Question

1. two - thirds of the members of a high school track team are female. there are 60 athletes on the track team and 40% of them are sprinters. of the sprinters, only 10 of them are female, and the rest of the female athletes compete in long - distance distance races. complete the table below to represent the information about the high school track team. then determine the conditional relative frequency for each row.

Explanation:

Step1: Calculate total number of sprinters

There are 60 athletes and 40% are sprinters. So the number of sprinters is $60\times0.4 = 24$.

Step2: Calculate number of long - distance athletes

Number of long - distance athletes is $60 - 24=36$.

Step3: Calculate number of female athletes

Two - thirds of 60 athletes are female, so $60\times\frac{2}{3}=40$ female athletes.

Step4: Calculate number of male athletes

Number of male athletes is $60 - 40 = 20$.

Step5: Calculate number of male sprinters

There are 24 sprinters and 10 are female, so number of male sprinters is $24 - 10=14$.

Step6: Calculate number of female long - distance athletes

There are 40 female athletes and 10 are sprinters, so number of female long - distance athletes is $40 - 10 = 30$.

Step7: Calculate number of male long - distance athletes

There are 20 male athletes and 14 are sprinters, so number of male long - distance athletes is $20 - 14 = 6$.

Step8: Calculate conditional relative frequencies

For sprinters row:

• Proportion of female sprinters: $\frac{10}{24}\approx0.417$
• Proportion of male sprinters: $\frac{14}{24}\approx0.583$

For long - distance row:

• Proportion of female long - distance athletes: $\frac{30}{36}\approx0.833$
• Proportion of male long - distance athletes: $\frac{6}{36}\approx0.167$

The completed table:

	Sprinter	Long - Distance	Total
Male	14	6	20
Total	24	36	60

Answer:

The completed table is shown above with conditional relative frequencies calculated as described in Step 8.