普查对象类别 | 顺利 | 不顺利 | 合计 |
A类家庭 | 180 | 200 | |
B类家庭 | 60 | 300 | |
合计 |
(2)普查领导小组为了了解公民对这次普查的认识情况,准备采取分层抽样的方法从该试点小区抽取5户家庭户主,再从这5户家庭户主中,随机抽取2户家庭户主进行谈话交流,求至少有1户家庭户主是来自A类家庭的概率.
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
参考数据:
P(K2≥P) | 0.10 | 0.05 | 0.025 | 0.010 | 0.001 |
k | 2.706 | 3.841 | 5.024 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eba00d21791a55dd6d4fad308eddecb.png)
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498163885719552/2500047343034368/STEM/236d26eb70c34cfa8c01b95c2ef866d5.png?resizew=221)
一般关注 | 强烈关注 | 合计 | |
男 | 45 | ||
女 | 10 | 55 | |
合计 | 100 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
(2)现已从“强烈关注”的网友中按性别分层抽样选取了5人,再从这5人中选取2人,求这2人中至少有1名女性的概率.
参考公式及数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776d32c5963be22b0fe71ddd0248c7cb.png)
0.050 | 0.010 | |
3.841 | 6.635 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f43c77e96f7f0cc838495752f9363.png)
性别 | 是否喜欢羽毛球运动 | 合计 | |
是 | 否 | ||
男生 | |||
女生 | |||
合计 |
(2)已知该校男生与女生人数相同,将样本的频率视为概率,现从全校学生中随机抽取30名学生,设其中喜欢羽毛球运动的学生人数为X,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158ff94c6c79d0c0a4650a6b55def11f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8d4ec7654edddffa478de7d4d54872.png)
附:
![]() | 0.10 | 0.05 | 0.010 | 0.005 | 0.001 |
![]() | 2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38cfee12dbeeab57c707dca8643538a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
甲校:
分组 | [70,80) | [80,90) | [90,100) | [100,110) | [110,120) | [120,130) | [130,140) | [140,150] |
频数 | 1 | 2 | 9 | 8 | 10 | 10 | 3 |
分组 | [70,80) | [80,90) | [90,100) | [100,110) | [110,120) | [120,130) | [130,140) | [140,150] |
频数 | 2 | 3 | 10 | 15 | 15 | 3 | 1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)由以上统计数据填写下面2×2列联表,若按是否优秀来判断,是否有97.5%的把握认为两个学校的数学成绩有差异?
甲校 | 乙校 | 总计 | |
优秀 | |||
非优秀 | |||
总计 |
独立性检验临界值表:
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 |
(1)填写下列秃顶与患心脏病列联表∶
患心脏病 | 患其他病 | 总计 | |
秃顶 | |||
不秃顶 | |||
总计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)能够以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f3effd82c4566d202d46f338be20dc.png)
注∶
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2f70b01e964f4084816bd12125b714.png)
| 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://staticzujuan.xkw.com/quesimg/Upload/formula/e67a31be2724f6371377f4468aa6dab5.png)
男生成绩 | 女生成绩 | |
5,2,1 6,0 8,6,5,3,2 9,4,3,1,1 8,8,7 2,0 | 4 5 6 7 8 9 | 1,2 0,4,5 4,4,5,6,8 1,2,4,4,5,7,9 4,8,9 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61ff77a5e319070ec27e42230908dc.png)
喜欢 | 不喜欢 | 合计 | |
男生 | |||
女生 | |||
合计 |
(3)用样本估计总体,将样本频率视为概率,现从全校男生,女生中各抽取1人,求其中喜欢健身操的人数X的分布列及数学期望.
参考公式及数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![]() | 0.150 | 0.100 | 0.050 | 0.025 | 0.010 | 0.001 |
![]() | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb2cd115a12aae4b018c3a799e9659d.png)
年龄 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
频数 | 5 | 10 | 10 | 15 | 5 | 5 |
了解 | 4 | 5 | 8 | 12 | 2 | 1 |
年龄低于65岁的人数 | 年龄不低于65岁的人数 | 合计 | |
了解 | ![]() | ![]() | |
不了解 | ![]() | ![]() | |
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60387030a865e31ae81d19074ed61f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1518f7303c68bd06a664df4716346765.png)
参考公式和数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.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 |
年龄 | ||||||
频数 | 5 | 10 | 10 | 15 | 5 | 5 |
了解 | 4 | 5 | 8 | 12 | 2 | 1 |
年龄低于65岁的人数 | 年龄不低于65岁的人数 | 合计 | |
了解 | |||
不了解 | |||
合计 |
参考公式和数据K2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5891cbf04a9d257e4c9647e86c89985b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/079e2e3b-3ee2-4f13-8892-fe83589404d2.png?resizew=272)
(1)依茎叶图判断哪个小区的平均分高?
(2)现从甲小区不低于80分的家庭中随机抽取两户,求分数为87的家庭至少有一户被抽中的概率;
(3)如果规定分数不低于85分的家庭为优秀,请填写下面的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
甲 | 乙 | 合计 | |
优秀 | ![]() | ![]() | |
不优秀 | ![]() | ![]() | |
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/fc5881f1ce9b4172ca346032d0fd1e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d1f848e37491a80c619cc11dd1fbac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f959e5f8d89390f0f136f6acc9f6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f959e5f8d89390f0f136f6acc9f6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd550e1ad9bbf01687ffb4aab788ec.png)
![](https://img.xkw.com/dksih/QBM/2018/4/24/1931033716408320/1936081014595584/STEM/54c5deb7-8f27-4d31-9918-70093796e24b.png?resizew=300)
(I)在答题卡上填写下面的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0570f9b231be12b1f5476b10bbcac3c0.png)
文科生 | 理科生 | 合计 | |
获奖 | ![]() | ||
不获奖 | |||
合计 | ![]() |
![](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)
附表及公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
P(K2>k) | 0.15 | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 |
k | 2.072 | 0.706 | 3.841 | 5.024 | 6.635 | 7.879 |