名校
解题方法
1 . 已知某系统由一个电源和并联的
三个元件组成,在电源电压正常的情况下,至少一个元件正常工作才可保证系统正常运行,电源及各元件之间工作相互独立.
(1)电源电压
(单位:
)服从正态分布
,且
的累积分布函数为
,求
.
(2)在统计中,指数分布常用于描述事件发生的时间间隔.已知随机变量
(单位:天)表示某元件的使用寿命,
服从指数分布,其累积分布函数为
.
(ⅰ)设
,证明:
;
(ⅱ)若第
天只有元件
发生故障,求第
天系统正常运行的条件概率.
附:若随机变量
服从正态分布
,则
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(1)电源电压
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/515c70580e9f247fe27b2f0c964bc5ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166b72040b0aa1e70564fa174b91f6b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb8c83d6dd000e7c0180d91ed146a90.png)
(2)在统计中,指数分布常用于描述事件发生的时间间隔.已知随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d377090d1f35e2b0f2061052e238a8.png)
(ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9a9793d0ce6ccb20dc7972d59e73f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7ac9cc03bbbb308beaa88f424fc1dc.png)
(ⅱ)若第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f77553716bd8b2f4680893d6d496b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd61d3462563f0964a9fde5537eaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42373c7a83e1e876aa12d7e6ac028a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28613181e6953c9858da252bfd62c569.png)
您最近一年使用:0次
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2 . 某市联考后从全体考生中随机抽取42名,获取他们本次考试的数学成绩
和物理成绩
,绘制成如图散点图:
与
之间有线性相关关系,但图中有两个异常点
.经调查得知,
考生由于重感冒导致物理考试发挥失常,
考生因故未能参加物理考试.为了使分析结果更科学准确,剔除这两组数据后,对剩下的数据作处理,得到一些统计的值:
,其中
,
分别表示这40名同学的数学成绩、物理成绩,
与
的相关系数
.
(1)若不剔除
两名考生的数据,用42组数据作回归分析,设此时
与
的相关系数为
.试判断
与
的大小关系,并说明理由;
(2)求
关于
的线性回归方程,并估计如果
考生参加了这次物理考试(已知
考生的数学成绩为126分),物理成绩是多少?
(3)从概率统计规律看,本次考试该市的物理成绩
服从正态分布
,以剔除后的物理成绩作为样本,用样本平均数
作为
的估计值,用样本方差
作为
的估计值.试求该市共40000名考生中,物理成绩位于区间
的人数
的数学期望.
附:①回归方程
中:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446c21b8025405469a473aa0b32f9373.png)
②若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754a89032ac17e6f6afae4888fdc12dd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c2719fc8914037d61e5bac0e1c5980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d649a4ddb20c4242160669dd2c3aeedd.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/01c74a907dda6bb7d9d56d009d9df253.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/54712c3a7d07b9d319432ba79ea7cfe5.png)
![](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/7cc10faaf971fee2258a5cf3620743e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa363608f5f5ea1de6be403fae7fec6.png)
(1)若不剔除
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/a2833ddbe58a6f4e7585c69c698f0d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2833ddbe58a6f4e7585c69c698f0d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)求
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)从概率统计规律看,本次考试该市的物理成绩
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d80da4a6cb5f102be334006d875a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742d3e642d52e01899f66df411100838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c103ffa4e14fe8ed4c45fc5bb3d3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
附:①回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cf74bbdee085c44778ac6191e5016b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446c21b8025405469a473aa0b32f9373.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c1ed67167078ea4f5f1ee53ee14164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754a89032ac17e6f6afae4888fdc12dd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327ad12594450986c1635f073e122b6a.png)
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3 . 某企业使用新技术对某款芯片制造工艺进行改进.部分芯片由智能检测系统进行筛选,其中部分次品芯片会被淘汰,筛选后的芯片及未经筛选的芯片进入流水线由工人进行抽样检验.记
表示事件“某芯片通过智能检测系统筛选”,
表示事件“某芯片经人工抽检后合格”.改进生产工艺后,该款芯片的某项质量指标
服从正态分布
,现从中随机抽取
个,这
个芯片中恰有
个的质量指标
位于区间
,则下列说法正确的是( )(若
,
)
![](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/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6329846cb6ea154d7664bdb405960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecf693507874a4f0ad48589cef188b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5b4fbf10f7c293ee1810bfa26d6877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a597372e55596aa8b8d5f2fdf80e6b03.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() ![]() |
您最近一年使用:0次
2024-06-04更新
|
1254次组卷
|
8卷引用:湖南省长沙市第一中学2023-2024学年高三下学期2月开学考试数学试卷
湖南省长沙市第一中学2023-2024学年高三下学期2月开学考试数学试卷(已下线)7.5 正态分布(分层练习,8大题型)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第三册)(已下线)专题09 计数原理与随机变量及分布列(讲义)(已下线)第8章 概率单元综合能力测试卷-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)重庆市乌江新高考协作体2023-2024学年高二下学期第一阶段学业质量联合调研抽测(4月)数学试题单元测试B卷——第七章 随机变量及其分布江苏省决胜新高考2024届高三下学期4月大联考数学试题重庆市涪陵第五中学校2024届高三下学期第二次适应性考试数学试题
23-24高二下·全国·单元测试
4 .
