Question

northside 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 math club; 8 drive to school.
○ 50 students are randomly selected from the school; 12 drive to school.
○ 50 students are randomly selected from the 12th grade; 13 drive to school.
(b) there are 1250 students at northside high.
using your answer from part (a), estimate the number of students who drive to school.
□ students

Explanation:

Step1: Determine the best - representative survey

A good sample should be randomly selected from the entire population.

• Selecting from the math club: The math - club students may not be representative of all students (e.g., they may have different commuting habits).
• Selecting from the 12th - grade: 12th - grade students may have different driving - to - school rates than other grades (e.g., younger students may not drive).
• Selecting 50 students randomly from the school: This is a more representative sample of the entire student population.

Step2: Calculate the estimated number of students who drive

The proportion of students who drive in the sample is \(p=\frac{12}{50}\).
Let \(N = 1250\) be the total number of students.
We use the formula \(x=p\times N\).
Substitute \(p=\frac{12}{50}\) and \(N = 1250\) into the formula:

$$x=\frac{12}{50}\times1250$$

$$x = 12\times\frac{1250}{50}$$

$$x=12\times25$$

Answer:

(a) 50 students are randomly selected from the school; 12 drive to school.
(b) 300 students