不够良好 | 良好 | |
病例组 | 40 | 60 |
对照组 | 10 | 90 |
(2)从该地的人群中任选一人,A表示事件“选到的人卫生习惯不够良好”,B表示事件“选到的人患有该疾病”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59219d3b263f8ecb58e02db29d8b97a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe81efdee768286a6d88743aa24951cf.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72c4b3e2c73fea9ab11ca1dd30b8c47.png)
(ⅱ)利用该调查数据,给出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ae455379145148357df94ac2f034d4.png)
附
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
0.050 | 0.010 | 0.001 | |
k | 3.841 | 6.635 | 10.828 |
一级品 | 二级品 | 合计 | |
甲机床 | 150 | 50 | 200 |
乙机床 | 120 | 80 | 200 |
合计 | 270 | 130 | 400 |
(2)能否有99%的把握认为甲机床的产品质量与乙机床的产品质量有差异?
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
0.050 | 0.010 | 0.001 | |
k | 3.841 | 6.635 | 10.828 |
锻炼人次 空气质量等级 | [0,200] | (200,400] | (400,600] |
1(优) | 2 | 16 | 25 |
2(良) | 5 | 10 | 12 |
3(轻度污染) | 6 | 7 | 8 |
4(中度污染) | 7 | 2 | 0 |
(2)求一天中到该公园锻炼的平均人次的估计值(同一组中的数据用该组区间的中点值为代表);
(3)若某天的空气质量等级为1或2,则称这天“空气质量好”;若某天的空气质量等级为3或4,则称这天“空气质量不好”.根据所给数据,完成下面的2×2列联表,并根据列联表,判断是否有95%的把握认为一天中到该公园锻炼的人次与该市当天的空气质量有关?
人次≤400 | 人次>400 | |
空气质量好 | ||
空气质量不好 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
P(K2≥k) | 0.050 | 0.010 | 0.001 |
k | 3.841 | 6.635 | 10.828 |
![](https://img.xkw.com/dksih/QBM/2018/6/9/1963606031212544/1963626072768512/STEM/4029c4f58ca7425e98c37ad304f3856b.png?resizew=402)
(1)根据茎叶图判断哪种生产方式的效率更高?并说明理由;
(2)求40名工人完成生产任务所需时间的中位数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
超过![]() | 不超过![]() | |
第一种生产方式 | ||
第二种生产方式 |
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
语文成绩 | 合计 | |||
优秀 | 不优秀 | |||
数学 成绩 | 优秀 | 50 | 30 | 80 |
不优秀 | 40 | 80 | 120 | |
合计 | 90 | 110 | 200 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f43c77e96f7f0cc838495752f9363.png)
(2)在人工智能中常用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adaf7f84a5e8d95c176197fc69fd04d.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50baacc976f8b66c6c12ec167bbf774e.png)
(3)现从数学成绩优秀的样本中,按分层抽样的方法选出8人组成一个小组,从抽取的8人里再随机抽取3人参加数学竞赛,求这3人中,语文成绩优秀的人数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f503f0dec4cf2cc95ad9521c5eaf9f18.png)
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d9d0d66a7f8fc34082cf8c45f64839.png)
数学成绩优秀 | 数学成绩不优秀 | 合计 | |
经常整理 | |||
不经常整理 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)根据图1、图2中的数据,补全上方
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead9d6ff51996f3ebace6f212e11a9e4.png)
(3)用频率估计概率,在全市中学生中按“经常整理错题”与“不经常整理错题”进行分层抽样,随机抽取5名学生,再从这5名学生中随机抽取2人进行座谈.求这2名同学中经常整理错题且数学成绩优秀的人数X的分布列和数学期望.
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3599e8452732f75172651d838f31856d.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
月份 | 1 | 2 | 3 | 4 | 5 |
带货金额 | 350 | 440 | 580 | 700 | 880 |
![](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/11bc05f41215f9894e11d1df0465751a.png)
(2)求变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(3)该公司随机抽取55人进行问卷调查,得到如下不完整的列联表:
参加过直播带货 | 未参加过直播带货 | 总计 | |
女性 | 25 | 30 | |
男性 | 10 | ||
总计 |
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d578c9e7cf1c6a92c0cc28f7f91459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b329efddd8bbdbd3e1751b2e2936b641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9652d385c0442c3c9d276273436c4bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73de2b07f9ea523577727e8be46710e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde4f00e86e0791aa784801624be9d3d.png)
参考公式:相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368976f08508d324aa73ec6a9ceca54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2606e1508b23243588e79d56517f3161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f4d3ab5f8ec8405fe32fd181ce32.png)
附:
![](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 | |
2.072 | 2.706 | 3.841 | 5.024 |
满意 | 不满意 | |
男顾客 | 40 | 10 |
女顾客 | 30 | 20 |
(1)分别估计男、女顾客对该商场服务满意的概率;
(2)能否有95%的把握认为男、女顾客对该商场服务的评价有差异?
附:.
P(K2≥k) | 0.050 | 0.010 | 0.001 |
k | 3.841 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28927ff0dd8ffb94fe99863fedc255c0.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
2017.5 | 80.4 | 1.5 | 40703145.0 | 1621254.2 | 27.7 | 1226.8 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc51189c4268a8eaf04a24696ac415eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5024a1a47b50c81a1d6a5e926d3f2d.png)
(1)根据散点图判断,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b447ac3d1a965572c31b6e4c18d4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0067cc8ea9c27a7c45b835bd231de11c.png)
(2)已知2023年该机场飞往A地、B地和其他地区的航班比例分别为0.2、0.2和0.6.若以(1)中的预测值作为2023年该机场飞往A地航班放行准点率的估计值,且2023年该机场飞往B地及其他地区(不包含A、B两地)航班放行准点率的估计值分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb00d558e456638de8ff1788db5a8d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e76496989a451b5e945e3043f4af5ad.png)
(i)现从2023年在该机场起飞的航班中随机抽取一个,求该航班准点放行的概率;
(ii)若2023年某航班在该机场准点放行,判断该航班飞往A地、B地、其他地区等三种情况中的哪种情况的可能性最大,说明你的理由.
附:(1)对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1c6aadc0129bf86f4fff9dcfb924b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154100371e025fffe0ffae8be9567383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a14e40329de36fc4a1a3f8fbfafda12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0943f70585435955d528325e51ef013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29eaeed7261f564ae82dfeceef85deb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815e2869dc16e2ae7a7e1911e3afc8c3.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6634323a463191194dd14c3a9cbc7a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c6dbc06493f4d4614990e7822a5343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a404c71f17b741494e7ff25e8da9db.png)
非常喜欢 | 喜欢 | 合计 | |
A | 30 | 15 | |
B | x | y | |
合计 |
(1)现从100名观众中根据喜爱程度用分层抽样的方法抽取20名进行问卷调查,则应抽取喜爱程度为“非常喜欢”的A,B地区的人数各是多少?
(2)完成上述表格,并根据表格判断是否有95%的把握认为观众的喜爱程度与所在地区有关系.
(3)若以抽样调查的频率为概率,从A地区随机抽取3人,设抽到喜爱程度为“非常喜欢”的观众的人数为X,求X的分布列和期望.
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.05 | 0.010 | 0.001 | |
3.841 | 6.635 | 10.828 |