![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd24f8e406b87a6ccd8b4e21dff664a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/758991926f618ea3bf00063fb7cc814e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98b863a11fc612c1590cf8e031e174d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f4a03762b68193fb7c8f1c38c1ad89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
生三胎 | 不生三胎 | 合..计 | |
80后 | 10 | 40 | 50 |
90后 | 30 | 20 | 50 |
合计 | 40 | 60 | 100 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)根据调查数据,是否有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a363cc53497fdfac77b43f656424f973.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f8ec200973736ac8bcd9aa633855d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
参考数据:
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151e5633a5d0cc30b254167e3dda5803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8e63a3de229aa35d7e95b166802303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
选择“物理” | 选择“历史” | 总计 | |
男生 | 35 | 20 | 55 |
女生 | 15 | 30 | 45 |
总计 | 50 | 50 | 100 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![]() | 0.050 | 0.010 | 0.001 |
![]() | 3.841 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c4d12b3a705daab723ab243b6cc88.png)
(2)现已知这
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.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/a17161b28b6ad8f57abc5b11e1b6c671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17161b28b6ad8f57abc5b11e1b6c671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf1c295fd10f4dcc21955ce39560b5c6.png)
参加体育锻炼 | 未参加体育锻炼 | 总计 | |
男同学 | |||
女同学 | |||
总计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0557ecd5071a9c5fb9da5809f5aec9a.png)
(2)按分层抽样在未参加体育锻炼的学生中抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f9c62815ef797a21f276361d39912e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74fec878623fb050bf545f23504201e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/cfc4f8a9-10c8-49a5-867b-e61071a8ef81.png?resizew=280)
(1)求m和n的值;
(2)此次活动的100名志愿者通过现场和网络两种方式报名.他们报名方式的部分数据如下表所示.请完善下表,并通过计算说明能否有99.9%的把握认为“选择哪种报名方式与性别有关系”?
男 | 女 | 总计 | |
现场报名 | 50 | ||
网络报名 | 31 | ||
总计 | 50 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.05 | 0.01 | 0.005 | 0.001 | |
3.841 | 6.635 | 7.879 | 10.828 |
男性观众 | 女性观众 | 合计 | |
流泪 | 20 | ||
没有流泪 | 5 | 20 | |
合计 |
(2)以分层抽样的方式,从流泪与没有流泪的观众中抽取5人,然后从这5人中再随机抽取2人,求这2人都流泪的概率.
附:
![]() | 0.100 | 0.050 | 0.010 | 0.001 |
![]() | 2.706 | 3.841 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/bea06931-53ce-49d6-916c-a6fed19caeda.png?resizew=213)
非体育健康 | 体育健康 | 合计 | |
男生 | |||
女生 | 10 | 55 | |
合计 | 100 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)根据已知条件计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)将每天自主参加体育锻炼时间不低于50分钟的学生称为体育健康
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b26ea9b3e6e286874c5dca1badea723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b26ea9b3e6e286874c5dca1badea723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b26ea9b3e6e286874c5dca1badea723.png)
附:
0.05 | 0.010 | 0.005 | |
3.841 | 6.635 | 7.879 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50db494f12c37372080e4367d16e51f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
理智购物者 | 剁手党 | 合计 | |
男性 | 40 | 20 | 60 |
女性 | 30 | 50 | 80 |
合计 | 70 | 70 | 140 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86efdf59f1d353a1504987bdb0189ae6.png)
(2)小红近四年“双十一”网路购物消费如下表
年份 | 2017 | 2018 | 2019 | 2020 |
年份代码 | 1 | 2 | 3 | 4 |
消费金额 | 200 | 300 | 500 | 600 |
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
参考数据:
0.15 | 0.10 | 0.05 | 0.025 | 0.010 | |
2.072 | 2.706 | 3.841 | 5.024 | 6.635 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12bf97eb9bdf1fe6a80184f7c13ceaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebff20f21ae41fd8d1f1e3145895842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
经常应用 | 偶尔应用或者不应用 | 总计 | |
农村 | 40 |
| |
城市 | 60 | ||
总计 | 100 | 60 | 160 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
(1)补全2×2列联表,判断能否有99.5%的把握认为智慧课堂的应用与区域有关,并说明理由;
(2)在偶尔应用或者不应用智慧课堂的学校中,按照农村和城市的比例抽取6个学校进行分析,然后再从这6个学校中随机抽取2个学校所在的地域进行核实,记其中农村学校有X个,求X的分布列和数学期望.
附::
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
P(K2≥k0) | 0.1 | 0.050 | 0.010 | 0.005 | 0.001 |
k0 | 2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f851ee663d07bed1f1ca627d3079d77b.png)
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760532374732800/2766851235749888/STEM/824f06da-36c6-4ace-85cb-1a9f95b6eff2.png?resizew=282)
(1)请将样本频率分布直方图补充完整,并求出样本的中位数与平均数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
(2)在该样本中,经统计有男同学70人,其中40人打分在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402406a638566b51952e781a8a0b5516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402406a638566b51952e781a8a0b5516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402406a638566b51952e781a8a0b5516.png)
适应 | 不适应 | 合计 | |
男同学 | |||
女同学 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![]() | 0.100 | 0.050 | 0.010 | 0.001 |
![]() | 2.706 | 3.841 | 6.635 | 10.828 |
第x年 | 1 | 2 | 3 | 4 | 5 |
年销售量y(万台) | 5 | 8 | 14 | 22 | 31 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
购置传统燃油汽车 | 购置新能源电动车 | 总计 | |
车主为父亲 | 3 | ||
车主为母亲 | 2 | 6 | |
总计 | 20 |
(2)完成
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b4b06478c218a0e3421f8c52427c8b.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94b2c52f31cb38f3f4e558c1dea5565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a63c9b101dd6797948ffa03874c4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66db8762e5a2bb2fb50e8406784e3cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da04166ce89001821666c449f5f9a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2f70b01e964f4084816bd12125b714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
临界值表供参考:
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
66 | 450 | 2.236 | 2.449 |