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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 80 students, it is found that 19 are in band, 11 are in drama, and 9 participate in both.

 

                                   Band      Not in Band     Total

            Drama              9                                   11

            Not in Drama

            Total                 19                                 80

 

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 500 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) (4 points)

 May 3, 2023
 #1
avatar+135 
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Part A. 33

Part B. 8

Part C. 145

Step-by-step explantion:

Part A:

If 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.

 

Part B:

There were 8 in only drama.

 

Part C:

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.

 May 3, 2023
 #2
avatar+207 
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I'm not sure all of that is correct.

First, part B. If only 11 total students are in drama, and 9 of them are in band, then only 2 of them are in drama but not band.

Then, for part A, 19+11-9 students are in either drama or band, which is 21, so 80-21=59 students are in neither.

For part C, if 19/80 were in band, then change the ratio to 118.75/500 students in band.

I think that acyclics misread the question and gave answers to a different problem.

 May 3, 2023

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