题干

由于当前学生课业负担较重,造成青少年视力普遍下降,现从某高中随机抽取16名学生,经校医用对数视力表检查得到每个学生的视力状况的茎叶图(以小数点前的一位数字为茎,小数点后的一位数字为叶)如图:

(Ⅰ)指出这组数据的众数和中位数;

(Ⅱ)若视力测试结果不低丁5.0,则称为“好视力”,求校医从这16人中随机选取3人,至多有1人是“好视力”的概率;

(Ⅲ)以这16人的样本数据来估计整个学校的总体数据,若从该校(人数很多)任选3人,记ξ表示抽到“好视力”学生的人数,求ξ的分布列及数学期望.

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答案(点此获取答案解析)

解:(Ⅰ)∵4.6和4.7都出现三次,

∴众数:4.6和4.7;中位数:4.75

(Ⅱ)由题意知本题是一个古典概型,

设Ai表示所取3人中有i个人是“好视力”,

至多有1人是“好视力”记为事件A,包括有一个人是好视力和有零个人是好视力,

P(

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阅读理解

    What are American high schools like? Well, I'm happy to tell you what I know.

    When I started school here, it had already been a week since the school opened. At this school, freshmen usually go on a trip for about three days at the beginning of school. Unfortunately I missed that wonderful trip, which would have been the best time to get to know my classmates. I was really sad. I wished I'd known about it earlier.

    Despite the disappointment, however, I gradually adapted to my new life and school.

    There is a space in the basement of the teaching building where students chat and meet each other. As we do not always have the same classrooms and classmates, the school wants us to get to know each other there. Students usually come to school early, sit in that space and have fun. Around the space, there are many lockers for students to leave their books in, so that students do not have to carry a heavy schoolbag everywhere.

    It really surprises me that we have almost no textbooks. We only have textbooks for World History and Algebra 2 and they are big and heavy, like bricks. For other classes, we only need binders (活页夹) with paper in them. Without textbooks, students learn things freely and actively. For example, my humanities teacher just teaches us what is in her mind at the time. We never know what we will learn.

    Another difference between American schools and Chinese schools is that American schools care about students' morality more than their academic studies. For example, if you do not finish your homework, you will just be asked to do it later, but if you cheat or lie, you will get a warning or even be kicked out.

    I think that most students here are good at schoolwork as well, but compared to Chinese students, they can make learning a more joyful experience. I think we should take the good points from our two different kinds of education to perfect our approach to studying.