良 | 优 | 合计 | |
甲生产线 | 40 | 80 | 120 |
乙生产线 | 80 | 100 | 180 |
合计 | 120 | 180 | 300 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3866b3757d05ceb0d14427142fb52e9d.png)
(2)现对产品进行进一步分析,在测评结果为“良”的产品中按生产线用分层抽样的方法抽取了6件产品.若在这6件产品中随机抽取3件,求这3件产品中产自于甲生产线的件数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附表及公式:
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/1a9c3a380e9229f1f709f929f2cc03b3.png)
符合发射状态 | 不符合发射状态 | |
传统依次测试 | 5m | 5 |
合并测试 | 40 | 2m |
(2)能否有99%的把握认为发射状态与测试方式有关?
(3)为进一步分析合并测试是否是影响符合发射状态的技术原因,在50次合并测试模拟实验中,用分层抽样的方法抽取10次模拟实验,再从这10次模拟实验中随机抽取3次进行复盘分析,记抽到不符合发射状态的模拟实验的次数为X,求X的分布列及期望.
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
0.050 | 0.010 | 0.001 | |
k | 3.841 | 6.635 | 10.828 |
(1)是否有99.5%的把握认为视力正常与否与是否长时间使用电子产品有关?
(2)如果用这150名学生中,长时间使用电子产品的学生和非长时间使用电子产品的学生视力正常的在各自范围内所占比率分别代替该校长时间使用电子产品的学生和非长时间使用电子产品的学生视力正常的概率,且每位学生视力正常与否相互独立,现从该校学生中随机抽取3人(2个非长时间使用和1个长时间使用电子产品),设随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8efe2590d969c8929747d78ab8dc65.png)
![]() | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 |
![]() | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 |
年份 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |
年份代码![]() | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
运营里程![]() ![]() | 1.3 | 1.6 | 1.9 | 2.2 | 2.5 | 2.9 | 3.5 | 3.9 |
(1)甲同学用曲线y=bx+a来拟合,并算得相关系数r1=0.97,乙同学用曲线y=cedx来拟合,并算得转化为线性回归方程所对应的相关系数r2=0.99,试问哪一个更适合作为y关于x的回归方程类型,并说明理由;
(2)根据(1)的判断结果及表中数据,求y关于x的回归方程(系数精确到0.01).
参考公式:用最小二乘法求线性回归方程的系数公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215cae0102f8e8b59d30ca9c7cf967b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d42e0e0801d4f8740ea22878569f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19a03e39654915510f4857036ef2c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548d751fb4e3e44cfc50927bb448c9a3.png)
年份编号![]() | 1 | 2 | 3 | 4 | 5 |
该地区新能源汽车保有量![]() | 1.5 | 2.6 | 3.4 | 4.9 | 7.8 |
该地区纯电动汽车保有量![]() | 1.3 | 2.1 | 2.8 | 4.0 | 6.4 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2610622e372559d7466e80ef7b1fc2af.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)从表中数据可以看出2018~2022年,该地区新能源汽车保有量中纯电动汽车保有量占比均超过80%,说明纯电动汽车一直是新能源汽车的主流产品.若甲、乙、丙3人从2018~2022年中各随机选取1个年份(可以重复选取),记取到满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de17436c2d8bc8cf9046665f0ed117b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
参考数据:
![]() | ![]() | ![]() | ![]() | ![]() |
1.25 | 22.62 | 1.1 | 1.5 | 11.4 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c26fa1e573812fab6a173a4eb0ed38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1697fa54776dc8a5a6135c4ebe26fe.png)
参考公式:对一组数据
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a14e40329de36fc4a1a3f8fbfafda12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad70d88bd467c0f0104b4f4115ef7aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2186481e5a3e999f662c3907b3303041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa133eed915c6f7515d21e1b09f17c82.png)
①烧开一壶水有诸多因素,本建模的变量设定为燃气用量与旋钮的旋转角度,其他因素假设一样;
②由生活常识知,旋转角度很小或很大,一壶水甚至不能烧开或造成燃气浪费,因此旋转角度设定在10°到90°间,建模实验中选取5个代表性数据:18°,36°,54°,72°,90°.
