![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e096c00e1457d41a5c84a575db5519e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c92ce7bf3d055c56360344b17ee93c.png)
男生 | 女生 | 合计 | |
了解 | |||
不了解 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)①为弄清学生不了解亚运会项目的原因,采用分层抽样的方法从抽取的不了解亚运会项目的学生中随机抽取9人,再从这9人中抽取3人进行面对面交流,“至少抽到一名女生”的概率;
②将频率视为概率,用样本估计总体,从该校全体学生中随机抽取10人,记其中对亚运会项目了解的人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附表:
0.10 | 0.05 | 0.025 | 0.010 | 0.001 | |
2.706 | 3.841 | 5.024 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
了解情况 | 了解 | 不了解 |
人数 | 140 | 60 |
男 | 女 | 合计 | |
了解 | 80 | ||
不了解 | 40 | ||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.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/7b72fcdc709e77910cd36a26369648b3.png)
(1)完善列联表,并判断是否有99%的把握认为性别与获得比赛优秀的结果相关.若该学校1000名学生都参加这一比赛,且各位学生是否获得优秀相互独立,以列联表中的数据所统计出的频率为概率,试估计这1000名学生中有多少学生能获得优秀.
(2)现有3个体验航天员训练活动的名额随机分配给在比赛中获得优秀的学生,设获得体验名额的女生人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
性别 优秀 | 男 | 女 | 总计 |
是 | 10 | ||
否 | 85 | ||
总计 | 50 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06463d22892a6876b2826f4db582e62.png)
数学成绩x | 145 | 130 | 120 | 105 | 100 |
物理成绩y | 110 | 90 | 102 | 78 | 70 |
(2)本次考试中,规定数学成绩达到125分为优秀,物理成绩达到100分为优秀.若该班数学优秀率与物理优秀率分别为50%和60%,且除去抽走的5名同学外,剩下的同学中数学优秀但物理不优秀的同学共有5人,请把下面的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
物理优秀 | 物理不优秀 | 合计 | |
数学优秀 | |||
数学不优秀 | |||
合计 | 60 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18cb3748184fe7d0a31e8be7fab5340f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af0e5d6c40fa0ae05ed9b59a60be5d5.png)
K2=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dfb43eae40a12e896ac96dc14a4103.png)
P( | 0.50 | 0.40 | 0.25 | 0.15 | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 |
0.455 | 0.708 | 1.323 | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
材料一 在某学校的一个由50人组成的理科班中,为备战高考,数学张老师为全班同学订购了一组套卷,并要求学生一周完成2套,但实际调查发现全班同学每周完成的试卷数的均值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0ac7b0e090c46683c7f33597337ebc.png)
材料二 据同一学校的高三生的观点,可以将学生从两方面分为几类.一般而言,活跃在班级中的“学霸”具有以下特点:①能够合理安排各科学习时间,成绩优异;
②能在100分钟内完成一张标准的数学试卷,70分钟内完成一张标准的物理试卷;
而班级中的“题霸”在材料一的条件下会在一周完成3套及以上的数学试卷(仅讨论该套卷).现对上述班级的50人按此标准进行分类,得到如下的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
学霸 题霸 | 是 | 否 | 合计 |
是 | 6 | ||
否 | |||
合计 | 12 |
(1)假设除“题霸”外的学生一周均完成2套试卷,结合材料一估计该班级“题霸”数的最大值;
(2)根据(1)的结果完成上述列联表,并判断是否有90%的把握判断“是题霸”与“是学霸”有关;
(3)结合材料二、三,计算若物理陈老师实施且同学们严格遵守该理论的前提下,一位学生在一周内能够多完成的物理试卷张数的期望(保留两位有效数字).
附表:①根据当地的高考政策,完成一张标准物理试卷的时间为75分钟;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.15 | 0.10 | 0.05 | 0.01 | |
| 2.072 | 2.706 | 3.841 | 6.635 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92128c6c226ce688bc160fb86854f2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30290c23cf5058b29f69803bbd434654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5021dda43ea360fb7b1102c1a462693a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30290c23cf5058b29f69803bbd434654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30290c23cf5058b29f69803bbd434654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06fc7811f9525e8b8c833746d6af5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30290c23cf5058b29f69803bbd434654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
(1)完成下面的列联表,并判断是否有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b253ec362b46012c30d1eb2d3030ee2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30290c23cf5058b29f69803bbd434654.png)
平均车速超过![]() | 平均车速不超过![]() | 合计 | |
男性驾驶人数 | |||
女性驾驶人数 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30290c23cf5058b29f69803bbd434654.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/bdaa19de263700a15fcf213d64a8cd57.png)
参考公式与数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63501b254962e1190b092bbf4a568027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![]() | 0.150 | 0.100 | 0.050 | 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/355390efe2ad5920e12e022306149ddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
分数大于等于120分 | 分数不足120分 | 合计 | |
周做题时间不少于15小时 | 4 | 19 | |
周做题时间不足15小时 | |||
合计 | 45 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
(2)若将频率视为概率,从全校大于等于120分的学生中随机抽取20人,求这些人中周做题时间不少于15小时的人数的期望和方差.
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b5a1255d4d82a04c22c1c2387bf88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90798e9f322fbb9d44f3b9fa046bfcc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db95b5fb299327cc412f9cc5656e1c6d.png)
新工艺 | 500 | 499 | 503 | 500 | 505 | 500 | 502 | 499 | 500 | 498 |
502 | 496 | 498 | 501 | 500 | 497 | 498 | 503 | 500 | 499 | |
旧工艺 | 497 | 502 | 499 | 495 | 502 | 494 | 500 | 496 | 506 | 503 |
499 | 496 | 505 | 498 | 503 | 502 | 496 | 498 | 501 | 505 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
合格品 | 不合格品 | 合计 | |
新工艺 | 20 | ||
旧工艺 | 20 | ||
合计 | 10 | 40 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90198de4171921876c6a76f880377f46.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9c3a380e9229f1f709f929f2cc03b3.png)
(1)根据所给数据,完成下面2×2列联表,并依据小概率值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
康复 | 末康复 | 单位: | |
甲组 | |||
乙组 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附表:
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f503f0dec4cf2cc95ad9521c5eaf9f18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
注:双盲实验:是指在实验过程中,测验者与被测验者都不知道被测者所属的组别,(实验组或对照组),分析者在分析资料时,通常也不知道正在分析的资料属于哪一组.旨在消除可能出现在实验者和参与者意识当中的主观偏差和个人偏好.安慰剂:是指没有药物治疗作用,外形与真药相像的片、丸、针剂.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/71dd6a5a-22f7-4c08-850a-270eb505aac3.png?resizew=263)
(1)在试产初期,某新型全自动高速口罩生产流水线有四道工序,前三道工序完成成品口罩的生产且互不影响,第四道是检测工序,包括红外线自动检测与人工抽检.已知批次I的成品口罩生产中,前三道工序
的次品率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd19eedbe1799458eeff436d3d6f228a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b5203c0ba33ef256feef5d90e4351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf70dcf166f133d192fcacef8e873819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30fc863005671baf1193aa0b501198b6.png)
(2)已知某批次成品口罩的次品率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c8578f06897aa6fb84aa95c797d3d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233ae3d4719641e1e59495b1a3de2a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233ae3d4719641e1e59495b1a3de2a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a97535bd0b7a60cad5153da48d43d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![]() | 0.050 | 0.010 | 0.005 | 0.001 |
![]() | 3.841 | 6.635 | 7.879 | 10.828 |