Question

in a study, 1,085 out of 2,321 people did not receive a flu vaccination. 465 people were vaccinated and tested positive for the flu. a total of 1,371 participants tested negative. create a two - way table for this scenario.
incorrect. some tiles were in the wrong place.

Explanation:

Step1: Find total vaccinated

We know total people is 2321, and not vaccinated is 1085. So vaccinated = 2321 - 1085 = 1236.

Step2: Find negative for vaccinated

Vaccinated total is 1236, positive is 465. So negative vaccinated = 1236 - 465 = 771.

Step3: Find total positive

Positive vaccinated is 465, positive not vaccinated: total positive is 1371 (since 2321 - 950 = 1371? Wait, no, total negative is 950? Wait, total negative is 950? Wait, total people 2321, total positive 1371, so total negative 2321 - 1371 = 950. Then not vaccinated positive: total positive 1371 - 465 = 906? Wait, no, let's re - organize.

Wait, the two - way table has rows: Positive, Negative, Total; columns: Vaccinated, Not Vaccinated, Total.

We know:

- Total people: 2321 (bottom right total)
- Not vaccinated total: 1085 (so vaccinated total = 2321 - 1085 = 1236)
- Total positive: 1371 (so total negative = 2321 - 1371 = 950)
- Vaccinated positive: 465 (so vaccinated negative = 1236 - 465 = 771)
- Not vaccinated positive: 1371 - 465 = 906? Wait, no, wait the given numbers: 1085, 771, 1236, 950, 1371, 485, 600. Wait, maybe I misread.

Wait, the problem says: 1085 not vaccinated, 465 vaccinated positive, total negative 950, total positive 1371, total people 2321.

So:

- Vaccinated column:
- Positive: 465
- Negative: 771 (since 465 + 771 = 1236, which is vaccinated total: 2321 - 1085 = 1236)
- Not vaccinated column:
- Total: 1085
- Positive: 1371 - 465 = 906? No, wait the given numbers have 600? Wait, maybe the total positive is 1371, total negative is 950.

Not vaccinated negative: total negative (950) - vaccinated negative (771) = 179? No, this is confusing. Wait, let's use the given numbers.

Wait, the tiles are: 1085, 771, 1236, 950, 1371, 485, 600.

Let's build the table:

| | Vaccinated | Not Vaccinated | Total |
|----------|------------|----------------|-------|
| Positive | 465 |? | 1371 |
| Negative |? |? | 950 |
| Total |? | 1085 | 2321 |

First, vaccinated total: 2321 - 1085 = 1236. So vaccinated total (bottom of vaccinated column) is 1236.

Vaccinated negative: 1236 - 465 = 771. So vaccinated negative is 771.

Total negative is 950, so not vaccinated negative: 950 - 771 = 179? No, but 179 is not in the tiles. Wait, maybe total positive is 1371, so not vaccinated positive: 1371 - 465 = 906? No. Wait, the tiles include 600, 485. Wait, maybe I made a mistake.

Wait, let's start over:

1. Total people: 2321 (given in the table's total row, total column)
2. Not vaccinated total: 1085 (so vaccinated total = 2321 - 1085 = 1236)
3. Total positive: 1371 (so total negative = 2321 - 1371 = 950)
4. Vaccinated positive: 465 (so vaccinated negative = 1236 - 465 = 771)
5. Not vaccinated positive: 1371 - 465 = 906? No, 906 is not a tile. Wait, the tiles are 1085, 771, 1236, 950, 1371, 485, 600.

Wait, maybe the total negative is 950, so not vaccinated negative = 950 - 771 = 179 (not a tile). So maybe my initial approach is wrong.

Wait, the problem says "a total of 1,371 participants tested negative" – no, wait the original text: "A total of 1,371 participants tested negative" – no, wait the original text: "In a study, 1,085 out of 2,321 people did not receive a flu vaccination. 465 people were vaccinated and tested positive for the flu. A total of 1,371 participants tested negative. Create a two - way table for this scenario."

Ah! I misread. Total negative is 1371? Wait, no: "A total of 1,371 participants tested negative" – so total negative = 1371, then total positive = 2321 - 1371 = 950.

That's the mistake! So:

- Total people: 2321
- Not vaccinated: 1085, so vaccinated = 2321 - 1085 = 1236
- Total negative: 1371, so total positive = 2321 - 1371 = 950
- Vaccinated positive: 465, so vaccinated negative = 1236 - 465 = 771
- Not vaccinated negative: 1371 - 771 = 600
- Not vaccinated positive: 950 - 465 = 485
- Let's check:

Vaccinated column: positive 465, negative 771, total 465 + 771 = 1236 (correct)

Not vaccinated column: positive 485, negative 600, total 485+600 = 1085 (correct)

Positive row: 465 + 485 = 950 (correct)

Negative row: 771+600 = 1371 (correct)

Total row: 1236 + 1085 = 2321 (correct)

So the two - way table is:

| | Vaccinated | Not Vaccinated | Total |
|----------|------------|----------------|-------|
| Positive | 465 | 485 | 950 |
| Negative | 771 | 600 | 1371 |
| Total | 1236 | 1085 | 2321 |

Answer:

The two - way table is:

	Vaccinated	Not Vaccinated	Total
Negative	771	600	1371
Total	1236	1085	2321