Question 5 (3 points)

A local college wants to determine student interest in athletics and in academic clubs. The college surveys a random group of students, and the results of the survey are described below.

A total of 240 students were included in the survey.
Thirty-five percent of the students were interested in athletics.
Three-fifths of the students were interested in academic clubs.
A total of 26 students were interested in both athletics and academic clubs.
Complete the two-way table below to represent the survey results by filling in each of the 9 cells with an appropriate number of students.

Interested in Athletics NOT Interested in Athletics Total
Interested in Academic Clubs 1 2 3
Not Interested in Academic Clubs 4 5 6
Total 7 8 9



Word Bank:
58 156 118 26 144 38 84 96 240

Blank 1:
Blank 2:
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Blank 9:

Athlet. | No Athlet

Acad. 26 | 118 = 144
No Acad. 58 | 38 = 96
_____________________
Totals 84 | 156 = 240

Ya Welcome!

are yoi corret

Yes, the answers I provided are correct.

how

I determined the answers by using the information provided in the problem and applying it to the appropriate cells in the two-way table. Here is the process I used:

1. From the problem statement, we know that 35% of the 240 students were interested in athletics. Therefore, there were 0.35 x 240 = 84 students who were interested in athletics.

2. We also know that 3/5 of the students were interested in academic clubs. So, there were 3/5 x 240 = 144 students who were interested in academic clubs.

3. The problem tells us that 26 students were interested in both athletics and academic clubs, so we can fill in that number in the cell where the two categories intersect.

4. To fill in the remaining cells, we can subtract the number of students already accounted for from the total number of students surveyed (240). For example, to find the number of students who are interested in athletics but not academic clubs, we can subtract the number who are interested in both from the total who are interested in athletics: 84 - 26 = 58. This number goes in the cell where "Interested in Athletics" and "Not Interested in Academic Clubs" intersect.

5. By following similar steps for the other cells, we can fill in the entire table as shown in the answer above.

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