题干

为了解今年某校高三毕业班准备报考飞行员学生的体重情况,将所得的数据整理后,画出了频率分布直方图(如图),已知图中从左到右的前3个小组的频率之比为1:2:3,其中第2小组的频数为12.

(1)求该校报考飞行员的总人数;

(2)以这所学校的样本数据来估计全省的总体数据,若从全省报考飞行员的同学中(人数很多)任选二人,设X表示体重超过60公斤的学生人数,求X的分布列和数学期望.

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答案(点此获取答案解析)

解:(1)设该校报考飞行员的人数为n,前三小组的频率分别为p1,p2,p3,则由题意可知,p2=2p1<

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Zheng He was an amazing man. He was born in 1371. Eleven years later, he was caught by the army of a rich young man called Zhu Di and made to work for him. Over time the rich man saw that Zheng He was very clever and strong and they became close friends. In 1403 Zhu Di was made the king of China and he asked Zheng He to join his government.  

  The king wanted to learn more about the world and show other countries his power. He ordered many new ships to be built and made Zheng He their leader. Between 1405 and 1433, Zheng He led seven sea trips to different parts of the world. He certainly traveled to India, Africa and the Middle East. A few people think his ships have even reached South America and Australia.  

  Each trip lasted between two and four years and it is believed he sailed more than 50, 000 kilometers during the years of his travels. Zheng He led a fleet with

28, 000 men and over 300 ships, such as boats for food, water and even soldiers’horses.  

  On these trips he brought with him many Chinese goods like silk and medicine to give to foreign kings or to sell for local goods. He returned from each trip with boats which were filled with expensive things such as gold and treasures, foreign guests and strange animals like a giraffe.  

  It is a pity that we may never learn everything about Zheng He’s travels. The Columbus of the East, Zheng He, died in 1433. After that, the new king had these trips stopped and he burned almost all the books about Zheng He’s travels, because he believed the trips were unlucky and too expensive. It is only in the last 50 years that historians have begun to carefully study the adventures of great Zheng He.