某支数学建模队收集了“烧开一壶水”的实验数据,如下表:
项目 旋转角度 | 开始烧水时燃气表计数/dm3 | 水烧开时燃气表计数/dm3 |
18° | 9080 | 9210 |
36° | 8958 | 9080 |
54° | 8819 | 8958 |
72° | 8670 | 8819 |
90° | 8498 | 8670 |
(1)用列表法整理数据(x,y);
x(旋转角度:度) | 18 | 36 | 54 | 72 | 90 |
y(燃气用量:dm3) |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929ef3bed0a4bdd22f39e036506dc481.png)
(3)有队员用二次函数进行模拟,得到的函数关系为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f353ee6670d9ef325c4c136ac0a4009d.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/049e6f2c2477d83ed61b924312324769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba08ae7991e1c7f402d2dee55cf6487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c38676d3c67a929aa0046ccffdce10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6700d1e416f60cb8e78acc3fac74118.png)
线性回归模型
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100e75efe6c50f3b02ece1d82eada213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3868b5717d3d28dcbe9b165b524fd0a.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ec30e9316c79d956b7c9a483a91632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebff20f21ae41fd8d1f1e3145895842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c563f2112f3e912cee025625ae2d7f34.png)
性能评分 汽车款式 | 1 | 2 | 3 | 4 | 5 | |
基础班 | 基础版1 | 2 | 2 | 3 | 1 | 0 |
基础版2 | 4 | 4 | 5 | 3 | 1 | |
豪华版 | 豪华版1 | 1 | 3 | 5 | 4 | 1 |
豪华版2 | 0 | 0 | 3 | 5 | 3 |
(2)当评分不小于4时,认为该款车性能优秀,否则认为性能一般.根据上述样本数据,完成以下列联表,并依据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead9d6ff51996f3ebace6f212e11a9e4.png)
汽车性能 | 汽车款式 | 合计 | |
基础班 | 豪华版 | ||
一般 | |||
优秀 | |||
合计 |
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187714e660234f0b72f2b47d3ea685a.png)
0.10 | 0.05 | 0.01 | 0.005 | |
2.706 | 3.841 | 6.635 | 7.879 |
套餐 | A | B | C | D | E | F |
月资费x(元) | 38 | 48 | 58 | 68 | 78 | 88 |
购买人数y(万人) | 16.8 | 18.8 | 20.7 | 22.4 | 24.0 | 25.5 |
![]() | ![]() | ![]() | ![]() |
75.3 | 24.6 | 18.3 | 101.4 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec9c64ba3d651388f38fa6b4e906b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa53bed2d3835b5e403d54537d78486.png)
(1)根据所给数据,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知流量套餐受关注度通过指标
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c3981108d692b59f1dc95238d01ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a7850ac9920379dfe6826bcb55aa70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e996b7b8c30ad6e58ea7dc83612756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bda794805ef8e94ea3e69957921856c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d964e0e03b8faeae316bcc4b24c560.png)
保护动物意识强 | 保护动物意识弱 | 合计 | |
男性 | 70 | 30 | 100 |
女性 | 40 | 60 | 100 |
合计 | 110 | 90 | 200 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f43c77e96f7f0cc838495752f9363.png)
(2)将频率视为概率,现从该市女性的市民中用随机抽样的方法每次抽取1人,共抽取3次.记被抽取的3人中“保护动物意识强”的人数为X,若每次抽取的结果是相互独立的,求X的分布列和数学期望
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc79c66ebaacd709ec9965b90a22b14.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/e7dc70b5e1ba847b9918a50f67bfbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
月份代码![]() | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
销售量![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9dd42eb53c22e23470ac77e177f2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f844d6067b4222d697de6a03df3b9c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf044e67c18fa5caa61f8be7c5775de.png)
(1)请用相关系数说明销售量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)公司经营期间的广告宣传费
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f4e99b1318fe84474df6be2fba3296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b965f0184255d69113add4d95bdacb6.png)
参考公式及数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923557f74987174405af890c9a772c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3cd243c6a6d1cf40c0f3a06368b575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb540658171f0b12b6481f6a100eb84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e227c5eb5b5c62749a6c583b1b4f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5df87fdb08d9dff828611e29b6e53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab80e47b339cd2e24c6cd611293d8939.png)