题干

某中学有员工160人,其中中高级教师48人,一般教师64人,管理人员16人,行政人员32人,从中抽取容量为20的一个样本.以此例说明,无论使用三种常用的抽样方法中的哪一种方法,总体中的每个个体抽到的概率都相同.
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答案(点此获取答案解析)

解:①(简单随机抽样)可采用抽签法,

将160人从1到160编号,然后从中抽取20个签,

与签号相同的20个人被选出.显然每个个体抽到的概率为 .

②(系统抽样法)将160人从1到160编号,

按编号顺序分成20组,每组8人,

先在第一组中用抽签法抽出k号(1≤k≤8),

其余组的k+8n(n=1,2,3,19)也被抽到,

显然每个个体抽到的概率为 .

③(分层抽样法)四类人员的人数比为3:4:1:2,

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    Travelling around the world with children is difficult enough, while attempting it without using motorized transport is even more of challenge.Even so, Dario Schworer a 42-year-old climatologist and mountain guide, and his 33-year-old wife Sabine are on a journey to do just that.

    The Swiss couple want to travel across the world's oceans and climb the highest mountain on every continent to promote Earth-friendly ways of life.

    "We are collecting good examples of dealing with climate change and living in harmony with nature and we want to spread such ideas." Schworer said."We want to help people affected by global warming and to inspire children for the future."

    Recently after having spent three months teaching children in the Everest region, the couple want to show it is possible to travel through the world's climate zones using just human-power and forces of nature.

    In the 47 countries they have visited they have collected 22 tons of trash, taught people in Ecuador how the sun's rays can be used to clean water and inspired a person in Chile to build a house on water with recycled plastic bottles as a foundation.They have also collected trash in the mountains of Nepal with school children.

    So far they have communicated with 45,000 children from South America, Australia and Asia, giving presentations about the importance of recycling and using alternative energy like solar and wind power.

    When they began their adventure in 2003 they had no children of their own.But since then two has become five: daughter Sabine is now five years old, Andri was born in Chile and baby Neo was born in Australia.

    Initially the couple thought they would complete their travels in four years, but now, they believe it could take seven more.

    "Since our belief is the need to respect nature, we travel only when conditions are good," Schworer said.