East High wants to estimate the number of seniors who plan to go to a 4 -year college. Answer the following. \( \begin{array}{l}\text { (a) Which of the following surveys probably would best represent the entire population of } \\ \text { seniors? } \\ 20 \text { student council members are randomly selected; } 13 \text { plan to go to a } 4 \text {-year } \\ \text { college. } \\ \text { 20 seniors are randomly selected; } 15 \text { plan to go to a } 4 \text {-year college. } \\ 20 \text { honor roll students are randomly selected from the senior class; } 17 \text { plan to go to } \\ \text { a 4-year college. }\end{array} \begin{array}{l}\text { (b) There are } 700 \text { seniors at East High. } \\ \text { Using your answer from part (a), estimate the number of seniors who plan to go to a } \\ \text { 4-year college. } \\ \text { seniors }\end{array} \)
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The survey that best represents the entire population of seniors is the one where 20 seniors are randomly selected with 15 planning to attend a 4-year college. This is because it includes a random sample of the general senior population rather than a specific subgroup, like student council members or honor roll students, who may not reflect the overall interests of all seniors. To estimate the number of seniors at East High planning to go to a 4-year college, use the proportion from part (a). If out of 20 sampled seniors, 15 plan to attend, that makes the proportion 15/20 or 0.75. Therefore, if there are 700 seniors, you can estimate that approximately 700 x 0.75 = 525 seniors are likely to attend a 4-year college.
