Question

A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table.

Which of the following correctly represents the given data in the problem?
A. a = 24, g = 48, h = 22, i = 80
B. a = 22, c = 80, d = 24, i = 48
C. a = 24, b = 48, c = 22, i = 48
D. a = 24, c = 48, e = 22, i = 80

Answer 1

The correct option that represents the given data in the problem is option C, a = 24, b = 48, c = 22, i = 80.

Step-by-step explanation:

The given data in the problem can be represented in a two-way table:

| | In Band | Not In Band | Total |

|Play Sport| 24 | ? | ? |

|No Sport | ? | 22 | ? |

|Total | 48 | ? | 80 |

We know that 24 students both play in the band and play a sport. And 22 students are not in the band and do not play a sport. Since the total number of students in the band is 48, the number of students who play a sport but are not in the band can be calculated by subtracting 24 from 48. This gives us 24 students. The number of students who are not in the band but play a sport can be calculated by subtracting 24 from 80. This gives us 56 students. Therefore, the table can be filled in as follows:

| | In Band | Not In Band | Total |

|Play Sport| 24 | 56 | 80 |

|No Sport | 24 | 22 | 46 |

|Total | 48 | ? | 80 |

Therefore, the correct option that represents the given data in the problem is option C, a = 24, b = 48, c = 22, i = 80.

Answer 2

a = 24, c = 48, e = 22, i = 80

Step-by-step explanation:

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