解题方法
1 . 2021年3月教育部印发了《关于进一步加强中小学生睡眠管理工作的通知》,该《通知》指出,高中生每天睡眠时间应达到
小时. 某学校为了解学生的睡眠情况,从高一和高二年级中随机抽取各40名学生,统计他们一周平均每天的睡眠时间作为样本,统计结果如图.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/11/89678992-8b91-4783-8d8b-9ffb9214b894.png?resizew=463)
(1)从该校高一年级学生中随机抽取
人,估计该生平均每天的睡眠时间不少于
小时的概率;
(2)从该校高二年级学生中随机抽取
人,这
人中平均每天的睡眠时间为
小时或
小时的人数记为
,求
的分布列和数学期望
;
(3)从该校高一年级学生中任取
人,其平均每天的睡眠时间记为
,从该校高二年级学生中任取
人,其平均每天的睡眠时间记为
,试比较方差
与
的大小.(只需写出结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/11/89678992-8b91-4783-8d8b-9ffb9214b894.png?resizew=463)
(1)从该校高一年级学生中随机抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
(2)从该校高二年级学生中随机抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749082d415fedaedd79359ea0878ee14.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/9fc79c66ebaacd709ec9965b90a22b14.png)
(3)从该校高一年级学生中任取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351bb3f3c54604330fa5b6c2bc3a7502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177b7f56650f15cdcabd287ee39554d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60b23afe62d007e6e338e8216f33b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424bcf45473f1ba2856d544b06132e8e.png)
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