解题方法
1 . 某校高三期中考试后,数学教师对本次全部学生的数学成绩按1∶20进行分层抽样,随机抽取了20名学生的成绩为样本,成绩用茎叶图记录如图所示,但部分数据不小心丢失,同时得到如下表所示的频率分布表:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/048d171b-7c29-4fd1-96df-54dc19901642.png?resizew=104)
(1)求表中
,
的值及成绩在![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58d9a123e465dace224231f54ee94e8.png)
范围内的样本数;
(2)从成绩在
内的样本中随机抽取4个样本,设其中成绩在
内的样本个数为随机变量
,求
的分布列及数学期望
;
(3)若把样本各分数段的频率看作总体相应各分数段的概率,现从全校高三期中考试数学成绩中随机抽取5个,求其中恰有2个成绩在
内的概率.
分数段(分) | ![]() | ![]() | ![]() | ![]() | ![]() | 总计 |
频数 | ![]() | |||||
频率 | ![]() | 0.25 |
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/048d171b-7c29-4fd1-96df-54dc19901642.png?resizew=104)
(1)求表中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58d9a123e465dace224231f54ee94e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e19c4b01c4a0e8c775c6564b8e6ba33.png)
(2)从成绩在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c173e50c9a0505ad6b0c6b379fe1e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8c2a91a15e1f7b296b64d3bd2e7551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
(3)若把样本各分数段的频率看作总体相应各分数段的概率,现从全校高三期中考试数学成绩中随机抽取5个,求其中恰有2个成绩在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43452b10c6b4f0ac03753add466c479.png)
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