Question
Half of the students at Garden Grove Middle School ride the bus to school. Use the random number
table below to conduct a simulation. In the table, an even digit (including 0) represents a student who
rides the bus, and an odd digit represents a student who does not ride the bus.
Random Numbers
231749 629344 382307 783250 813254
472305 828489 184387 576495 954218
312893 429784 419054 245397 285133
967543 728934 821340 912865 327540
Part A
Look at the top left cell in the table. The digits in the cell represent 6 randomly selected students.
Describe what these digits show about students who ride the bus in this group. Show your work or
explain your answer.
Enter your answer and your work or explanation in the box provided.
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33.33
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Assessment 2
64
Part B
Repeat the simulation for all 20 cells. What is the probability that at least 4 out of 6 randomly selected
students ride the bus to school? Show your work or explain your answer.
Enter your answer and your work or explanation in the box provided.
Part C
Now count the number of cells in which fewer than 3 students ride the bus to school.
Describe the results.
Enter your answer in the box provided.
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Assessment 2
65
GO ON
Part D
Based on the simulation, what is the probability that fewer than 3 out of 6 randomly selected students
ride the bus to school? Show your work or explain your answer.
Enter your answer and your work or explanation in the box provided.
table below to conduct a simulation. In the table, an even digit (including 0) represents a student who
rides the bus, and an odd digit represents a student who does not ride the bus.
Random Numbers
231749 629344 382307 783250 813254
472305 828489 184387 576495 954218
312893 429784 419054 245397 285133
967543 728934 821340 912865 327540
Part A
Look at the top left cell in the table. The digits in the cell represent 6 randomly selected students.
Describe what these digits show about students who ride the bus in this group. Show your work or
explain your answer.
Enter your answer and your work or explanation in the box provided.
Downloaded by S. FARSAKH at SOUTHEAST MIDDLE SCHOOL. This resource expires on 6/30/2025.
33.33
©Curriculum Associates, LLC Copying is not permitted.
Assessment 2
64
Part B
Repeat the simulation for all 20 cells. What is the probability that at least 4 out of 6 randomly selected
students ride the bus to school? Show your work or explain your answer.
Enter your answer and your work or explanation in the box provided.
Part C
Now count the number of cells in which fewer than 3 students ride the bus to school.
Describe the results.
Enter your answer in the box provided.
Downloaded by S. FARSAKH at SOUTHEAST MIDDLE SCHOOL. This resource expires on 6/30/2025.
0.35
25
©Curriculum Associates, LLC Copying is not permitted.
Assessment 2
65
GO ON
Part D
Based on the simulation, what is the probability that fewer than 3 out of 6 randomly selected students
ride the bus to school? Show your work or explain your answer.
Enter your answer and your work or explanation in the box provided.
Answers
GPT-4o mini
To conduct a simulation based on the provided random number table, we will analyze the results from the digits in the cells one by one. We’ll consider even digits (0, 2, 4, 6, 8) as students who ride the bus and odd digits (1, 3, 5, 7, 9) as students who do not ride the bus.
### Part A
**Analyzing the first cell (231749):**
- The digits are: 2, 3, 1, 7, 4, 9.
- Even digits (bus riders): 2, 4 (2 students ride the bus).
- Odd digits (non-riders): 3, 1, 7, 9 (4 students do not ride the bus).
**Summary of the first cell:**
- Out of 6 students, 2 ride the bus (33.33%).
- Therefore, in this group of 6 students, approximately 33.33% ride the bus.
### Part B
**Simulating for all 20 cells and tallying results:**
1. 231749: 2 ride (even)
2. 629344: 4 ride (even)
3. 382307: 3 ride (even)
4. 783250: 4 ride (even)
5. 813254: 4 ride (even)
6. 472305: 3 ride (even)
7. 828489: 4 ride (even)
8. 184387: 3 ride (even)
9. 576495: 3 ride (even)
10. 954218: 4 ride (even)
11. 312893: 3 ride (even)
12. 429784: 4 ride (even)
13. 419054: 3 ride (even)
14. 245397: 3 ride (even)
15. 285133: 3 ride (even)
16. 967543: 2 ride (even)
17. 728934: 4 ride (even)
18. 821340: 4 ride (even)
19. 912865: 3 ride (even)
20. 327540: 4 ride (even)
**Tallying the number of cells with at least 4 students riding the bus:**
- 4 or more bus riders: Cells 2, 4, 5, 7, 8, 10, 12, 14, 16, 17, 18, 20 (12 cells).
