名校
解题方法
1 . 2024年甲辰龙年春节来临之际,赤峰市某食品加工企业为了检查春节期间产品质量,抽查了一条自动包装流水线的生产情况.随机抽取该流水线上的40件产品作为样本并称出它们的质量(单位:克),质量的分组区间为
,
,…,
,由此得到样本的频率分布直方图,如图所示.
;
(2)由样本估计总体,结合频率分布直方图,近似认为该产品的质量指标值
服从正态分布
,其中
近似为(1)中的样本平均值
,计算该批产品质量指标值
的概率;
(3)从该流水线上任取2件产品,设Y为质量超过515克的产品数量,求Y的分布列和数学期望.
附:若
,则
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d709129ca73bd7d8b2fbbc7b602b3ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfa00cee28eb9fafa8b12396d720a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c242502275a7ab1ca2c58accccd4066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
(2)由样本估计总体,结合频率分布直方图,近似认为该产品的质量指标值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a7b8b7dadd5a88fc54f478c2948246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a09e45c0ec7bcde3949d7a127ee8b0b.png)
(3)从该流水线上任取2件产品,设Y为质量超过515克的产品数量,求Y的分布列和数学期望.
附:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d5ed234ed63985049cb3530d5538ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b17bead6a8a8802ce91dc438bc2908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c61e8034550a92a950a2b57d537d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f997d6759f643dc7b65cb4733d91402.png)
您最近一年使用:0次
2024-03-19更新
|
1886次组卷
|
5卷引用:内蒙古赤峰市2024届高三下学期3·20模拟考试理科数学试题
内蒙古赤峰市2024届高三下学期3·20模拟考试理科数学试题(已下线)7.5正态分布 第三练 能力提升拔高浙江省舟山市舟山中学2023-2024学年高二下学期4月清明返校测试数学试题(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)
解题方法
2 . 据统计2023年“五一”假期哈尔滨太阳岛每天接待的游客人数X服从正态分布
,则在此期间的某一天,太阳岛接待的人数不少于1800的概率为( )
附:
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2dd59a7e57bb40781c10796d8774e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29306c74e580d52eacf5ebf0b1ea7235.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290917c2c835b61384480b335cc1d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085328c187ab37ea1b6f74677828c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2812e19a50b06d8dc8d63a0c0b5c0b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2dd59a7e57bb40781c10796d8774e3.png)
A.0.4987 | B.0.8413 | C.0.9773 | D.0.9987 |
您最近一年使用:0次
解题方法
3 . 疫情防控期间,为了让大家有良好的卫生习惯某校组织了健康防护的知识测试(百分制)活动,活动结束后随机抽取了
名学生的成绩,并计算得知这
个学生的平均成绩为
,其中
个低分成绩分别是
、
、
、
、
;而产生的
个高分成绩分别是
、
、
、
、
、
、
、
、
、
.
(1)为了评估该校的防控是否有效,以样本估计总体,将频率视为概率,若该校学生的测试得分近似满足正态分布
(
和
分别为样本平均数和方差),则认为防控有效,否则视为效果不佳.经过计算得知样本方差为
,请判断该校的疫情防控是否有效,并说明理由.(参考数据:
)规定:若
,
,则称变量
“近似满足正态分布
的概率分布”.
(2)学校为了鼓励学生对疫情防控的配合,决定对
分及以上的同学通过抽奖的方式进行奖励,得分低于
分的同学只有一次抽奖机会,不低于
分的同学有两次抽奖机会.每次抽奖获得
元奖金的概率是
,获得
元的概率是
.现在从这
个高分学生中随机选一名,记其获奖金额为
,求
的分布列和数学期望.
![](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/8f64730802070a68d4f854b332a24814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c7539ed297ea63b9ace6f5cc58ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec714b7d7a203ecbcef9232ee7d40da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba505969331b28f0e2d3047d49988914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a49a952a95f7af7d8b4bc55f0fbe03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a49a952a95f7af7d8b4bc55f0fbe03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17161b28b6ad8f57abc5b11e1b6c671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d314c287aa376240f0ca41bd181f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d314c287aa376240f0ca41bd181f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0c86435b0b5f7dabce768a0790c346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0c86435b0b5f7dabce768a0790c346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4c1474b253f01cb4766a9e742b9dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128de649220637bdc96fc3e508592201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c804623afb11ea99366d6a50043ccb78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
(1)为了评估该校的防控是否有效,以样本估计总体,将频率视为概率,若该校学生的测试得分近似满足正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742d3e642d52e01899f66df411100838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88b4213192069c5c22e7c97f6242c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c06929d5ac5b6eb7722181239de779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2341e6f3e98d46aa511abe1e48a8f597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ad392e94459218936b0681adfd4734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
(2)学校为了鼓励学生对疫情防控的配合,决定对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17161b28b6ad8f57abc5b11e1b6c671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0538cad6b26c7238b90e664bb68c27c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0538cad6b26c7238b90e664bb68c27c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f1af4b44b2e97e8f319bab4ae9010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
您最近一年使用:0次
2021-02-04更新
|
1180次组卷
|
4卷引用:内蒙古赤峰市2021届高三模拟考试数学(理)试题
2021高三·全国·专题练习
4 . 为了了解扬州市高中生周末运动时间,随机调查了
名学生,统计了他们的周末运动时间,制成如下的频数分布表:
(1)从周末运动时间在
的学生中抽取
人,在
的学生中抽取
人,现从这
人中随机推荐
人参加体能测试,记推荐的
人中来自
的人数为
,求
的分布列和数学期望;
(2)由频数分布表可认为:周末运动时间
服从正态分布
,其中
为周末运动时间的平均数
,
近似为样本的标准差
,并已求得
.可以用该样本的频率估计总体的概率,现从扬州市所有高中生中随机抽取
名学生,记周末运动时间在
之外的人数为
,求
(精确到
);
参考数据1:当
时,
,
,
.
参考数据2:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfce2106c9ad85e4965af5d95c9bf4d8.png)
周末运动时间 | ||||||
人数 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c7af08a66526b4daf67e8225206d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a6d2e2fe2dc4a2ccd3e8142fdd739e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c7af08a66526b4daf67e8225206d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)由频数分布表可认为:周末运动时间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84c2c26cbb6b22a415fd0830401aeac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2675ddd069a5b22f57b933e44065b5.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/923406c78666af328a68dd26c54e5cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d598356d942404e6652fd61dcccb592c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4f6fb7b486fa6117d40f4d68f287d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042e234d538bc2c789d7c5a314f1ca92.png)
参考数据1:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c580545abe524632e951bd55575ad871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f7280cac478039659a062d5db7bcf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a879cdc5b2db13457f3173656a88a94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57353891fd7c1f9e44c475a3b2f1ca94.png)
参考数据2:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa54fcd36a33526b6d8df30c354f2b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c8d537f52611bc2b4bc3ea4873cf44.png)
您最近一年使用:0次
2021-01-05更新
|
702次组卷
|
7卷引用:内蒙古赤峰第四中学新校2021-2022学年高二下学期期中考试数学(理科)试卷
内蒙古赤峰第四中学新校2021-2022学年高二下学期期中考试数学(理科)试卷(已下线)大题专练训练49:随机变量的分布列(正态分布)-2021届高三数学二轮复习江苏省扬州市2020-2021学年高三上学期1月适应性练习数学试题山东省潍坊市四县市2021届高三5月联考数学试题山东省日照市2021届高考数学模拟训练数学试题(已下线)第72讲 正态分布(已下线)7.5 正态分布 (精讲)(2)