Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Question

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%

Answer 1

To fill in the joint frequency values in the table, we can start by organizing the data we have:

1. Total students = 154
2. Students who played laser tag = 85
3. Students who roller skated = 80
4. Students who roller skated and played laser tag = 39

Now, let's denote the relevant values in the table:

Total number of students who roller skated and did not play laser tag:

• Roller skate (total) = 80
• Played laser tag while roller skating = 39
• Thus, roller skate and no laser tag = 80 - 39 = 41

Total number of students who did not roller skate:

• Total students = 154
• Students who roller skated = 80
• Thus, no roller skate = 154 - 80 = 74

Students who did not roller skate but played laser tag:

• Total laser tag players = 85
• Students who played laser tag while roller skating = 39
• Thus, no roller skate and played laser tag = 85 - 39 = 46

Students who neither roller skated nor played laser tag:

• Not roller skating & not playing laser tag = Total students - (Students who roller skated + Students who played laser tag - Students who did both)
• That is: 154 - (80 + 85 - 39)
• So, 154 - 126 = 28

Now, let's summarize this information 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 |

Now, let's calculate the percentages for each cell based on the number of students:

• Roller Skate & Laser Tag: \( \frac{39}{154} \) × 100 = 25%
• Roller Skate & No Laser Tag: \( \frac{41}{154} \) × 100 = 27%
• No Roller Skate & Laser Tag: \( \frac{46}{154} \) × 100 = 30%
• No Roller Skate & No Laser Tag: \( \frac{28}{154} \) × 100 = 18%
• Total: Roller Skate = \( \frac{80}{154} \) × 100 = 52%
• Total: No Roller Skate = \( \frac{74}{154} \) × 100 = 48%

Now, we can complete the percentage values in the table:

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

So, the answers in boxes are:

• Roller Skate & No Laser Tag: 27%
• No Roller Skate & No Laser Tag: 18%
• Total for Laser Tag in the last row: 55%

Final percentages filled:

| | Laser Tag | No Laser Tag | Total | |-------------------|-----------|--------------|-------| | Roller Skate | 25% | 41% | 52% | | No Roller Skate | 30% | 18% | 48% | | Total | 55% | 45% | 100% |