**Probability that at least 4 out of 6 students ride the bus:**
- Total occurrences = 20 cells; Successes (4 or more riders) = 12.
- Probability = 12/20 = 0.6 or 60%.
### Part C
**Count the number of cells in which fewer than 3 students ride the bus:**
- Fewer than 3 riders: Cells 1 (2 riders), 6 (2 ride), 11 (3 ride), 13 (2 ride) (4 cells total).
**Results:**
- There are 4 occurrences in which fewer than 3 students ride the bus out of 20 simulated cells.
### Part D
**Probability that fewer than 3 out of 6 students ride the bus:**
- Total occurrences = 20 cells; Successes (fewer than 3 riders) = 4.
- Probability = 4/20 = 0.2 or 20%.
### Summary of Answers:
- **Part A:** Approximately 33.33% of students ride the bus in the first cell.
- **Part B:** The probability that at least 4 out of 6 students ride the bus is 60%.
- **Part C:** There are 4 cells where fewer than 3 students ride the bus.
- **Part D:** The probability that fewer than 3 out of 6 students ride the bus is 20%.
### Part A
**Analyzing the first cell (231749):**
- The digits are: 2, 3, 1, 7, 4, 9.
- Even digits (bus riders): 2, 4 (2 students ride the bus).
- Odd digits (non-riders): 3, 1, 7, 9 (4 students do not ride the bus).
**Summary of the first cell:**
- Out of 6 students, 2 ride the bus (33.33%).
- Therefore, in this group of 6 students, approximately 33.33% ride the bus.
### Part B
**Simulating for all 20 cells and tallying results:**
1. 231749: 2 ride (even)
2. 629344: 4 ride (even)
3. 382307: 3 ride (even)
4. 783250: 4 ride (even)
5. 813254: 4 ride (even)
6. 472305: 3 ride (even)
7. 828489: 4 ride (even)
8. 184387: 3 ride (even)
9. 576495: 3 ride (even)
10. 954218: 4 ride (even)
11. 312893: 3 ride (even)
12. 429784: 4 ride (even)
13. 419054: 3 ride (even)
14. 245397: 3 ride (even)
15. 285133: 3 ride (even)
16. 967543: 2 ride (even)
17. 728934: 4 ride (even)
18. 821340: 4 ride (even)
19. 912865: 3 ride (even)
20. 327540: 4 ride (even)
**Tallying the number of cells with at least 4 students riding the bus:**
- 4 or more bus riders: Cells 2, 4, 5, 7, 8, 10, 12, 14, 16, 17, 18, 20 (12 cells).
**Probability that at least 4 out of 6 students ride the bus:**
- Total occurrences = 20 cells; Successes (4 or more riders) = 12.
- Probability = 12/20 = 0.6 or 60%.
### Part C
**Count the number of cells in which fewer than 3 students ride the bus:**
- Fewer than 3 riders: Cells 1 (2 riders), 6 (2 ride), 11 (3 ride), 13 (2 ride) (4 cells total).
**Results:**
- There are 4 occurrences in which fewer than 3 students ride the bus out of 20 simulated cells.
### Part D
**Probability that fewer than 3 out of 6 students ride the bus:**
- Total occurrences = 20 cells; Successes (fewer than 3 riders) = 4.
- Probability = 4/20 = 0.2 or 20%.
### Summary of Answers:
- **Part A:** Approximately 33.33% of students ride the bus in the first cell.
- **Part B:** The probability that at least 4 out of 6 students ride the bus is 60%.
- **Part C:** There are 4 cells where fewer than 3 students ride the bus.
- **Part D:** The probability that fewer than 3 out of 6 students ride the bus is 20%.