Question

central high wants to estimate the number of students who drive to school. answer the following. (a) which of the following surveys probably would best represent the entire student population? 50 students are randomly selected from the 10th grade; 9 drive to school. 50 students are randomly selected from the school; 11 drive to school. 50 students are randomly selected from the glee club; 14 drive to school. (b) there are 1250 students at central high. using your answer from part (a), estimate the number of students who drive to school. students

Explanation:

Step1: Determine the best survey

A good sample should be randomly selected from the entire population (the whole school). Selecting from only 10th - grade (restricted grade) or glee - club (restricted group) is a biased sample. Selecting 50 students randomly from the school is the best representative.

Step2: Set up the proportion

Let \(x\) be the number of students who drive to school out of 1250 students.
We know that the proportion of students who drive in the sample is \(\frac{11}{50}\). For the population of \(N = 1250\) students, we set up the proportion \(\frac{x}{1250}=\frac{11}{50}\)

Step3: Solve the proportion

Cross - multiply: \(50x=11\times1250\)
\(50x = 13750\)
Divide both sides by 50: \(x=\frac{13750}{50}=275\)

Answer:

(a) \(50\) students are randomly selected from the school; \(11\) drive to school.
(b) \(275\) students