Question

mariana collects data on players at a high school football camp. she chooses three random samples of players, each containing 25 players. the table shows her data. based on the data, complete the estimation about the population. about 20% of the players at the football camp are 10th graders. there are 75 players at the camp. which is the best estimate of the number of 10th graders at the camp? 5 10 15 25

Explanation:

Step1: Calculate the total number of 10th - graders in the samples

The number of 10th - graders in Sample 1 is 6, in Sample 2 is 4, and in Sample 3 is 5.
The total number of 10th - graders in the samples is \(6 + 4+5=15\).
The total number of players in the samples is \(25\times3 = 75\).

Step2: Use the proportion to estimate the number of 10th - graders in the population

We know that the proportion of 10th - graders in the samples is \(\frac{15}{75}=0.2\).
If the total number of players in the population (at the camp) is \(N = 75\), and let \(x\) be the number of 10th - graders in the population.
Using the formula \(x=N\times\) proportion. Substituting \(N = 75\) and proportion \(=0.2\), we get \(x=75\times0.2\).

Answer:

15