Question

washington high wants to estimate the number of seniors who plan to go to a 4-year college. answer the following.
(a) which of the following surveys probably would best represent the entire population of seniors?
25 student council members are randomly selected; 16 plan to go to a 4-year college.
25 seniors are randomly selected; 17 plan to go to a 4-year college.
25 honor roll students are randomly selected from the senior class; 18 plan to go to a 4-year college.
(b) there are 350 seniors at washington high.
using your answer from part (a), estimate the number of seniors who plan to go to a 4-year college.
_____ seniors

Explanation:

Step1: Identify representative sample

A sample that randomly selects from the entire senior population is the most representative. The option "25 seniors are randomly selected; 17 plan to go to a 4-year college" targets the full senior group, not a subset like student council or honor roll.

Step2: Calculate sample proportion

Find the proportion of seniors in the sample planning to attend a 4-year college.
$\text{Proportion} = \frac{17}{25}$

Step3: Scale to total senior population

Multiply the proportion by the total number of seniors (350) to estimate the total.
$\text{Estimated number} = 350 \times \frac{17}{25}$
Simplify: $350 \div 25 = 14$, then $14 \times 17 = 238$

Answer:

(a) 25 seniors are randomly selected; 17 plan to go to a 4-year college.
(b) 238 seniors