网络是第五代移动通信网络的简称,是新一轮科技革命最具代表性的技术之一.
年初以来,我国
网络正在大面积铺开.A市某调查机构为了解市民对该市
网络服务质量的满意程度,从使用了
手机的市民中随机选取了
人进行了问卷调查,并将这
人根据其满意度得分分成以下
组:
、
、
、
、
,统计结果如图所示:
市市民对
网络满意度得分
(单位:分)近似地服从正态分布
,其中
近似为样本平均数
,
近似为样本的标准差
,并已求得
.若
市恰有
万名
手机用户,试估计这些
手机用户中满意度得分位于区间
的人数(每组数据以区间的中点值为代表);
(2)该调查机构为参与本次调查的
手机用户举行了抽奖活动,每人最多有
轮抽奖活动,每一轮抽奖相互独立,中奖率均为
.每一轮抽奖,若中奖,奖金为
元话费且继续参加下一轮抽奖;若未中奖,则抽奖活动结束,现小王参与了此次抽奖活动.
(ⅰ)求小王获得
元话费的概率;
(ⅱ)求小王所获话费总额
的数学期望(结果精确到
).
参考数据:若随机变量z服从正态分布
,即
,则
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84029954b75b305b237c4872db1d4eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701554763bdbbf2689a8dae07608da38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84029954b75b305b237c4872db1d4eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84029954b75b305b237c4872db1d4eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84029954b75b305b237c4872db1d4eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd550e1ad9bbf01687ffb4aab788ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd550e1ad9bbf01687ffb4aab788ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fc138be9688253cbdeae2808eb74ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486c7705dbd7b7b9ec5dd17b4891088b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea146d8ec45e63ad14683fd31064de66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1a32a9f2b04fc931c6a0da0b7485e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47248d88a8876e1177cbd3ba43b11bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfc26b8bdcd1fd3781c4593217c725e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d659d74275842d7d1b590edd9ec5479e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84029954b75b305b237c4872db1d4eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84029954b75b305b237c4872db1d4eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbf829e847b2ea353fe5de179c32f16.png)
(2)该调查机构为参与本次调查的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84029954b75b305b237c4872db1d4eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
(ⅰ)求小王获得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def7f5a19d0608e6bb2ddaaea5a0c965.png)
(ⅱ)求小王所获话费总额
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c4d12b3a705daab723ab243b6cc88.png)
参考数据:若随机变量z服从正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfc26b8bdcd1fd3781c4593217c725e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e0a11f0d9d949d0ecd39c7f0903672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef68528b10f467b68130f2fd1a5d8ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20935e26e360e05b52e580a93abd9538.png)
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解题方法
5 . 某年级共200人参加进行物理测试,满分100分,(参考数据:
,
,
)学生的抽测结果
服从正态分布
,其中60分为及格线,80分为良好线,90分为优秀线,则抽测结果在及格线以上学生人数大约为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba13a1c86bb91b2fab6616ea2432474d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de0ccda20243330a347b3886adb79b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e482586d954bf740ff654322168a4c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e8e3fc375df829368b2127d2b66de0.png)
A.137 | B.168 | C.191 | D.195 |
您最近一年使用:0次
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解题方法
6 . 已知随机变量
服从正态分布
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552595efb8eb89a970a1abbb0c955cca.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b204a6f61bd3e1085c3d50720c109561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe0171a0d4874966a49a88a702f25b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552595efb8eb89a970a1abbb0c955cca.png)
您最近一年使用:0次
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解题方法
7 . 已知随机变量
,则
( )
注:若
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766301d99a2fdd3bc255c94a6dd10b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d618e6b3619b7947f6ee1c80c6ebd889.png)
注:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c1ed67167078ea4f5f1ee53ee14164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08265ddd6f7d52775f21e68c49438f5.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-05-03更新
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981次组卷
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4卷引用:江西省吉安市多校联考2023-2024学年高二下学期3月月考数学试题
江西省吉安市多校联考2023-2024学年高二下学期3月月考数学试题(已下线)专题3.4正态分布(五个重难点突破)-2023-2024学年高二数学下学期重难点突破及混淆易错规避(人教A版2019)(已下线)7.5 正态分布(6大题型)精练-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第三册)安徽省滁州市九校2023-2024学年高二下学期4月期中联考数学试题
8 . 正态曲线及其性质
(1)正态曲线:我们称
,
,其中
,
时为参数,为正态密度函数,称它的图象为正态密度曲线,简称正态曲线.
