1 . 某食品厂为了检查一条自动包装流水线的生产情况,随即抽取该流水线上
件产品作为样本算出他们的重量(单位:克)重量的分组区间为
,
,……
,由此得到样本的频率分布直方图,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/3d8c8fd9-0f74-4b08-877c-50f0da27fd9b.png?resizew=297)
(1)根据频率分布直方图,求重量超过
克的产品数量.
(2)在上述抽取的
件产品中任取
件,设
为重量超过
克的产品数量,求
的分布列.
(3)从流水线上任取
件产品,求恰有
件产品合格的重量超过
克的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b72ac611ae66b86761e080761d9aabc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7542352feb3c45e2cb39dfa85ae0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c376aef687a9551c6825b8d82844f3c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21c2524e572cbad4562990958110dd5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/3d8c8fd9-0f74-4b08-877c-50f0da27fd9b.png?resizew=297)
(1)根据频率分布直方图,求重量超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0f2d6758b1f258feccb4e26306c385.png)
(2)在上述抽取的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b72ac611ae66b86761e080761d9aabc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0f2d6758b1f258feccb4e26306c385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
(3)从流水线上任取
![](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/1b0f2d6758b1f258feccb4e26306c385.png)
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2016-12-12更新
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2824次组卷
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11卷引用:2010年普通高等学校招生全国统一考试(广东A卷)数学(理科)
2010年普通高等学校招生全国统一考试(广东A卷)数学(理科)(已下线)2010年高考试题分项版理科数学之专题十一 概率统计【全国百强校】甘肃省兰州第一中学2017-2018学年高二下学期期末考试数学(理)试题湖北省武汉市第二中学2019-2020学年高二上学期期末数学试题河北省鹿泉第一中学2019-2020学年高二下学期4月月考数学试题内蒙古集宁一中(西校区)2019-2020学年高二下学期第二次月考数学(理)试题广东省阳江市第一中学2021届高三上学期数学大练习(二)试题北京市第八中学2021届高三上学期期中练习数学试题重庆市朝阳中学2022届高三上学期开学考试数学试题福建省福州高级中学2021-2022学年高二下学期第四学段(期末)考试数学试题北京名校2023届高三一轮总复习 第9章 统计与概率 9.8 离散型随机变量及其分布列
真题
2 . ![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/a3c2c4d2-a858-487d-b819-d30532dd31a8.png?resizew=512)
根据空气质量指数API(为整数)的不同,可将空气质量分级如下表:
对某城市一年(365天)的空气质量进行监测,获得的API数据按照区间
,
,
,
,
,
进行分组,得到频率分布直方图如图.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/d516ef36-351f-4f4f-9e46-577e92bae7cf.png?resizew=311)
(1)求直方图中
的值;
(2)计算一年中空气质量分别为良和轻微污染的天数;
(3)求该城市某一周至少有2天的空气质量为良或轻微污染的概率.
(结果用分数表示.已知
,
,![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/e48593053e974a9ea0c1e21f8debca33.png?resizew=91)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/795d291b7a8c44bbae3a21840e53b468.png?resizew=37)
,
)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/a3c2c4d2-a858-487d-b819-d30532dd31a8.png?resizew=512)
根据空气质量指数API(为整数)的不同,可将空气质量分级如下表:
对某城市一年(365天)的空气质量进行监测,获得的API数据按照区间
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/7cf9abf995654f47a6f32b4260c7fe46.png?resizew=41)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/6bb18fda8b904ad2b8e5eb1a857fc81f.png?resizew=57)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/4ba32b24f85445da9153ae95cb594691.png?resizew=64)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/128cfb11d54745109af04ab2fe356332.png?resizew=65)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/e8006f4ebfa84590a11dea5409e56f02.png?resizew=67)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/799bbf7eb3e74e10b94286beaefdb11f.png?resizew=67)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/d516ef36-351f-4f4f-9e46-577e92bae7cf.png?resizew=311)
(1)求直方图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)计算一年中空气质量分别为良和轻微污染的天数;
(3)求该城市某一周至少有2天的空气质量为良或轻微污染的概率.
(结果用分数表示.已知
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/bf23dfa738154f32bcced3afe00126dd.png?resizew=77)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/01a4c232b9f34591864711e60bcaf997.png?resizew=60)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/e48593053e974a9ea0c1e21f8debca33.png?resizew=91)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/795d291b7a8c44bbae3a21840e53b468.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/af474569c9ec4c47807e8de675e27e11.png?resizew=149)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569630264287232/1569630332502016/STEM/685c3e9c55674eee997cee8cc43bb718.png?resizew=81)
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