Question

jorge asked each of the 24 students in his class if they play a musical instrument. he also asked each student if they play a sport. he gathered the following results: . 6 students play both a musical instrument and a sport. . 3 students play neither a musical instrument nor a sport. . 14 students in total play a sport. can you help jorge organize the results into a two - way frequency table? plays a sport does not play a sport plays a musical instrument does not play a musical instrument

Explanation:

Step1: Find number of students who play a sport but not an instrument

We know 14 students play a sport and 6 play both. So number of students who play a sport but not an instrument is \(14 - 6=8\).

Step2: Find number of students who do not play a sport

Total students are 24 and 3 play neither. So number of students who play something is \(24 - 3 = 21\). Since 14 play a sport, number of students who do not play a sport is \(21-14 = 7\).

Step3: Find number of students who play an instrument but not a sport

We know 6 play both and total students who play something is 21. So number of students who play an instrument but not a sport is \(21-(8 + 6)=7\).

Step4: Find number of students who do not play an instrument and do not play a sport

Given as 3.

Step5: Find number of students who do not play an instrument and play a sport

We found it in Step1 as 8.

Answer:

	Plays a sport	Does not play a sport
Does not play a musical instrument	8	3