Maths Olympiad Prep

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Combinatorics Difficulty 3.0 Junior Find the answer

A certain school has 25 students with sports talent, 35 with art talent, and 40 with music talent. If a stratified sampling method is used to select a total of 40 students, then the number of students with music talent selected is ______.

A number or a short expression. Spacing and $ signs are ignored.

Solution

According to the stratified sampling method, the number of students selected from each group should be proportional to the size of the group. There are 25 sports-talented, 35 art-talented, and 40 music-talented students, making a total of 25+35+40=10025 + 35 + 40 = 100 students.

If we are to select 40 students from the total, the expected number of music-talented students selected would be:
40100×40=40100×40=410×40=16 students.\frac{40}{100} \times 40 = \frac{40}{100} \times 40 = \frac{4}{10} \times 40 = \boxed{16} \text{ students}.

By establishing a proportional relationship based on the definition of stratified sampling, we can draw conclusions. This problem mainly examines the application of stratified sampling, and establishing a proportional relationship based on the conditions provided is key to solving the problem. It is a relatively basic concept.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.