Question
20
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%
% 52%
No Roller Skate 30%
%
%
Total
% 45% 100
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%
% 52%
No Roller Skate 30%
%
%
Total
% 45% 100
Answers
GPT-4o mini
To fill in the joint frequency values in the table, we first need to determine various quantities based on the provided data:
1. Total students: 154
2. Students who played laser tag: 85
3. Students who roller skated: 80
4. Students who both played laser tag and roller skated: 39
### Step 1: Calculate students who roller skated and did not play laser tag
This can be calculated as:
\[ \text{Roller Skated and No Laser Tag} = \text{Total Roller Skated} - \text{Played Laser Tag and Roller Skated} \]
\[ = 80 - 39 = 41 \]
### Step 2: Calculate students who didn't roller skate but played laser tag
This can be calculated as:
\[ \text{No Roller Skate and Played Laser Tag} = \text{Total Played Laser Tag} - \text{Played Laser Tag and Roller Skated} \]
\[ = 85 - 39 = 46 \]
### Step 3: Calculate students who didn't roller skate and didn't play laser tag
Total students who did not roller skate:
\[ \text{Total Not Roller Skating} = \text{Total Students} - \text{Total Roller Skated} \]
\[ = 154 - 80 = 74 \]
Out of these 74 students, we know that 46 played laser tag:
\[ \text{No Roller Skate and No Laser Tag} = \text{Total Not Roller Skating} - \text{No Roller Skate and Played Laser Tag} \]
\[ = 74 - 46 = 28 \]
### Step 4: Compile the joint frequency values
Now, let's summarize the counts we derived:
- Roller Skate and Laser Tag: 39
- Roller Skate and No Laser Tag: 41
- No Roller Skate and Laser Tag: 46
- No Roller Skate and No Laser Tag: 28
### Step 5: Fill in the table and calculate the percentages:
- **Roller Skate and Laser Tag:** 39
- **Roller Skate and No Laser Tag:** 41
- **No Roller Skate and Laser Tag:** 46
- **No Roller Skate and No Laser Tag:** 28
Now we can calculate the percentages:
Total with Roller Skate = 39 + 41 = 80
Total with No Roller Skate = 46 + 28 = 74
- **Roller Skate and Laser Tag:**
\[ \frac{39}{154} \approx 25\% \text{ (Already Provided)} \]
- **Roller Skate and No Laser Tag:**
\[ \frac{41}{154} \approx 27\% \]
- **No Roller Skate and Laser Tag:**
\[ \frac{46}{154} \approx 30\% \text{ (Already Provided)} \]
- **No Roller Skate and No Laser Tag:**
\[ \frac{28}{154} \approx 18\% \]
### Final Table with Percentages:
| | Laser Tag | No Laser Tag | Total |
|---------------------|-----------|--------------|-------|
| roller Skate | 39 (25%) | 41 (27%) | 80 |
| No Roller Skate | 46 (30%) | 28 (18%) | 74 |
| Total | 85 (55%) | 69 (45%) | 154 |
### Final Percent Values:
- Roller Skate and No Laser Tag: 27%
- No Roller Skate and No Laser Tag: 18%
- Total: 100%
Final entries for your table:
- Roller Skate and No Laser Tag: 27%
- No Roller Skate and No Laser Tag: 18%
- Total (Laser Tag): 55%
- Total (No Laser Tag): 45%
So you should fill in the table as:
- Roller Skate and No Laser Tag: 27%
- Total for No Roller Skate and No Laser Tag: 18%
I hope this helps!
1. Total students: 154
2. Students who played laser tag: 85
3. Students who roller skated: 80
4. Students who both played laser tag and roller skated: 39
### Step 1: Calculate students who roller skated and did not play laser tag
This can be calculated as:
\[ \text{Roller Skated and No Laser Tag} = \text{Total Roller Skated} - \text{Played Laser Tag and Roller Skated} \]
\[ = 80 - 39 = 41 \]
### Step 2: Calculate students who didn't roller skate but played laser tag
This can be calculated as:
\[ \text{No Roller Skate and Played Laser Tag} = \text{Total Played Laser Tag} - \text{Played Laser Tag and Roller Skated} \]
\[ = 85 - 39 = 46 \]
### Step 3: Calculate students who didn't roller skate and didn't play laser tag
Total students who did not roller skate:
\[ \text{Total Not Roller Skating} = \text{Total Students} - \text{Total Roller Skated} \]
\[ = 154 - 80 = 74 \]
Out of these 74 students, we know that 46 played laser tag:
\[ \text{No Roller Skate and No Laser Tag} = \text{Total Not Roller Skating} - \text{No Roller Skate and Played Laser Tag} \]
\[ = 74 - 46 = 28 \]
### Step 4: Compile the joint frequency values
Now, let's summarize the counts we derived:
- Roller Skate and Laser Tag: 39
- Roller Skate and No Laser Tag: 41
- No Roller Skate and Laser Tag: 46
- No Roller Skate and No Laser Tag: 28
### Step 5: Fill in the table and calculate the percentages:
- **Roller Skate and Laser Tag:** 39
- **Roller Skate and No Laser Tag:** 41
- **No Roller Skate and Laser Tag:** 46
- **No Roller Skate and No Laser Tag:** 28
Now we can calculate the percentages:
Total with Roller Skate = 39 + 41 = 80
Total with No Roller Skate = 46 + 28 = 74
- **Roller Skate and Laser Tag:**
\[ \frac{39}{154} \approx 25\% \text{ (Already Provided)} \]
- **Roller Skate and No Laser Tag:**
\[ \frac{41}{154} \approx 27\% \]
- **No Roller Skate and Laser Tag:**
\[ \frac{46}{154} \approx 30\% \text{ (Already Provided)} \]
- **No Roller Skate and No Laser Tag:**
\[ \frac{28}{154} \approx 18\% \]
### Final Table with Percentages:
| | Laser Tag | No Laser Tag | Total |
|---------------------|-----------|--------------|-------|
| roller Skate | 39 (25%) | 41 (27%) | 80 |
| No Roller Skate | 46 (30%) | 28 (18%) | 74 |
| Total | 85 (55%) | 69 (45%) | 154 |
### Final Percent Values:
- Roller Skate and No Laser Tag: 27%
- No Roller Skate and No Laser Tag: 18%
- Total: 100%
Final entries for your table:
- Roller Skate and No Laser Tag: 27%
- No Roller Skate and No Laser Tag: 18%
- Total (Laser Tag): 55%
- Total (No Laser Tag): 45%
So you should fill in the table as:
- Roller Skate and No Laser Tag: 27%
- Total for No Roller Skate and No Laser Tag: 18%
I hope this helps!