Question

Complete the two-way frequency table below, which shows the relationship between students who participate in band and drama in a particular high school. From a sample of 70 students, it is found that 29 are in band, 17 are in drama, and 9 participate in both. Band Not in Band Total Drama 9 17 Not in Drama Total 29 70 Part A: How many students are not in band or drama? Explain your answer using complete sentences. (1 point) Part B: How many students in this sample are in drama but not in band? Explain your answer using complete sentences. (1 point) Part C: If there are 350 students in the entire school, how many students can the band instructor expect to participate in the first band practice of the year? Show your work or explain your answer using complete sentences. (2 points)

Answer 1

a) 33; b) 8; c) 145

Explanation:

There were 29 students in band. This includes the 9 in both band and drama; this leaves 20 in only band.

There were 17 students in drama. This includes the 9 in both band and drama; this leaves 8 in only drama.

There were 70 students sampled; this means that

70-(20+8+9) = 70-37 = 33 students in neither band nor drama.

There were 8 in only drama.

Since there were 29/70 in band, this means the director can assume he will have

29/70(350) = 29/70(350/1) = 10150/350 = 145 to show up the first day.