一个袋子中装有三个大小相同的小球,其中1个黑球,2个白球.企业所有员工从袋子中有放回的随机摸两次球,每次摸出一球.约定“若两次摸到的球的颜色不同,则按方式一回答问卷,否则按方式二回答问卷”.
方式一:若第一次摸到的是白球,则在问卷中画“○”,否则画“×”;
方式二:若你对新绩效方案满意,则在问卷中画“○”,否则画“×”.
当所有员工完成问卷调查后,统计画○,画×的比例.用频率估计概率,由所学概率知识即可求得该企业员工对新绩效方案的满意度的估计值.其中满意度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b595a1f46f84fc56bbcb3f27491b6130.png)
(1)求每名员工两次摸到的球的颜色不同的概率
(2)若该企业某部门有9名员工,用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)若该企业的所有调查问卷中,画“○”与画“×”的比例为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259150cf534c96faef62a1d5e8b5d238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8e63a3de229aa35d7e95b166802303.png)
选择“大理” | 选择非“大理” | 合计 | |
男生 | 15 | ||
女生 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
(2)为了进一步了解学生进行选科的理由,随机选取了男生4名,女生2名进行访谈,再从中抽取2名代表作详细交流,求至少抽到1名女生的概率.
附表及公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.05 | 0.025 | 0.010 | 0.005 | 0.001 | |
3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/4/07551ab7-ffa1-413d-8a22-0a4a2a08deda.png?resizew=282)
(1)求该100名学生竞赛成绩的中位数;(结果保留整数)
(2)从竞赛成绩在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df5009593aca7d979398640ef258e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63b4889ed36ef4a892fd23f4f668c2f.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)以样本的频率估计概率,从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e699fd1e807d744cf5a324ea883a53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d25a3f31b6018b19168b596a2147e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b92e48e4637716248072ae5bd2c71df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
性别 | 满意度 | 合计 | |
不满意 | 满意 | ||
男生 | |||
女生 | |||
合计 |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/fb60988b-6b7e-4547-bd29-b024b8c95a92.png?resizew=258)
(1)求频率分布直方图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知在不满意的学生中男生占比
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357821e0e5595eaf3028df63d47b2c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bdaf501302beeec9d077be02909e3bd.png)
(3)若按是否满意用比例分层随机抽样的方法从100名学生中抽取10人,现从抽取的10名学生中进行调研,每轮调研一人,调研视为不放回抽取,调研到不满意的学生就停止抽取,且第四轮抽取不管结果如何都停止抽取,记停止抽取时抽取轮数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
附:临界值表
![]() | 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/e7dc70b5e1ba847b9918a50f67bfbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768fb3d9309c4ce5c6e86dc75ecf0cbe.png)
(2)某火车站共设有4个安检入口,每个入口每次只能进入1位乘客,求一个4人小组进站的不同方案种数.
6 . 2023年春节期间,科幻电影《流浪地球2》上映,获得较好的评价,也取得了很好的票房成绩.某平台为了解观众对该影片的评价情况(评价结果仅有“好评”“差评”),从平台所有参与评价的观众中随机抽取400人进行调查,数据如下表所示(单位:人):
好评 | 差评 | 合计 | |
男性 | 80 | 200 | |
女性 | 90 | ||
合计 | 400 |
(1)把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0255cd2084765f7019367ff6e575b9d6.png)
(2)若将频率视为概率,从抽取的400人中所有给出“好评”的观众中随机抽取3人,用随机变量X表示被抽到的女性观众的人数,求X的分布列和数学期望.
参考公式:,其中
.
参考数据:
0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 | |
2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/17/d8bdea91-8e92-47a3-8bae-542743baa5c1.png?resizew=232)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c7539ed297ea63b9ace6f5cc58ca8.png)
成绩 | ||||
频数 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128de649220637bdc96fc3e508592201.png)
男生 | 女生 | 合计 | |
防疫标兵 | |||
非防疫标兵 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776d32c5963be22b0fe71ddd0248c7cb.png)
0.100 | 0.050 | 0.025 | 0.010 | 0.005 | 0.001 | |
2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/18/b00469fa-5ba3-436d-8584-cac85034a2a4.png?resizew=243)
30名女生成绩频数分布表:
成绩 | ||||
频数 | 10 | 10 | 6 | 4 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
男生 | 女生 | 合计 | |
防疫标兵 | |||
非防疫标兵 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb525270c748eddaaecc4a549cca250e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249e3b183dd54f10772b54d615302067.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776d32c5963be22b0fe71ddd0248c7cb.png)
0.100 | 0.050 | 0.025 | 0.010 | 0.005 | 0.001 | |
2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
一个袋子中装有三个大小相同的小球,其中1个黑球,2个白球.企业所有员工从袋子中有放回的随机摸两次球,每次摸出一球.约定“若两次摸到的球的颜色不同,则按方式Ⅰ回答问卷,否则按方式Ⅱ回答问卷”.
方式Ⅰ:若第一次摸到的是白球,则在问卷中画“○”,否则画“×”;
方式Ⅱ:若你对新绩效方案满意,则在问卷中画“○”,否则画“×”.
当所有员工完成问卷调查后,统计画○,画×的比例.用频率估计概率,由所学概率知识即可求得该企业员工对新绩效方案的满意度的估计值.其中满意度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62919377758b84e368f598ff2c9e65b.png)
(1)若该企业某部门有9名员工,用X表示其中按方式Ⅰ回答问卷的人数,求X的数学期望;
(2)若该企业的所有调查问卷中,画“○”与画“×”的比例为4:5,试估计该企业员工对新绩效方案的满意度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58d9a123e465dace224231f54ee94e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a40cf767fd2a684f2f1ed9216836792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8c2a91a15e1f7b296b64d3bd2e7551.png)
(2)若该市所有参赛学生的成绩X近似服从正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57db59c20e7a352a161bc589d36938e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
(i)若该市共有10000名学生参加了竞赛,试估计参赛学生中成绩超过79分的学生数(结果四舍五入到整数);
(ii)若从所有参赛学生中(参赛学生数大于10000)随机取3名学生进行访谈,设其中竞赛成绩在64分以上的学生数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
附参考数据,若随机变量X服从正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8f8641d4e8bbabc1e726417ac3c8cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1c9871a68a9f90d1a27d3559aa974a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9546031173beb4c429883aae0e16e03b.png)