(2)正态分布:若随机变量X的概率分布密度函数为
,则称随机变量X服从正态分布,记为_________ .特别地,当
,
时,称随机变量X服从________ 正态分布.
(3)正态分布的期望与方差:若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b9249c10ae3896e2ee96bfa1a153e5.png)
______ ,
_______ .
(4)正态曲线的特点:
①非负性:对
,
,它的图象在x轴的上方.
②定值性:曲线与x轴之间的面积为1.
③对称性:曲线是单峰的,它关于直线________ 对称.
④最大值:曲线在
处达到峰值
.
⑤当
无限增大时,曲线无限接近x轴.
⑥当
一定时,曲线的位置由
确定,曲线随着
的变化而沿
轴平移,如图①.
⑦当
一定时,曲线的形状由
确定,
较小时曲线“瘦高”,表示随机变量X的分布比较集中;
较大时,曲线“矮胖”,表示随机变量X的分布比较分散,如图②.
,如图所示,X取值不超过
的概率
为图中区域A的面积,而
为区域B的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f3460bf7ce838cbfd78fabc04b6cee6.png)
.
(1)正态曲线:我们称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab88cb5e0bf24c07c4fa50757f755dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aedc1c8a16e306bcd6e5154f9ed6dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cefeddff52b02a43831beeb4bb6faa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da01e03ec2bd0c5965c2535ab6835ef9.png)
(2)正态分布:若随机变量X的概率分布密度函数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad39768ebe8d7a3a0fd09efe7e200ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6095d3cc6af6cc00646493bcfeda216.png)
(3)正态分布的期望与方差:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6c106c07c72c0e54503728911c1743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b9249c10ae3896e2ee96bfa1a153e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab40fadc58e24cf88c93e52b289e9cc.png)
(4)正态曲线的特点:
①非负性:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
②定值性:曲线与x轴之间的面积为1.
③对称性:曲线是单峰的,它关于直线
④最大值:曲线在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6887eae47401f3acc6f99ce6ca7c30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623112afbf2e4c16f94f07f361a84bf3.png)
⑤当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe916d05211cf74a2b1428a8bb8bbbbd.png)
⑥当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
⑦当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6c106c07c72c0e54503728911c1743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073f0aebd74634327d63d5310be981d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6b18c9e23f1b58b74f47c70667aa33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f3460bf7ce838cbfd78fabc04b6cee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d616424f5ab99deb3f310316e2c5171c.png)
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9 . 已知随机变量
服从正态分布
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778dfb406e5ca6131f7e39a1cdf145c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70c97a891f2abbbc4dc65f5003a4a48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d472692e41422ee19261de447a691f95.png)
A.0.13 | B.0.37 | C.0.63 | D.0.87 |
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解题方法
10 . 某区学生参加模拟大联考,假如联考的数学成绩服从正态分布,其总体密度函数为:
,且
,若参加此次联考的学生共有
人,则数学成绩超过
分的人数大约为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3599ad6f6a24cc384f20f28ad29e4342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0dc594bbede837b4e93c6b52752977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afcc28435321cee7c7f7b10ce0d0d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
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