![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/12/c7fb339c-5ba8-4463-9fb0-9a2e881be848.png?resizew=363)
(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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](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/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5286d5949970226c9f0fbf9ba39fbbb7.png)
(2)对现有生产线改进后生产批次
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
(3)已知某批次成品口罩的次品率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52138f465d05d22441d7c3bf4967e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52138f465d05d22441d7c3bf4967e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d435624bdae630c800002b80474d979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
α | 0.050 | 0.010 | 0.005 | 0.001 |
х | 3.841 | 6.635 | 7.879 | 10.828 |
非虚弱 | 虚弱 | 总计 | |
男 | a | b | 1170 |
女 | 880 | d | t |
总计 | 1870 | 600 | n |
(2)以频率估计概率,现从该地区随机调查两位男性65岁以上老年人,那么恰有一位老人虚弱的概率是多少?
附表及公式:
![](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 |
接种天花疫苗与否/人数 | 感染猴痘病毒 | 未感染猴痘病毒 |
未接种天花疫苗 | 30 | 60 |
接种天花疫苗 | 20 | 90 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a363cc53497fdfac77b43f656424f973.png)
(2)以样本中结束医学现察的密切接触者感染猴痘病毒的频率估计概率.现从该国所有结束医学观察的密切接触者中随机抽取4人进行感染猴痘病毒人数统计,求其中至多有1人感染猴痘病毒的概率:
(3)该国现有一个中风险村庄,当地政府决定对村庄内所有住户进行排查.在排查期间,发现一户3口之家与确诊患者有过密切接触,这种情况下医护人员要对其家庭成员逐一进行猴痘病毒检测.每名成员进行检测后即告知结果,若检测结果呈阳性,则该家庭被确定为“感染高危家庭”.假设该家庭每个成员检测呈阳性的概率均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f503f0dec4cf2cc95ad9521c5eaf9f18.png)
![]() | 0.1 | 0.05 | 0.010 |
![]() | 2.706 | 3.841 | 6.635 |
性别 | 打篮球 | 合计 | |
喜爱 | 不喜爱 | ||
男生 | 6 | ||
女生 | 10 | ||
合计 | 48 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
(1)请将上面的2×2列联表补充完整(不用写计算过程);
(2)根据小概率值α=0.05的独立性检验,能否据此推断喜爱打篮球与性别有关?
(3)现从女生中抽取2人进一步调查,设其中喜爱打篮球的女生人数为X,求X的分布列与均值.
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc70b5e1ba847b9918a50f67bfbe8f.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 |
AQI | ||||
空气质量 | 优良 | 轻度污染 | 中度污染 | 重度污染 |
天数 | 17 | 48 | 20 | 15 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bfc5e4b7cffc1c4ebd48b5dc9e78fc.png)
(2)若本次抽取得样本数据中有30天是在供暖季节,其中有8天为重度污染,完成下面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
重度污染 | 非重度污染 | 合计 | |
供暖季的天数 | |||
非供暖季的天数 | |||
合计 | 100 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
0.25 | 0.15 | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 | |
1.323 | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
肯定 | 否定 | 总计 | |
男生 | 25 | 35 | 60 |
女生 | 25 | 15 | 40 |
总计 | 50 | 50 | 100 |
参考公式与数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187714e660234f0b72f2b47d3ea685a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.10 | 0.05 | 0.025 | 0.010 | 0.005 | |
2.706 | 3.841 | 5.024 | 6.635 | 7.879 |
喜欢游泳 | 不喜欢游泳 | 合计 | |
男生 | 10 | ||
女生 | 20 | ||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
(1)请将上述列联表补充完整;
(2)判断是否有99.9%的把握认为喜欢游泳与性别有关?
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
高株 | 矮株 | 合计 | |
使用肥料A | 20 | 90 | 110 |
使用肥料B | 40 | 70 | 110 |
合计 | 60 | 160 | 220 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
(2)为了进一步研究,从这批植物高株中用分层抽样的方法抽出6株,再从这6株中抽出3株,求抽到“使用肥料A”植物的株数X的分布列和数学期望.
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc70b5e1ba847b9918a50f67bfbe8f.png)
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/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/7c6c7567972273b4ba733b47bf9d5408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![]() | ![]() | 合计 | |
男 | |||
女 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
(2)某团队进行预防
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93a232c88870d213a7b74a796a1ff4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c8578f06897aa6fb84aa95c797d3d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74b0aa7a6f6dcab7d9101b98504ae2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![]() | 0.10 | 0.05 | 0.01 | 0.005 | 0.001 |
![]() | 2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
性别 | 跑步 | 总计 | |
喜欢跑步 | 不喜欢跑步 | ||
男生 | 50 | 120 | |
女生 | 30 | ||
总计 | 200 |
(2)依据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bdaf501302beeec9d077be02909e3bd.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f503f0dec4cf2cc95ad9521c5eaf9f18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
参考数据:
0.10 | 0.05 | 0.010 | 0.001 | |
2.706 | 3.841 | 6.635 | 10.828 |