drivers 187.3

Total stopped drivers 19.3

Male drivers 95.4

Female drivers 91.9

Stopped Males 11.7

Stopped Females 7.6

Black and White Drivers 158.8

Other Ethnicity Drivers 28.5

White drivers 140.7

White eligible drivers age 16 157.3

Black drivers 18.1

Black eligible drivers age 16 24.5

stopped Black Drivers 2.2

stopped White Drivers 14.9

Above are the numbers (in millions) of persons in the population. The data was taken from the recent US Census. Create a univariate frequency / percentage distribution for each question.

1. What percent of stopped drivers are female?

2. What percent of total drivers do both Black and White drivers comprise?

3. What percent of Black and White drivers are White?

4. What percent of White eligible drivers are White drivers?

5. What percent of Black eligible drivers are Black drivers?

6. What percent of total stopped drivers were Black?

7. What percent of total stopped drivers were White?

8. What percent of Black drivers were stopped?

9. What percent of White drivers were stopped?

Problem B -- Answers

1. What percent of stopped drivers are female?

N = 19.3, K = 2

Stopped Males/ total stopped = (11.7 / 19.3) = .606 .

Stopped Females/ total stopped = (7.6 / 19.3) = .394

Frequency Proportion Percentage

Stopped Male 11.7 0.606 61%

Stopped Female 7.6 0.394 39%

Total Stopped 19.3

Answer: 39% of stopped drivers are female.

2. What percent of total drivers are Black and White?

N = 187.3, K = 2

B & W Drivers / Total drivers = (158.8 / 187.3) = .848

Other ethnicity drivers / Total drivers = (28.5 / 187.3) = .152

Frequency Proportion Percentage

B&W Drivers 158.8 0.848 85%

Other Drivers 28.5 0.152 15%

Total Drivers 187.3

Answer: 85% of total drivers are Black and White.

3. What percent of Black and White drivers are White?

N = 158.8, K = 2

White drivers / B & W drivers = (140.7 / 158.8) = .886

Black drivers / B & W drivers = (18.1 / 158.8) = .114

Frequency Proportion Percentage

White Drivers 140.7 0.886 89%

Black Drivers 18.1 0.114 11%

Total B & W Drivers 158.8

Answer: 89% of Black and White drivers are White.

4. What percent of White eligible drivers are White drivers?

N = 157.3, K = 2

White drivers/ white eligible drivers = (140.7 / 157.3) = .894

White no drive / White eligible drivers = (16.6 / 157.3) = .105

Frequency Proportion Percentage

White drive 140.7 0.894 89%

White No drive 16.6 0.106 11%

Total White age 16 157.3

Answer: 89% of White eligible drivers are White drivers.

5. What percent of Black eligible drivers are Black drivers?

N = 24.5, K = 2

Black drivers/ Black eligible drivers = (18.1 / 24.5) = .739

Black no drive / Black eligible drivers = (6.4 / 24.5) = .261

Frequency Proportion Percentage

Black drivers 18.1 0.739 74%

Black No drive 6.4 0.261 26%

Total Black age 16 24.5

Answer: 74% of Black eligible drivers are Black drivers.

6. What percent of total stopped were Black?

N = 19.3, K = 2

stopped Black / total stopped (2.2 / 19.3) = 11%

Frequency Proportion Percentage

Stopped Black 2.2 0.114 11%

Stopped not Black 17.1 0.886 89%

Total Stopped 19.3

Answer: 11% of total stopped were Black.

7. What percent of total stopped were White?

N = 19.3, K = 2

Stopped White / total stopped = (14.9 / 19.3) = 77%

Frequency Proportion Percentage

Stopped White 14.9 0.772 77%

Stopped not White 4.4 0.228 23%

Total Stopped 19.3

Answer: 77% of total stopped were White.

8. What percent of Black drivers were stopped?

N = 18.1, K = 2

Stopped Black / Black Drivers = (2.2 / 18.1) = 12%

Frequency Proportion Percentage

Stopped Black 2.2 0.122 12%

Black Not Stopped 15.9 0.878 88%

Total Black Drivers 18.1

Answer: 12% of Black drivers were stopped.

9. What percent of White drivers were stopped?

N = 140.7, K = 2

Stopped White / White Drivers = (14.9 / 140.7) = 12%

Frequency Proportion Percentage

Stopped White 14.9 0.106 11%

White Not Stopped 125.8 0.894 89%

Total Black Drivers 140.7

Answer: 11% of White drivers were stopped.

Problem C

A section of state highway was staked out by the Alabama Highway Patrol; they randomly stopped 4060 vehicles during a one month period (1695 Trucks, and 2365 Cars). Of the Car drivers there were 1896 males and 469 females. There were 360 drivers who tested legally intoxicated (African American = 40, Caucasian = 320). The intoxicated drivers numbered 331 Males and 29 Females. The Highway Patrol intends to use that sample to estimate vehicle use for taxation purposes, and how serious the DUI problem is, to include who is driving intoxicated. Create a univariate frequency distribution for each question:

1. What is the probability of any given vehicle selected at random being a Truck?

2. What is the probability of a car selected at random being driven by a Male?

3. What is the probability you would randomly select a car driven by a female out of the total population of all vehicles?

4. What is the probability of any given vehicle selected at random being operated by a driver who was legally intoxicated?

5. What is the probability of any given intoxicated driver selected at random being African American?

6. What is the probability of randomly selecting an Intoxicated Female out of the total population of all drivers?

Problem C Answers

1. What is the probability of any given vehicle selected at random being a Truck?

Univariate Distribution table: Cars and Trucks out of all vehicles

Frequency Proportion Percent

Car 2365 .583 58%

Truck 1695 .417 42%

Total 4060

The probability of randomly selecting a Truck is 42%.

2. What is the probability of a car selected at random being driven by a Male?

Univariate Distribution table: Males and Females out of Car Drivers

Frequency Proportion Percent

Male 1896 .802 80%

Female 469 .198 20%

Total 2365

The probability of randomly selecting a car driven by a Male is 80%.

3. What is the probability you would randomly select a car driven by a female out of the total population of all vehicles?

Univariate Distribution table: Female Car drivers out of all Drivers

Frequency Proportion Percent

All Others 3591 .884 88%

Female Car 469 .116 12%

Total 4060

The probability of randomly selecting a car driven by a Female is 12%.

4. What is the probability of any given vehicle selected at random being operated by a driver who was legally intoxicated?

Univariate Distribution table: Intoxicated drivers out of all drivers

Frequency Proportion Percent

Driver Not Intoxicated 3700 .911 91%

Driver Intoxicated 360 .089 9%

Total 4060

The probability of any given vehicle selected at random being operated by a driver who was legally intoxicated is 9%

5. What is the probability of any given intoxicated driver selected at random being African American?

Univariate Distribution table: Caucasians and African Americans out of all Intoxicated Drivers

Freq Prop Percent

Caucasian Intoxicated 320 .889 89%

African American Intoxicated 40 .111 11%

Total 360

The probability of randomly selecting an African American out of all intoxicated drivers is 11%.

6. What is the probability of randomly selecting an Intoxicated Female out of the total population of all drivers?

Univariate Distribution table: Intoxicated Female drivers out of the total population

Frequency Proportion Percent

All other drivers 4031 .993 99%

Female Intoxicated 29 .007 1%

Total 4060

6. The probability of randomly selecting an Intoxicated Female out of the total population of drivers is 1%