Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The sixth grade class went to a Family Fun Center. Out of the 154 students, 85 played laser tag. A total of 80 students roller skated and 39 of those played laser tag.

Fill in the missing joint frequency values in the table. Answers should be rounded to the nearest whole number percent.


Laser Tag No Laser Tag Total
Roller Skate 25%
27
% 52%
No Roller Skate 30%
%
%
Total
% 45% 100%

Answer 1

To fill in the joint frequency values in the table, we need to use the given information about the number of students who participated in laser tag and roller skating.

Given values:
- Total students = 154
- Students who played laser tag = 85
- Students who roller skated = 80
- Students who roller skated and played laser tag = 39

From this information, we can calculate the values for the table.

1. **Roller Skate and Laser Tag (R ∩ L)**: 39 (given)
2. **Roller Skate and No Laser Tag (R ∩ NL)**:
- Total roller skaters = 80
- Roller skaters who played laser tag = 39
- Therefore, No Laser Tag = 80 - 39 = 41
3. **No Roller Skate and Laser Tag (NR ∩ L)**:
- Total laser tag players = 85
- Students who played laser tag and roller skated = 39
- Therefore, No Roller Skate and Laser Tag = 85 - 39 = 46
4. **No Roller Skate and No Laser Tag (NR ∩ NL)**:
- Total students = 154
- Total who roller skated = 80
- Therefore, No Roller Skate = 154 - 80 = 74
- From those who did not roller skate, we know 46 played laser tag.
- So No Roller Skate and No Laser Tag = 74 - 46 = 28

Now we can fill in the joint frequency table:

| | Laser Tag | No Laser Tag | Total |
|-------------------|-----------|--------------|-------|
| Roller Skate | 39 | 41 | 80 |
| No Roller Skate | 46 | 28 | 74 |
| Total | 85 | 69 | 154 |

Next, we need to calculate the percentages:

- **For Roller Skate and Laser Tag**:
- 39 / 154 = 0.2532 (rounded to 25%)
- **For Roller Skate and No Laser Tag**:
- 41 / 154 = 0.2662 (rounded to 27%)
- **For No Roller Skate and Laser Tag**:
- 46 / 154 = 0.2987 (rounded to 30%)
- **For No Roller Skate and No Laser Tag**:
- 28 / 154 = 0.1818 (rounded to 18%)

Finally, we can fill in all the percentage values together:

| | Laser Tag | No Laser Tag | Total |
|-------------------|-----------|--------------|-------|
| Roller Skate | 25% | 27% | 52% |
| No Roller Skate | 30% | 18% | 48% |
| Total | 55% | 45% | 100% |

Here are the completed values you requested:
- Roller Skate and No Laser Tag: 27%
- No Roller Skate and No Laser Tag: 18%
- No Roller Skate and Total: 48%

Now the table is completed.