The contingency table shows how many people wore (Y) and did not wear (N) seat belts as well as how many survived (S) and died (D) in car accidents in a recent year. Wore seat belt Survived (S) Yes (Y) 370,313 No (N) 175,079 Total 545,392 Complete parts a through d below. S D a. What is the sample space for a randomly selected individual involved in an auto accident? Use a tree diagram to illustrate the possible outcomes. OA. O C. S D S D Died (D) 766 1314 2080 Sample space: {SS, SD, DS, DD} B. Y N S D S b. Using the data in the table, estimate (i) P(D), (ii) P(N). (i) P(D) 0.0038 (Round to four decimal places as needed.) D Sample space: {YS, YD, NS, ND} Total 371,079 176,393 547,472 *** (ii) P(N) 0.3222 (Round to four decimal places as needed.) c. Estimate the probability that an individual did not wear a seat belt and died. P(N and D) (Round to four decimal places as needed.) Y N S S D D Sample space: {YS, YS, ND, ND} OD. N Sample space: (YY,YN, NY,NN}
The contingency table shows how many people wore (Y) and did not wear (N) seat belts as well as how many survived (S) and died (D) in car accidents in a recent year. Wore seat belt Survived (S) Yes (Y) 370,313 No (N) 175,079 Total 545,392 Complete parts a through d below. S D a. What is the sample space for a randomly selected individual involved in an auto accident? Use a tree diagram to illustrate the possible outcomes. OA. O C. S D S D Died (D) 766 1314 2080 Sample space: {SS, SD, DS, DD} B. Y N S D S b. Using the data in the table, estimate (i) P(D), (ii) P(N). (i) P(D) 0.0038 (Round to four decimal places as needed.) D Sample space: {YS, YD, NS, ND} Total 371,079 176,393 547,472 *** (ii) P(N) 0.3222 (Round to four decimal places as needed.) c. Estimate the probability that an individual did not wear a seat belt and died. P(N and D) (Round to four decimal places as needed.) Y N S S D D Sample space: {YS, YS, ND, ND} OD. N Sample space: (YY,YN, NY,NN}
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
5.
![**Educational Resource: Seat Belt Use and Auto Accident Outcomes**
The contingency table illustrates the relationship between seat belt use (Yes "Y" or No "N") and survival outcomes (Survived "S" or Died "D") in auto accidents over a given year. It presents the following data:
- **Wore Seat Belt (Yes):**
- Survived (S): 370,313
- Died (D): 766
- Total: 371,079
- **Did Not Wear Seat Belt (No):**
- Survived (S): 175,079
- Died (D): 1,314
- Total: 176,393
Overall Total:
- Survived (S): 545,392
- Died (D): 2,080
- Grand Total: 547,472
**Tasks to Complete:**
**a. Sample Space for a Randomly Selected Individual:**
Choose the appropriate tree diagram to illustrate the possible outcomes for an individual in an auto accident.
Correct choice:
- **Diagram B:**
- Nodes & Sample space: (YS, YD, NS, ND)
**b. Probability Estimates:**
Using the table data, estimate:
(i) P(D) (Probability of Death): ≈ 0.0038 (rounded to four decimal places).
(ii) P(N) (Probability of Not Wearing a Seat Belt): ≈ 0.3222 (rounded to four decimal places).
**c. Probability of Not Wearing a Seat Belt and Dying:**
Estimate the probability using the data provided.
\[ \text{P(N and D)} \approx \, \text{(Round answer to four decimal places as needed.)} \]
**Visual Explanation:**
- Diagram B shows a tree structure with two branches: "Y" for wearing a seat belt and "N" for not wearing one, each branching further into "S" for survived and "D" for died, capturing all possible outcomes in the sample space: (YS, YD, NS, ND).
**Conclusion:**
This analysis uses set theory and probability principles to derive insights into seat belt usage's effect on survival outcomes in auto accidents.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf10b40a-fae6-4e8b-9b89-0711a68556bc%2F07bf1083-fa39-4310-9b3c-06fde8884270%2Fx6f1v7l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Resource: Seat Belt Use and Auto Accident Outcomes**
The contingency table illustrates the relationship between seat belt use (Yes "Y" or No "N") and survival outcomes (Survived "S" or Died "D") in auto accidents over a given year. It presents the following data:
- **Wore Seat Belt (Yes):**
- Survived (S): 370,313
- Died (D): 766
- Total: 371,079
- **Did Not Wear Seat Belt (No):**
- Survived (S): 175,079
- Died (D): 1,314
- Total: 176,393
Overall Total:
- Survived (S): 545,392
- Died (D): 2,080
- Grand Total: 547,472
**Tasks to Complete:**
**a. Sample Space for a Randomly Selected Individual:**
Choose the appropriate tree diagram to illustrate the possible outcomes for an individual in an auto accident.
Correct choice:
- **Diagram B:**
- Nodes & Sample space: (YS, YD, NS, ND)
**b. Probability Estimates:**
Using the table data, estimate:
(i) P(D) (Probability of Death): ≈ 0.0038 (rounded to four decimal places).
(ii) P(N) (Probability of Not Wearing a Seat Belt): ≈ 0.3222 (rounded to four decimal places).
**c. Probability of Not Wearing a Seat Belt and Dying:**
Estimate the probability using the data provided.
\[ \text{P(N and D)} \approx \, \text{(Round answer to four decimal places as needed.)} \]
**Visual Explanation:**
- Diagram B shows a tree structure with two branches: "Y" for wearing a seat belt and "N" for not wearing one, each branching further into "S" for survived and "D" for died, capturing all possible outcomes in the sample space: (YS, YD, NS, ND).
**Conclusion:**
This analysis uses set theory and probability principles to derive insights into seat belt usage's effect on survival outcomes in auto accidents.
Expert Solution
Step 1
| Wore seat belt | survived | Died | Total |
| Yes (Y) | 370,313 | 766 | 371,079 |
| No (N) | 175,079 | 1314 | 176,393 |
| Total | 545,392 | 2080 | 547,472 |
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman