好评 | 差评 | 合计 | |
男性 | 70 | 110 | |
女性 | 60 | ||
合计 | 220 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f43c77e96f7f0cc838495752f9363.png)
(2)从给出“好评”的观众中按性别用分层抽样的方法抽取10人,再从这10人中随机抽出3人送电影优惠券,记随机变量X表示这3人中女性观众的人数,求X的分布列和数学期望.
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc70b5e1ba847b9918a50f67bfbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
参考数据:
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
(1)设消费者的年龄为x,对共享汽车的体验评分为y.若根据统计数据,用最小二乘法得到y关于x的线性回归方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ee96cc031f00c12be7fb0f2e4621fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830e4a952feaba5491bafbb702377cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cd633b800a41a5a65ce1b25f122064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2991502b0be7df4183b9e42b6c53c6e4.png)
(2)现将100名消费者的年龄划分为“青年”和“中老年”,评分划分为“好评”和“差评”,整理得到如下数据,请将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
好评 | 差评 | 合计 | |
青年 | 16 | ||
中老年 | 12 | ||
合计 | 44 | 100 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929ef3bed0a4bdd22f39e036506dc481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9218b61bbc7b5304adf61be07f0a98ae.png)
相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb16efc462b888a96ddcd23b127686fb.png)
独立性检验中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9cfccce8c0c707a066f9c7d3f3e2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
临界值表:
0.050 | 0.010 | 0.001 | |
3.841 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c64cd583c538f89bb8ad7ac2b2e136a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1518f7303c68bd06a664df4716346765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49af36dc835291b83cf8b5dcc394a01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60387030a865e31ae81d19074ed61f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d14f09ca731b34df6bc85b1dc8e142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7942441160a2b27c2618e4e9220df53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0372a13ab2b06270a8296dfd7aeb20c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dddc7f2cb358e9d3bd242a6792f275f3.png)
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965895265624064/2966574706999296/STEM/56583e1d-ee6e-4e58-91ce-42db2f3d8c2f.png?resizew=326)
(1)若“青少年人”中有15人在关注两会,根据已知条件完成下面的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
(2)由(1)结果,从“青少年人”关注两会和不关注两会的人数按比例抽取6人,从这6人中选3人进行专访,这3人关注两会人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
关注 | 不关注 | 合计 | |
青少年人 | 15 | ||
中老年人 | |||
合计 | 50 | 50 | 100 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
0.05 | 0.010 | 0.001 | |
3.841 | 6.635 | 10.828 |
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2f70b01e964f4084816bd12125b714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![]() | 0.1 | 0.05 | 0.01 | 0.005 | 0.001 |
![]() | 2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
(1)参加调研的小学生有多少人?
(2)该科研机构将调研的情况统计后得到下表:
名称 | 喜爱使用该学习软件 | 不太喜爱使用该学习软件 | 总计 |
初中生 | 60 | 120 | 180 |
小学生 | 90 | ||
总计 |
天文爱好者 | 非天文爱好者 | 合计 | |
女 | 20 | 30 | 50 |
男 | 35 | 15 | 50 |
合计 | 55 | 45 | 100 |
(2)现从抽取的女性人群中,按“天文爱好者”和“非天文爱好者”这两种类型进行分层抽样抽取5人,然后再从这5人中随机选出3人,记其中“天文爱好者”的人数为X,求X的分布列和数学期望.
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb71f748309141707ffd1641c641f237.png)
0.10 | 0.05 | 0.010 | 0.005 | 0.001 | |
2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
得分 |
|
|
|
|
|
| |
男性人数 | 5 | 10 | 20 | 30 | 20 | 12 | 3 |
女性人数 | 5 | 10 | 15 | 35 | 20 | 13 | 2 |
(2)将抽取的200名社区居民对人工智能的了解程度分为“比较了解”(测试成绩不低于60分)和“不太了解”(测试成绩低于60分)两类,完成下面2×2列联表,并判断是否有90%的把握认为社区居民对人工智能的了解程度与性别有关?
不太了解 | 比较了解 | |
男性 | ||
女性 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.15 | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 | |
2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23466fd31d0666cb9f65dced41188359.png)
(1)根据所给数据完成下列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
优秀 | 不优秀 | 总计 | |
甲班 | |||
乙班 | |||
总计 |
(2)能否在犯错误的概率不超过0.010的前提下,认为成绩与班级有关系?
参考公式::
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
临界值表供参考:
![]() | 0.150 | 0.100 | 0.050 | 0.025 | 0.010 | 0.005 | 0.001 |
![]() | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/5/7ad6bbb9-c071-44bc-bbaf-8228aaeb87a8.png?resizew=218)
(1)在乙班的20个个体中,从不低于86分的成绩中随机抽取2人,求抽出的两个人均“成绩优秀”的概率;
(2)由以上统计数据填写
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
甲班( | 乙班( | 总计 | |
成绩优秀 | |||
成绩不优秀 | |||
总计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
0.25 | 0.15 | 0.10 | 0.05 | 0.025 | |
1.323 | 2.072 | 2.706 | 3.847 | 5.024 |