![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eba00d21791a55dd6d4fad308eddecb.png)
(1)请根据直方图中的数据填写下面的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
(2)现按照“课外体育达标”与“课外体育不达标”进行分层抽样,抽取8人,再从这8名学生中随机抽取3人参加体育知识问卷调查,记“课外体育不达标”的人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://img.xkw.com/dksih/QBM/2018/1/11/1857880314060800/1858914093858816/STEM/de43c207d29344688621eda7ccbaab0c.png?resizew=554)
![](https://img.xkw.com/dksih/QBM/2018/1/11/1857880314060800/1858914093858816/STEM/7cb4df0f44504bbaa3f51268c7979d39.png?resizew=346)
![](https://img.xkw.com/dksih/QBM/2018/1/11/1857880314060800/1858914093858816/STEM/b4cf490ca17a42a0b664bb867d934a63.png?resizew=326)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eba00d21791a55dd6d4fad308eddecb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/3d0be30c-0fac-4ac0-b5e8-f78d7c38e842.png?resizew=230)
(1)请根据直方图中的数据填写下面的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
课外体育不达标 | 课外体育达标 | 合计 | |
男 | 60 | ||
女 | 110 | ||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe2f70554fb7ffc670c0f9bedde6502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73514ef25f41ff0189d65313034bf695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5749e5138778591f1c99da74ab8a888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b98df418a221be80cd082639c5262de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f702ab683d2cc6d3a7ce1125797f8e1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/12/fe1bb95f-763f-4842-bf88-106c13a9830a.png?resizew=301)
(1)试根据频率分布直方图估计小区平均每户居民的平均损失;
(同一组中的数据用该组区间的中点值作代表);
(2)小明向班级同学发出倡议,为该小区居民捐款,现从损失超过4000元的居民中随机
抽出2户进行捐款援助,求抽出的2户居民损失均超过8000元的概率;
(3)台风后区委会号召该小区居民为台风重灾区捐款,小明调查的50户居民捐款情况如下表,
在图2表格空白外填写正确数字,并说明是否有95%以上的把握认为捐款数额超过或
不超过500元和自身经济损失是否超过4000元有关?
经济损失不超过4000元 | 经济损失超过4000元 | 合计 | |
捐款超过500元 | 30 | ||
捐款不超过500元 | 6 | ||
合计 |
![](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/31ea979a9e91e2f1d1ffd2f3c6ccebf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c452415b2ade7fc8a74e7624654839b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6efa7b9891f0371f6f0392fb086e705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb4ccbf8f3e7c2ed20de44714256534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0df5b38e19eb704481e963690276adf.png)
(Ⅰ)台风后居委会号召小区居民为台风重灾区捐款,小张调查的100户居民捐款情况如右下表格,在图2表格空白处填写正确数字,并说明是否有以上的把握认为捐款数额多于或少于500元和自身经济损失是否到4000元有关?
(Ⅱ)将上述调查所得到的频率视为概率. 现在从该地区大量受灾居民中,采用随机抽样方法每次抽取1户居民,抽取3次,记被抽取的3户居民中自身经济损失超过4000元的人数为. 若每次抽取的结果是相互独立的,求
的分布列,期望
和方差
.
附:临界值表
0.10 | 0.05 | 0.025 | |
![]() | 2.706 | 3.841 | 5.024 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/275753b45e1571d5777fcf649f4f05b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
2 | 3 | 4 | 5 | 6 | 7 | |
52.5 | 45 | 40 | 30 | 25 | 17.5 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
附:在线性回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d2855df8c2f9f00a288ff6c97c695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7620d51f97ef13c53e56b09fe82e4d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26333e31d7254a006bf8f7852a6b463.png)
(1)画出表中数据的散点图,并指出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3680f7d0d96efc5b207c8e9552e21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
表一:男生
![](https://img.xkw.com/dksih/QBM/2017/6/5/1702579728015360/1704302807080960/STEM/32e690025256417fb5b438d519437312.png?resizew=252)
表二:女生
![](https://img.xkw.com/dksih/QBM/2017/6/5/1702579728015360/1704302807080960/STEM/b2396dd2901c451380e97639e0635184.png?resizew=252)
(1)从表二的非优秀学生中随机抽取2人交谈,求所选2人中恰有1人测评等级为合格的概率;
(2)由表中统计数据填写下面的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://img.xkw.com/dksih/QBM/2017/6/5/1702579728015360/1704302807080960/STEM/9bf2a27f16e94e349f6d025496b583e3.png?resizew=261)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2f70b01e964f4084816bd12125b714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
参考数据:
0.10 | 0.05 | 0.01 | |
2.706 | 3.841 | 6.635 |
![](https://img.xkw.com/dksih/QBM/2017/4/19/1669121876918272/1669376289521664/STEM/7909ca0be47f46ab99febe7301086b77.png?resizew=279)
(1)分别计算甲、乙两班20个样本中,化学分数前十的平均分,并大致判断哪种教学方式的教学效果更佳;
(2)由以上统计数据填写下面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://img.xkw.com/dksih/QBM/2017/4/19/1669121876918272/1669376289521664/STEM/c6781e6c968d48369591ae9318acac1f.png?resizew=475)
附:参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63501b254962e1190b092bbf4a568027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
临界值表:
![]() | 0.10 | 0.05 | 0.025 | 0.010 |
![]() | 2.706 | 3.841 | 5.024 | 6.635 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db04f988e1aba18b0a3470d332908c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ae34624f8f116b37c06560710e63fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea8640c311d5f7d3c94cf817b332ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)画出示意图,验证说明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
(2)求这个正方形的第四个顶点对应的复数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1ffcf9f09e63e7291e749cba4505f77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b8ff51983bab65b77ddda8f297d097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649d17e60f38e8aedac7997ad470d7f8.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.050 | 0.025 | 0.010 | 0.001 | |
3.841 | 5.024 | 6.635 | 10.828 |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/13/813fbead-f731-4073-b0ad-c0d9ab53597b.png?resizew=295)
(1)求这些学生中成绩优秀的人数;
(2)已知这100名小学生中女生占
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f452908e724c9966128657203147834.png)
成绩“优秀” | 成绩“非优秀” | 总计 | |
男生 | |||
女生 | |||
总计 |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/da29901d-44e5-499d-bc3d-e11865176187.png?resizew=250)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/cdcf8944-889b-4332-a4b4-038c3c1e12fd.png?resizew=319)
(1)求这500名学生中获得专业三等奖学金的人数.
(2)若将每周课外平均学习时间超过35h的学生称为“努力型”学生,否则称为“非努力型”学生,画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
(3)若以频率作为概率,从该校任选1名学生,记该学生2022年获得的专业奖学金的金额为随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附表:
0.050 | 0.010 | 0.005 | 0.001 | |
3.841 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc70b5e1ba847b9918a50f67bfbe8f.png)