One hundred students were surveyed and asked if they participate in band and if they play a sport. The table below summarizes their responses.

Question

Plays a Sport
Does Not Play a
Participates in
Band
24
22
Does not participate in
46
8

Band
Of students that do NOT play a sport, what is the relative frequency of those who participate in band?

Answer 1

To calculate the relative frequency of students who participate in band and do not play a sport, you first need to find the number of students who do not play a sport and participate in band.

From the table:

• Students who do not play a sport and participate in band: 22
• Students who do not play a sport and do not participate in band: 8

The total number of students who do not play a sport is: $$22+8=30$$

Now, the relative frequency of students who participate in band among those who do not play a sport is calculated by dividing the number of students who do participate in band by the total number of students who do not play a sport:

$$\text{Relative Frequency}=\frac{\text{Number of students who participate in band and do not play a sport}}{\text{Total number of students who do not play a sport}}=\frac{22}{30}$$

Now, simplifying the fraction:

$$\frac{22}{30}=\frac{11}{15}\approx 0.7333$$

Therefore, the relative frequency of students who participate in band and do not play a sport is $\frac{11}{15}$ or approximately $0.7333$ (73.33%).